Reading 9 Taxes and Private Wealth Management in a Global Context

by Stephen M. Horan, PhD, CFA, CIPM, and Thomas R. Robinson, PhD, CFA

Stephen M. Horan, PhD, CFA, CIPM, is at CFA Institute (USA). Thomas R. Robinson, PhD, CFA, is at AACSB International (USA).

© 2008 CFA Institute. All rights reserved.

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LEARNING OUTCOMES

The candidate should be able to:

**compare basic global taxation regimes as they relate to the taxation of dividend income, interest income, realized capital gains, and unrealized capital gains;**

**determine the effects of different types of taxes and tax regimes on future wealth accumulation;**

**calculate accrual equivalent tax rates and after-tax returns;**

**explain how investment return and investment horizon affect the tax impact associated with an investment;**

**discuss the tax profiles of different types of investment accounts and explain their impact on after-tax returns and future accumulations;**

**explain how taxes affect investment risk;**

**discuss the relation between after-tax returns and different types of investor trading behavior;**

**explain the benefits of tax loss harvesting and highest-in/first-out (HIFO) tax lot accounting;**

**demonstrate how taxes and asset location relate to mean–variance optimization.**

1. INTRODUCTION

Private wealth managers have the basic goal of maximizing after-tax wealth subject to a client’s risk tolerance and portfolio constraints. Portfolio managers can add value in a number of ways, such as buying undervalued securities, selling overpriced securities, and improving asset allocations. This is challenging in highly efficient markets where informational advantages are difficult to exploit as market participants compete with each other in search of abnormal returns. Managing a portfolio efficiently from a tax perspective, however, is a reasonable goal in almost all markets. In most economies around the world, taxes have a significant impact on net performance and affect an adviser’s understanding of risk for the taxable investor. Tax rates, particularly those for high-net-worth (HNW) individuals, are non-trivial and typically affect returns more than portfolio management costs.

Despite a long history of high tax rates on investment returns, most modern portfolio theory is grounded in a pretax framework. This phenomenon is understandable because most institutional and pension portfolios are tax-exempt. As more wealth becomes concentrated with individuals, it is important to examine the impact of taxes on risk and return characteristics of a portfolio and wealth accumulation. The purpose of this reading is to outline basic concepts that serve as the foundation for building tax-aware investment models that can be applied in a global environment.

The approach developed here is valuable for several reasons. First, it can be applied in a broad range of circumstances representing different taxing jurisdictions, asset classes, and account types. Second, it can provide a framework with which advisers can better communicate the impact of taxes of portfolio returns to private clients and develop techniques to improve their after-tax performance. Third, tax codes change over time. The models developed here provide the adviser a framework to manage changes should they occur.

2. OVERVIEW OF GLOBAL INCOME TAX STRUCTURES

Tax structures (the specifics of how governments collect taxes) are determined by national, regional, and local jurisdictions in order to meet governmental funding needs. Major sources of government tax revenue include:

*Taxes on income*. These taxes apply to individuals, corporations, and often other types of legal entities. For individuals, income types can include salaries, interest, dividends, realized capital gains, and unrealized capital gains, among others. Income tax structure refers to how and when different types of income are taxed.

*Wealth-based taxes*. These include taxes on the holding of certain types of property (e.g., real estate) and taxes on the transfer of wealth (e.g., taxes on inheritance).

*Taxes on consumption.* These include sales taxes (which are taxes collected in one step from the final consumer on the price of a good or service) and value-added taxes (which are collected in intermediate steps in the course of producing a good or service but borne ultimately by the final consumer).

This reading’s focus will be on the taxes that most directly affect tax planning for investments, specifically taxes on investment income to individuals and, secondarily, wealth-based taxes.

In many cases, the tax system is used to encourage or discourage certain activities (for example, investing in domestic companies or encouraging retirement savings). Tax structures vary globally and can change as the needs and objectives of the governmental jurisdiction change. In such a dynamic environment, the investment manager needs to understand the impact of different tax structures on investment returns and wealth. Rather than delineate specific country tax rules, this reading provides a framework for managers to understand and implement investment strategies in a dynamic environment where different tax environments may apply to different clients and tax environments can change over time.

2.1. International Comparisons of Income Taxation

We reviewed the taxation of different types of income, particularly investment income, around the world in order to summarize the major tax regimes.1 The review was based on data from over 50 countries as reported in the Deloitte Touche Tohmatsu International Business Guides, which were available during the summer of 2007. This summary provided the basis for our discussion of the common elements of individual income taxation around the world and our classification of different countries into general income tax regimes.

2.2. Common Elements

In most tax jurisdictions, a tax rate structure applies to ordinary income (such as earnings from employment). Other tax rates may apply to special categories of income such as investment income (sometimes referred to as capital income for tax purposes). Investment income is often taxed differently based on the nature of the income: interest, dividends, or capital gains and losses. Most of the countries examined in our review have a progressive ordinary tax rate structure. In a progressive rate structure, the tax rate increases as income increases. For example:

**Taxable Income (€)Tax on****Column 1Percentage on Excess****Over Column 1OverUp to**015,000–2315,00028,0003,4502728,00055,0006,9603855,00075,00017,2204175,00025,42043

In such an environment, if an individual has taxable income of €60,000, the first €15,000 is taxed at 23 percent; the next €13,000 (i.e., from €15,000 to €28,000) is taxed at 27 percent; and so on. The amount of tax due on taxable income of €60,000 would be €17,220 + 0.41(€60,000 − €55,000) or €19,270. This would represent an average tax rate of €19,270/€60,000 or 32.12 percent. In tax planning for investments, it is useful to think about how much tax would be paid on additional income, known as the marginal tax rate. The marginal rate, or rate on the next €1 of income, would be 41 percent in this example. This taxpayer could have €15,000 more in income before moving into the next tax bracket (a new marginal rate of 43 percent). Some countries do not have a progressive tax system and instead impose a flat tax. In a flat tax structure, all taxable income is taxed at the same rate. For example, at the time of this writing, Russia had a flat tax rate of 13 percent.

Many countries provide special tax provisions for interest income. These special provisions included an exemption for certain types of interest income (for example, Argentina exempted interest income from Argentine banks for residents), a favorable tax rate on interest income (for example, Italy taxed some interest income at 12.5 percent even though the minimum marginal rate is 23 percent), or an exclusion amount where some limited amount of interest income is exempt from tax (for example, Germany provided such an exclusion). Some fixed income instruments are indexed for inflation and this inflation adjustment may not be subject to taxation in some jurisdictions. Unless special provisions exist, interest income, including inflation adjustments, is taxed at the tax rates applicable to ordinary income (ordinary rates).

Similarly, dividend income may have special provisions. In some cases there are exemptions, special tax rates, or exclusions as described above for interest income. In other cases, there may be provisions for mitigating double taxation because dividends are a distribution of company earnings and the company may have already paid tax on the earnings. Tax credits can be used to mitigate the effects of double taxation. For example, the dividend can be taxed at ordinary rates but the individual is entitled to a credit for a portion of the taxes paid by the company (referred to as “franking” in some jurisdictions such as Australia). As with interest income, absent special rules dividend income is taxed at ordinary rates.

Finally, capital gains (losses) may have special provisions or rates. These often vary depending upon how long the underlying investment has been held. Generally, long term gains are treated more favorably than short term gains. Long term is defined differently in different jurisdictions; for example, in the data examined, we observed required holding periods of six months, one year, two years, and five years. Special provisions observed included total exemption of capital gains or long-term capital gains from taxation (for example, Austria exempted long-term gains), exemption of a certain percentage of gains from taxation (for example, Canada exempted 50 percent of gains), a favorable tax rate on capital gains (for example, Brazil provided a flat 15 percent rate for capital gains), or indexing the cost of the investment for inflation (for example, India permitted inflation indexing for some investments). In some cases, countries provided more favorable provisions for domestic companies or companies traded on a local exchange (sometimes applied to both dividend income and capital gains). In most cases, only realized gains were taxed (when the investment was sold). In rare cases, countries impose a tax on unrealized gains (appreciation of the investment prior to sale) either annually, upon exiting the country to relocate domicile, or upon inheritance.2

**EXAMPLE 1**

Tax Rates

Vanessa Wong is a new client living in a jurisdiction with a progressive tax rate structure. She expects to have taxable ordinary income of €70,000 this year. The tax rate structure in her jurisdiction is as follows:

**Taxable Income (€)Tax on****Column 1Percentage on Excess****Over Column 1OverUp to**030,000–2030,00060,0006,0003060,00090,00015,0004090,00027,00050

**Wong’s marginal tax rate is closest to:**

**35%.**

**40%.**

**50%.**

**Wong’s average tax rate is closest to:**

**27%.**

**35%.**

**40%.**

Solution to 1:

B is correct. Wong’s marginal tax rate is 40 percent. Because Wong’s income is over €60,000 but below €90,000, her next €1 of income would be taxed at 40 percent.

Solution to 2:

A is correct. Wong’s tax liability would be €15,000 + 0.40 (€70,000 − €60,000) = €19,000. With a tax liability of €19,000 and taxable income of €70,000, her average tax rate would be about 27 percent (€19,000/€70,000).

2.3. General Income Tax Regimes

Each country’s income tax structure can be classified as either progressive or flat. Income tax regimes can be further distinguished based on the taxation of investment returns in taxable accounts. Interest income is either taxed at ordinary rates or at favorable rates under special provisions. In this review, interest income is considered to be taxable at ordinary rates unless significant exceptions apply. Similar classifications were used for dividends and capital gains. Seven different tax regimes were observed in the sample of countries examined. Exhibit 1 classifies common elements of tax regimes and is further explained below.

**Exhibit 1. Classification of Income Tax Regimes**

**Regime1 — Common Progressive2 — Heavy Dividend Tax3 — Heavy Capital Gain Tax4 — Heavy Interest Tax5 — Light Capital Gain Tax6 — Flat and Light7 — Flat and Heavy**Ordinary Tax Rate StructureProgressiveProgressiveProgressiveProgressiveProgressiveFlatFlatInterest IncomeSome interest taxed at favorable rates or exemptSome interest taxed at favorable rates or exemptSome interest taxed at favorable rates or exemptTaxed at ordinary ratesTaxed at ordinary ratesSome interest taxed at favorable rates or exemptSome interest taxed at favorable rates or exemptDividendsSome dividends taxed at favorable rates or exemptTaxed at ordinary ratesSome dividends taxed at favorable rates or exemptSome dividends taxed at favorable rates or exemptTaxed at ordinary ratesSome dividends taxed at favorable rates or exemptTaxed at ordinary ratesCapital GainsSome capital gains taxed favorably or exemptSome capital gains taxed favorably or exemptTaxed at ordinary ratesSome capital gains taxed favorably or exemptSome capital gains taxed favorably or exemptSome capital gains taxed favorably or exemptTaxed at ordinary ratesExample CountriesAustria

Brazil

China

Czech Republic

Finland

France

Greece

Hong Kong

Hungary

Ireland

Italy

Japan

Latvia

Malaysia

Netherlands

Nigeria

Philippines

Poland

Portugal

Singapore

South Africa

Sweden

Thailand

United Kingdom

United States

VietnamArgentina

Indonesia

Israel

VenezuelaColombiaCanada

Denmark

Germany

Luxembourg

PakistanAustralia

Belgium

India

Kenya

Mexico

New Zealand

Norway

Spain

Switzerland

Taiwan

TurkeyKazakhstan

Russia

Saudi Arabia (Zakat)Ukraine

*Sources*: Classified based on information provided in International Business Guides from Deloitte Touche Tohmatsu (available at www.deloitte.com) and online database of worldwide taxation provided by PricewaterhouseCoopers (www.taxsummaries.pwc.com).

*Common Progressive Regime*: This regime has progressive tax rates for ordinary income, but favorable treatment in all three investment income categories: interest, dividends, and capital gains. This was the most common regime observed. Even though categorized as “common,” there is variation within this regime with some countries treating some interest income as ordinary and other interest income as tax exempt, while other countries provide for exemption or special treatment for all interest.

*Heavy Dividend Tax Regime*: This regime has a progressive tax system for ordinary income and favorable treatment for some interest and capital gains but taxes dividends at ordinary rates.

*Heavy Capital Gain Tax Regime*: This regime has a progressive tax system for ordinary income and favorable treatment for interest and dividends, but taxes capital gains at ordinary rates. Only one such country was observed.

*Heavy Interest Tax Regime*: This regime has a progressive tax system for ordinary income and favorable treatment for dividends and capital gains, but taxes interest income at ordinary rates.

*Light Capital Gain Tax Regime*: This regime has a progressive tax system for ordinary income, interest, and dividends, but favorable treatment of capital gains. This was the second most commonly observed regime.

*Flat and Light Regime*: This regime has a flat tax system and treats interest, dividends, and capital gains favorably.

*Flat and Heavy Regime*: This regime has a flat tax system for ordinary income, dividends, and capital gains. It does not have favorable treatment for dividends and capital gains, but has favorable treatment for interest income.

2.4. Other Considerations

In addition to the different tax regimes in which different types of income are taxed at possibly different rates, there are other important dimensions in tax planning for investments. Some countries permit the use of tax deferred retirement accounts. A tax deferred account

**defers taxation on investment returns within the account;**

**may permit a deduction for contributions;**

**may occasionally permit tax free distributions.**

On the other hand, a few countries impose a wealth tax on accumulations on a periodic basis which reduces after-tax returns and accumulations similar to income taxes.

In the next section we will examine how taxes affect after-tax returns and accumulations. We also examine the impact of tax deferred accounts and wealth taxes. In a later section we will discuss planning opportunities suitable for the various tax regimes.3

3. AFTER-TAX ACCUMULATIONS AND RETURNS FOR TAXABLE ACCOUNTS

Taxes on investment returns have a substantial impact on performance and future accumulations. This section develops models to estimate the tax impact on future accumulations in various tax environments. These models enable the investment adviser to evaluate potential investments for taxable investors by comparing returns and wealth accumulations for different types of investments subject to different tax rates and methods of taxation (accrued annually or deferred).

3.1. Simple Tax Environments

As the preceding analysis of global tax regimes suggests, investment returns can be taxed in a number of different ways. This section begins with some straightforward methods that illustrate basic concepts and serve as building blocks for more complex environments.

All but four of the countries studied in the tax regime analysis have a progressive income tax system.4 The discussion in this section assumes uniform marginal tax rates based on the investor’s current tax bracket which is effectively flat for some range of income. Models that accommodate multiple tax brackets grow in complexity very quickly. Also, investors are often subject to a single rate on the margin, limiting the usefulness of an analysis based on multiple tax brackets. Finally, much of the intuition and analysis that is derived in a flat tax framework applies in a setting with multiple tax brackets.

3.1.1. Returns-Based Taxes: Accrual Taxes on Interest and Dividends

One of the most straightforward methods to tax investment returns is to tax an investment’s annual return at a single tax rate, regardless of its form. Accrual taxes are levied and paid on a periodic basis, usually annually, as opposed to deferred taxes that are postponed until some future date. Most of the countries examined above tax interest income on an accrual basis annually, either at ordinary rates or at favorable rates as the result of special provisions. Germany, Greece, Canada, Colombia, and the United States, for example, tax most interest income at ordinary rates, although some interest income may receive favorable tax treatment. Japan, China, Finland, the Czech Republic, and the United Kingdom tax interest income at a special fixed rate. Dividends, like interest income, are typically taxed in the year they are received, albeit often at different rates.

When returns are subject to accrual taxes, the after-tax return is equal to the pretax return, *r*, multiplied by (1 − *ti*) where *ti* represents the tax rate applicable to investment income. For the purposes of this section, we consider an investment with a return that is entirely taxed at a single uniform rate.

The amount of money accumulated for each unit of currency invested after *n* years, assuming that returns (after taxes at rate *ti* are paid) are reinvested at the same rate of return, *r*, is simply

**Equation (1)**

*FVIFi* = [1 + *r*(1 — *ti*)]*n*

Equation 1 is simply a future value interest factor (FVIF) based on an after-tax return. For example, €100 invested at 6 percent per annum for ten years in an environment in which returns are taxed each year at a rate of 30 percent will accumulate to be €100[1 + 0.06(1 − 0.30)]10 = €150.90. Had returns not been taxed, this investment would have grown to €100[1 + 0.06(1 − 0.00)]10 = €179.08, a difference of €28.18. Notice that taxes reduce the potential gain on investment by (€179.08 − €150.90)/(€179.08 − €100.00) = €28.18/€79.08 = 35.6 percent, which is more than the ordinary income tax rate. This suggests that the tax drag on capital accumulation compounds over time when taxes are paid each year. (Tax drag refers to the negative effect of taxes on after-tax returns.) By contrast, when taxes on gains are deferred until the end of the investment horizon, the tax rate equals the tax drag on capital accumulation as we shall see in the next section.

Exhibit 2 illustrates the impact of taxes on capital growth for various investment horizons and rates of return and demonstrates several conclusions. First, when investment returns are taxed annually, the effect of taxes on capital growth is greater than the nominal tax rate as noted above. Second, the adverse effects of taxes on capital growth increase over time. That is, the proportional difference between pretax and after-tax gains grows as the investment horizon increases. Third, the tax drag increases as the investment return increases, all else equal. Fourth, return and investment horizon have a multiplicative effect on the tax drag associated with future accumulations. Specifically, the impact of returns on the tax effect is greater for long investment horizons, and the impact of investment horizon is greater for higher returns because figures in the bottom right corner change more rapidly than figures in the upper left corner.

**Exhibit 2. Proportion of Potential Investment Growth Consumed by Annual Taxes on Return**

**Investment Horizon in Years ( n)r (%)510152025303540**20.3080.3190.3300.3400.3510.3620.3730.38440.3170.3380.3590.3810.4030.4250.4470.46960.3250.3560.3890.4210.4540.4860.5180.54980.3330.3750.4180.4610.5030.5450.5840.622100.3410.3930.4460.4990.5500.5980.6430.684120.3480.4110.4740.5350.5930.6460.6940.737140.3560.4290.5010.5690.6330.6890.7390.781160.3640.4460.5260.6010.6690.7270.7760.818180.3710.4620.5510.6310.7010.7600.8080.848

*Note*: The calculations assume a 30 percent annual tax rate on investment returns.

Conceptually, this framework could apply to securities, such as fixed-income instruments or preferred stock, in which most or possibly all of the return is subject to annual taxes. This is an oversimplification, of course, but we will address that concern below.

**EXAMPLE 2**

Accrual Taxes

Vladimir Kozloski is determining the impact of taxes on his expected investment returns and wealth accumulations. Kozloski lives in a tax jurisdiction with a flat tax rate of 20 percent which applies to all types of income and is taxed annually. Kozloski expects to earn 7 percent per year on his investment over a 20 year time horizon and has an initial portfolio of €100,000.

**What is Kozloski’s expected wealth at the end of 20 years?**

**What proportion of potential investment gains were consumed by taxes?**

Solution to 1:

FV = €100,000 × *FVIFi*

= €100,000 × [1 + 0.07(1–0.20)]20

= €297,357.

Solution to 2:

Ignoring taxes, FV = €100,000 [1 + 0.07]20 = €386,968. The difference between this and the after tax amount accumulated from above is €89,611. The proportion of potential investment gains consumed by taxes was €89,611/€286,968 = 31.23 percent.

3.1.2. Returns-Based Taxes: Deferred Capital Gains

Another straightforward method of taxing returns is to focus on capital gains, the recognition of which can usually be deferred until realized, instead of interest income and dividends, which are generally taxable each year. A portfolio of non-dividend-paying stocks could fall under this type of framework. The analysis of global tax systems in the previous section indicates that it is very rare for unrealized investment gains to be taxed, so this implicit deferral mechanism has nearly universal application.

If the tax on an investment’s return is deferred until the end of its investment horizon, *n*, and taxed as a capital gain at the rate *tcg*, then the after-tax future accumulation for each unit of currency can be represented in several ways, including the following:

**Equation (2a)**

*FVIFcg* = (1 + *r*)*n* — [(1 + *r*)*n* — 1]*tcg*

**Equation (2b)**

*FVIFcg* = (1 + *r*)*n*(1 — *tcg*) + *tcg*

The first term of Equation 2a represents the pretax accumulation. The bracketed term is the capital gain (i.e., future accumulation less the original basis), while the entire second term represents the tax obligation on that gain. Viewed differently, the first term of Equation 2b represents the future accumulation if the entire sum (including the original basis) were subject to tax. The second term returns the tax of the untaxed cost (also known as cost basis or basis) associated with the initial investment.

For example, €100 invested at 6 percent for ten years in an environment in which capital gains are taxed at the end of that time at a rate of 30 percent will accumulate to be €100[(1 + 0.06)10(1 − 0.30) + 0.30] = €155.36. Notice that this sum is greater than the €150.90 accumulated in the previous example using Equation 1, where returns are taxed annually at the same rate. This comparison illustrates the value of tax deferral.

Notice, as well, that the after-tax investment gain equals the pretax investment gain multiplied by one minus the tax rate. That is, €55.36 = €79.08 × (1 − 0.30). Whereas the tax drag on after-tax accumulations subject to annual accrual taxes compounds over time, the tax drag from deferred capital gains is a fixed percentage regardless of the investment return or time horizon. In other words, when deferral is permitted, the proportion of potential investment growth consumed by taxes is always the same as the tax rate, 30 percent in this case, which is less than that presented in Exhibit 2 when there was annual taxation.

Because the tax drag in Exhibit 2 increases with the investment return and time horizon, the value of a capital gain tax deferral also increases with the investment return and time horizon. One implication of the value of tax deferral is that investments taxed on a deferred capital gain basis can be more tax efficient (i.e., tax advantaged) than investments with returns that are taxed annually, all else equal, even if the marginal tax rate on the two is the same. Moreover, the difference compounds over time. The tax regime analysis from Exhibit 1 reveals that relatively few jurisdictions tax components of equity returns (dividends and capital gains) more heavily than interest income. There are rare exceptions where dividends (but usually not capital gains) are taxed to a greater extent than interest (such as the Heavy Dividend Tax Regime countries in Exhibit 1). Moreover, even if the tax rate on deferred capital gains is greater than the tax rate on interest income, the value of the deferral can more than offset a lower tax rate on annually taxed income, especially over time.

Exhibit 3 illustrates the value of tax deferral and its compounding effects more generally by presenting the ratio of after-tax accumulation in a deferred capital gain regime to after-tax accumulation in a regime in which returns are taxed annually. For example, with a 6 percent annual return, 20-year time horizon and a 30 percent tax rate, the accumulation of €100 in a deferred capital gain environment, is €100[(1 + 0.06)20(1 − 0.30) + 0.30] = €254.50. In an annual taxation environment, it is €100[1 + 0.06(1 − 0.30)]20 = €227.70. Therefore, a deferred capital gain environment accumulates €254.50/€227.70 = 1.118 times the amount accumulated in an annual taxation environment. The relative accumulations can be substantially larger when gains are deferred for long time horizons, especially for high returns. It is important to note, however, that the advantages of tax deferral can be offset or even eliminated if securities taxed on an accrual basis have greater risk-adjusted returns.

**Exhibit 3. Ratio of Future Accumulations: Accumulation in a Deferred Capital Gain Environment to Accumulation in an Annual Taxation Environment**

**Investment Horizon in Years ( n)r (%)510152025303540**21.0011.0041.0081.0151.0231.0331.0451.05841.0031.0141.0311.0561.0861.1231.1651.21361.0071.0301.0671.1181.1811.2571.3461.44781.0121.0501.1131.1981.3051.4321.5821.754101.0181.0751.1691.2941.4531.6441.8712.136121.0251.1041.2321.4051.6241.8922.2142.598141.0331.1371.3031.5291.8182.1772.6163.149161.0411.1721.3801.6662.0352.5003.0803.799181.0501.2101.4641.8142.2732.8623.6124.561

*Note*: The calculations assume a 30 percent annual tax rate on investment returns and a 30 percent tax rate on deferred capital gains.

In many countries, the rate applied to capital gains is lower than the rate applied to interest income. In such cases, the investor gets a dual benefit from returns in the form of capital gains: deferral of taxation and a favorable tax rate when gains are realized. The capital gain tax rate may also vary depending on the holding period. Longer holding periods may receive a lower tax rate to encourage long-term rather than short-term investment. Australia, for example, taxes short-term gains (i.e., holding period less than 12 months) at ordinary rates. Only half the gains on assets held for more than 12 months are taxed, however, making the effective long-term capital gain tax rate half of the rate on ordinary income. In such cases the investor gets a dual benefit; deferral of taxation and a favorable rate on realized gains. The holding period can vary. Belgium and the Czech Republic, for example, require a five-year holding period to receive preferential tax treatment on capital gains.

**EXAMPLE 3**

Deferred Capital Gains

Assume the same facts as in Example 2. Kozloski invests €100,000 at 7 percent. However, the return comes in the form of deferred capital gains that are not taxed until the investment is sold in 20 years hence.

**What is Kozloski’s expected wealth at the end of 20 years?**

**What proportion of potential investment gains were consumed by taxes?**

Solution to 1:

FV = €100,000 × *FVIFcg* = €100,000 × [(1 + 0.07)20(1 — t) + t]

= €100,000 × [(1 + 0.07)20(1–0.20) + 0.20] = €329,575.

Solution to 2:

Ignoring taxes, FV = €100,000 [1 + 0.07]20 = €386,968. The difference between this and the after-tax amount accumulated from above is €57,393. The proportion of potential investment gains consumed by taxes was €57,393/€286,968 = 20.0 percent. This result compares favorably to the potential investment gains consumed by taxes in Example 2.

3.1.3. Cost Basis

In taxation, cost basis is generally the amount that was paid to acquire an asset. It serves as the foundation for calculating a capital gain, which equals the selling price less the cost basis. The taxable gain increases as the basis decreases. In consequence, capital gain taxes increase as the basis decreases. In some circumstances, this basis may be adjusted under tax regulations or carry over from another taxpayer. The previous capital gains examples assume that cash is newly invested so that the cost basis was equal to the current market value. That is, the tax liability at the end of the investment horizon is based on the difference between the pretax ending value and the current market value today.

In many cases, an investment being evaluated today was purchased some time ago and has a cost basis that is different from the current market value. If a security has risen in value since its initial purchase, the cost basis may be less than its current market value. Cost basis affects an investment’s after-tax accumulation because it determines the taxable capital gain. Specifically, the after-tax cash flow from liquidation increases as the cost basis increases, holding all else equal. Put differently, an investment with a low cost basis has a current embedded tax liability because, if it were liquidated today, capital gain tax would be owed even before future capital growth is considered. Newly invested cash has no such current tax liability.

If the cost basis is expressed as a proportion, *B*, of the current market value of the investment, then the future after-tax accumulation can be expressed by simply subtracting this additional tax liability from the expression in either Equation 2a or 2b. In other words,

**Equation (3a)**

*FVIFcgb* = (1 + *r*)*n*(1 — *tcg*) + *tcg* — (1 — *B*)*tcg*

Notice that if cost basis is equal to the initial investment, then *B* = 1 and the last term simply reduces to Equation 2b. The lower the cost basis, however, the greater the embedded tax liability and the lower the future accumulation. Distributing and canceling terms produces

**Equation (3b)**

*FVIFcgb* = (1 + *r*)*n*(1 — *tcg*) + *tcgB*

This form resembles Equation 2b, and the last term represents the return of basis at the end of the investment horizon. The lower the basis, the lower is the return of basis. For example, suppose an investment has a current market value of €100 and a cost basis of €80. The gain when realized will be subject to a capital gains tax of 30 percent. The cost basis is equal to 80 percent of the current market value of €100. If it grows at 6 percent for 10 years, the future after-tax accumulation is €100 [(1.06)10(1 − 0.30) + (0.30)(0.80)] = €149.36, which is €6 less than the €155.36 accumulation that would result if the basis were equal to €100. The €6 difference represents the tax liability associated with the embedded capital gain.

**EXAMPLE 4**

Cost Basis

Continuing with the facts in Examples 2 and 3, Kozloski has a current investment with a market value of €100,000 and cost basis of €80,000. The stock price grows at 7 percent per year for 20 years.

**Express the cost basis as a percent of the current market value.**

**What is Kozloski’s expected wealth after 20 years?**

Solution to 1:

Cost basis/Current market value = *B* = €80,000/€100,000 = 0.80.

Solution to 2:

FV = €100,000 × *FVIFcbg*

= €100,000 × [(1 + 0.07)20(1–0.20) + 0.20(0.80)]

= €325,575.

This amount is €4,000 smaller than Kozloski’s expected wealth in Example 3, in which it was assumed that the cost basis equaled the current market value.

3.1.4. Wealth-Based Taxes

Some jurisdictions impose a wealth tax, which is applied annually to a specific capital base. Often the wealth tax is restricted to real estate investments (e.g., Australia, Singapore, Belgium, Germany, and the United Kingdom). In other countries, it is levied on aggregate assets including financial assets above a certain threshold (e.g., Colombia). If limited to real estate holdings, the tax may be levied at the federal level or a municipal level. In any case, the wealth tax rate tends to be much lower than capital gains or interest income rates because it applies to the entire capital base — i.e., principal and return — rather than just the return.

The expression for an after-tax accumulation subject to a wealth tax is therefore different from the previous scenarios in which only incremental gains are taxed. If wealth is taxed annually at a rate of *tw*, then after *n* years each unit of currency accumulates to

**Equation (4)**

*FVIFw* = [(1 + *r*)(1 — *tw*)]*n*

For example, if wealth capital is taxed at 2 percent, then €100 invested at 6 percent for ten years will grow to [(1.06)(1 − 0.02)]10 = €146.33. Because the form of a wealth tax differs from the form of taxes on either investment returns or deferred capital gains, this figure is not comparable to the previous two examples. This figure is substantially less than the pretax accumulation of €179.08, however. In other words, the two percent wealth tax consumed 41.4 percent of the investment growth that would have accrued over ten years in the absence of a wealth tax (i.e., (€79.08 − €46.33)/€79.08).

Exhibit 4 illustrates the impact of a wealth tax on investment growth for various rates of return and investment horizons. Because wealth taxes apply to the capital base, the absolute magnitude of the liability they generate (measured in units of currency) is less sensitive to investment return than taxes based on returns. Consequently, the proportion of investment growth that it consumes decreases as returns increase. Viewed differently, a wealth tax consumes a greater proportion of investment growth when returns are low. In fact, when returns are flat or negative, a wealth tax effectively reduces principal. Like the previous two types of taxes, however, the wealth tax consumes a greater share of investment growth as the investment horizon increases.

**Exhibit 4. Proportion of Investment Growth Consumed by Wealth Taxes**

**Investment Horizon in Years ( n)r (%)510152025303540**40.5400.5640.5880.6110.6350.6570.6790.70060.3800.4140.4490.4830.5170.5500.5830.61480.3010.3410.3820.4230.4640.5050.5440.581100.2530.2980.3440.3900.4370.4820.5260.567120.2220.2700.3200.3710.4210.4700.5170.560140.2000.2500.3040.3580.4120.4640.5120.557160.1830.2370.2930.3500.4060.4600.5100.556180.1710.2260.2850.3450.4030.4580.5080.555

*Note*: The calculations assume a 2 percent annual wealth tax.

**EXAMPLE 5**

Wealth Tax

Olga Sanford lives in a country that imposes a wealth tax of 1.0 percent on financial assets each year. Her €400,000 portfolio is expected to return 6 percent over the next ten years.

**What is Sanford’s expected wealth at the end of ten years?**

**What proportion of investment gains was consumed by taxes?**

Solution to 1:

FV = €400,000[(1.06)(1 − 0.01)]10 = €647,844.

Solution to 2:

Had the wealth tax not existed, FV = €400,000(1.06)10 = €716,339. This sum represents a €316,339 investment gain compared to a €247,844 gain in the presence of the wealth tax. Therefore, the one percent wealth tax consumed 21.65 percent of the investment gain (i.e., (€316,339 − €247,844)/€316,339).

3.2. Blended Taxing Environments

The discussion in the previous section is an oversimplification because each model assumes that investment gains were taxed according to only one of a number of possible taxes. In reality, portfolios are subject to a variety of different taxes depending on the types of securities they hold, how frequently they are traded, and the direction of returns. The different taxing schemes mentioned above can be integrated into a single framework in which a portion of a portfolio’s investment return is received in the form of dividends (*pd*) and taxed at a rate of *td*; another portion is received in the form of interest income (*pi*) and taxed as such at a rate of *ti*; and another portion is taxed as realized capital gain (*pcg*) at *tcg*. The remainder of an investment’s return is unrealized capital gain, the tax on which is deferred until ultimately recognized at the end of the investment horizon.5 These return proportions can be computed by simply dividing each income component by the total dollar return.

**EXAMPLE 6**

Blended Tax Environment

Zahid Kharullah has a balanced portfolio of stocks and bonds. At the beginning of the year, his portfolio has a market value of €100,000. By the end of the year, the portfolio was worth €108,000 before any annual taxes had been paid, and there were no contributions or withdrawals. Interest of €400 and dividends of €2,000 were reinvested into the portfolio. During the year, Kharullah had €3,600 of realized capital gains. These proceeds were again reinvested into the portfolio.

**What percentage of Kharullah’s return is in the form of interest?**

**What percentage of Kharullah’s return is in the form of dividends?**

**What percentage of Kharullah’s return is in the form of realized capital gain?**

**What percentage of Kharullah’s return is in the form of deferred capital gain?**

Solution to 1:

*pi* = €400/€8,000 = 0.05 or 5 percent.

Solution to 2:

*pd* = €2,000/€8,000 = 0.25 or 25 percent.

Solution to 3:

*pcg* = €3,600/€8,000 = 0.45 or 45 percent.

Solution to 4:

Unrealized gain = €8,000 − €400 − €2,000 − €3,600 = €2,000. Expressed as a percentage of return, €2,000/€8,000 = 0.25, or 25 percent. The unrealized gain is the portion of investment appreciation that was not taxed as either interest, dividends, or realized capital gain.

In this setting, the annual return after realized taxes can be expressed as

*r** = *r*(1 — *piti* — *pdtd* — *pcgtcg*)

In this case, *r* represents the pre-tax overall return on the portfolio. From the preceding example, note that the pre-tax return was 8 percent [(€108,000/€100,000) − 1], however there would be taxes due on the interest, dividends and realized capital gains. The effective annual after-tax return, *r**, reflects the tax erosion caused by a portion of the return being taxed as ordinary income and other portions being taxed as realized capital gain and dividends. It does not capture tax effects of deferred unrealized capital gains. One can view this expression as being analogous to the simple expression in which after-tax return equals the pretax return times one minus the tax rate. The aggregate tax rate has several components in this case, but the intuition is the same.6

**EXAMPLE 7**

Blended Tax Environment: After Tax Return

Continuing with the facts in Example 6, assume that dividends and realized capital gains are taxed at 15 percent annually while interest is taxed at 35 percent annually.

**What is the annual return after realized taxes?**

**Assuming taxes are paid out of the investment account, what is the balance in the account at the end of the first year?**

Solution to 1:

*r** = *r*(1 — *piti* — *pdtd* — *pcgtcg*)

= 8%[1 — (0.05 × 0.35) — (0.25 × 0.15) — (0.45 × 0.15)]

= 7.02%

Solution to 2:

Using the income data from above,

**Income TypeIncome Amount (€)Tax Rate (%)Tax Due (€)**Interest40035140Dividends2,00015300Realized capital gains3,60015540Total tax due980

#### After paying taxes there would be €107,020 in the account (€108,000 − €980). Note that this is consistent with the 7.02 percent return computed for the first question.

#### A portion of the investment return has avoided annual taxation, and tax on that portion would then be deferred until the end of the investment horizon. Holding the tax rate on capital gains constant, the impact of deferred capital gain taxes will be diminished as more of the return is taxed annually in some way as described above. Conversely, as less of the return is taxed annually, more of the return will be subject to deferred capital gains. One can express the impact of deferred capital gain taxes using an effective capital gain tax rate that adjusts the capital gains tax rate *tcg* to reflect previously taxed dividends, income, or realized capital gains. The effective capital gains tax rate can be expressed as7

*T** = *tcg*(1 — *pi* — *pd* — *pcg*)/(1 — *piti* — *pdtd* — *pcgtcg*)

#### The adjustment to the capital gains tax rate takes account of the fact that some of the investment return had previously been taxed as interest income, dividends, or realized capital gain before the end of the investment horizon and will not be taxed again as a capital gain.

#### The future after-tax accumulation for each unit of currency in a taxable portfolio can then be represented by

**Equation (5)**

*FVIFTaxable* = (1 + *r**)*n*(1 — *T**) + *T** — (1 — *B*)*tcg*

#### Although this formulation appears unwieldy, (1 + *r**)*n*(1 − *T**) + *T** is analogous to the after-tax accumulation for an investment taxed entirely as a deferred capital gain in Equation 3. The only difference is that *r** is substituted for *r*, and *T** is substituted for *tcg* in most places.8

#### Different assets and asset classes generate different amounts of return as interest income, dividends, or capital gain, and will thus have different values for *pi*, *pd*, and *pcg*. Moreover, Equation 5 can replace the equations introduced in the previous sections.9 For example, the return on a hypothetical taxable bond with no capital appreciation or depreciation over the course of a tax year might be taxed entirely at ordinary rates so that *pi* = 1, *pd* = 0, and *pcg* = 0. If the cost basis is equal to market value (i.e., *B* = 1), the expression for the after-tax future value simply reduces to [1 + *r*(1 − *ti*)]*n*.

#### On the other hand, the return for a passive investor with a growth portfolio of non-dividend paying stocks and no portfolio turnover may be entirely tax-deferred such that *pd* = 0, *pi* = 0 and *pcg* = 0, and the future value reduces to (1 + *r*)*n*(1 − *tcg*) + *tcg*. The return for an active investor with a similar growth portfolio might be composed entirely of realized long-term capital gains and taxed annually at *tcg* in which case *pd* = *pi* = 0 and *pcg* = 1, and the after-tax future value is [1 + *r*(1 − *tcg*)]*n*.

#### Most accounts conform to none of these extremes, but can be accommodated by simply specifying the proper distribution rates for interest income, dividends, and capital gain. It is useful then to have an understanding of how investment style affects the tax-related parameters (e.g., *pi, pd,* and *pcg*).

**EXAMPLE 8**

#### Blended Tax Environment: Future Long Term Accumulation

#### Continuing with the facts in the previous example, assume there is a five-year investment horizon for the account. Annual accrual taxes will be paid out of the account each year with the deferred tax on previously unrealized capital gains paid at the end of the five-year horizon. The account is rebalanced annually. Consider a €100,000 portfolio with the return and tax profile listed in Panel A of Exhibit 5. What is the expected after-tax accumulation in five years?

**Exhibit 5. Hypothetical Tax Profile**

**Panel A: Tax ProfileAnnual**

**Distribution Rate (***p*)Tax Rate (*T*)Ordinary Income (*i*)5%35%Dividends (*d*)25%15%Capital Gain (*cg*)45%15%Investment Horizon (*n*)5 yearsAverage Return (*r*)8%Cost Basis€100,000

*p*)Tax Rate (

*T*)

**Panel B: Intermediate Accumulation Calculations**Annual after-tax return (*r**)7.02%Effective capital gains tax rate (*T**)4.27%

#### In this case, 25 percent of the return is composed of dividends; 5 percent is composed of realized short-term capital gains; and 45 percent is composed of realized long-term gains. These figures imply that the remaining 25 percent (i.e., 1 − 0.05 − 0.25 − 0.45) of portfolio returns are deferred capital gains and not taxed until the end of the investment horizon.

#### The annual return after realized taxes, *r**, is 0.08[1 − (0.05)(0.35) − (0.25)(0.15) − (0.45)(0.15)] = 7.02 percent as computed previously. This figure reflects the annual return after having accounted for the tax drag imposed by annually levied taxes on the portion of return composed of elements like dividends, interest, and realized capital gains. It does not take into account, however, tax obligations from gains not yet realized; that effect is considered in the effective capital gains tax rate, *T**, which equals 0.15[(1 − 0.05 − 0.25 − 0.45)/(1 − 0.05 × 0.35 − 0.25 × 0.15 − 0.45 × 0.15)] = 0.15(0.25/0.8775) = 4.27 percent. The figure is relatively low in this example because a relatively small proportion of return, 25 percent, is subject to deferred capital gains tax.

#### Because the cost basis and the current market value portfolio are both €100,000, the cost basis expressed as a percent of current market value is 1.00. Substituting these intermediate results into Equation 5, the expected future accumulation of the portfolio in 5 years equals €100,000[(1 + *r**)*n*(1 — *T**) + *T** − (1 − *B*)*tcg*] = €100,000[(1.0702)5(1 − 0.0427) + 0.0427 − (1 − 1.00)0.15] = €138,662.

#### 3.3. Accrual Equivalent Returns and Tax Rates

#### Because returns can come in various forms and be taxed in various ways, an overall understanding of the impact of taxes on return can be obscure. A useful way to summarize the impact of taxes on portfolio returns is to calculate an accrual equivalent after-tax return. Conceptually, an accrual equivalent after-tax return is the tax-free return that, if accrued annually, produces the same after-tax accumulation as the taxable portfolio.10 For example, in the previous example Kharullah’s €100,000 portfolio earned an 8 percent return before taxes and will grow to €138,662 over a 5 year period after accrued and deferred taxes are considered. The tax-free return that will accumulate €138,662 over 5 years is the accrual equivalent return. The difference between the accrual equivalent return and the taxable return of 8 percent is a measure of the tax drag imposed on the portfolio.

#### An analogous way to measure tax drag is with the accrual equivalent tax rate. An accrual equivalent tax rate finds the annual accrual tax rate (of the simple form described in Section 3.1.1) that would produce the same after-tax accumulation as a tax system based in whole or in part on deferred realized gains (such as those described in Sections 3.1.2 or 3.2). Both these concepts recognize that deferring taxes through unrealized gains does not eliminate the tax liability but moves its payment through time.

#### 3.3.1. Calculating Accrual Equivalent Returns

#### Calculating accrual equivalent returns is straightforward. In the previous example, the €100,000 portfolio has an after-tax accumulation 5 years hence of €138,662. The accrual equivalent return is found by solving for the return that equates the standard future value formula to the after-tax accumulation and solving for the return. In this example, we solve the following equation for *RAE*:

#### €100,000(1 + *RAE*)5 = €138,662

#### The accrual equivalent return, *RAE*, is 6.756 percent. Notice that this rate is less than the annual return after realized taxes, *r**, of 7.02 percent because the accrual equivalent return incorporates the impact of deferred taxes on realized gains as well as taxes that accrue annually. The accrual equivalent return is always less than the taxable return, *r*. It approaches the annual return after realized taxes, however, as the time horizon increases. This phenomenon demonstrates the value of tax deferral. The value of deferral in this example is relatively modest, however, because only 25 percent of the tax obligation associated with the return is assumed to be deferred. If more of the return is in the form of deferred gains, the value of the deferral increases.

#### 3.3.2. Calculating Accrual Equivalent Tax Rates

#### The accrual equivalent tax rate is derived from the accrual equivalent return. It is the hypothetical tax rate, *TAE*, that produces an after-tax return equivalent to the accrual equivalent return. In our example, it is found by solving for *TAE* in the following expression:

**Equation (6)**

*r*(1 — *TAE*) = *RAE*

#### In the blended tax regime example, 0.08(1 − *TAE*) = 0.06756. Solving for *TAE*, the accrual equivalent tax rate is therefore, 0.1555 or 15.55 percent. This rate is much lower than the marginal tax rate on ordinary income and only slightly higher than the favorable rate on dividends and capital gains in this example because a relatively small portion (i.e., 5 percent) of the portfolio’s return is generated from highly taxed income. Most of the return receives preferential tax treatment in either the form of a reduced rate for dividends or a reduced rate on realized capital gains combined with valuable deferral for unrealized gains. As a result, investments with this tax profile are relatively tax efficient. The accrual equivalent tax rate would increase if either the return had a larger component taxed at ordinary rates, or if dividends and capital gains received less favorable treatment. In either case, *RAE*would be smaller, implying a higher value of *TAE* for a given level of pretax return *r* in Equation 6.

#### The accrual equivalent tax rate can be used in several ways. First, it can be used to measure the tax efficiency of different asset classes or portfolio management styles. Second, it illustrates to clients the tax impact of lengthening the average holding periods of stocks they own. Third, it can be used to assess the impact of future tax law changes. If the client’s tax rate is likely to change in the future, the manager can determine the impact of the expected change on the accrual equivalent tax rate. The future tax rate could change for several reasons such as tax law changes, changes in client circumstances, or the client taking advantage of tax rules designed to encourage certain behaviors such as charitable contributions which may be deductible in some tax regimes.

**EXAMPLE 9**

#### Accrual Equivalent Return

#### We extend Example 3 with the same facts repeated here: Vladimir Kozloski is determining the impact of taxes on his expected investment returns and wealth accumulations. Kozloski lives in a tax jurisdiction with a flat tax rate of 20 percent, which applies to all types of income and is taxed annually. He expects to earn 7 percent per year on his investment over a 20-year time horizon and has an initial portfolio of €100,000. The 7 percent return is expected to come from deferred capital gains, which are not taxed until sold in 20 years. Kozloski’s expected wealth at the end of 20 years is:

#### FV = €100,000 × *FVIFcg* = €100,000 × [(1 + 0.07)20(1–0.2) + 0.2]

#### = €329,575

**What is the accrual equivalent return?**

**What is the accrual equivalent tax rate?**

#### Solution to 1:

#### €100,000(1 + *RAE*)20 = €329,575

*RAE* = 6.1446 percent

#### Kozloski would be just as well off if he could find a tax-free investment earning 6.1446 percent.

#### Solution to 2:

#### 0.07(1 — *TAE*) = 0.061446

*TAE* = 12.22 percent

#### This rate is lower than the stated tax rate on dividends because there is an advantage from the deferral of taxes.

#### 4. TYPES OF INVESTMENT ACCOUNTS

#### The previous section examined models for taxable accounts in which the tax profile was determined by the asset class and/or the portfolio management style. The impact of taxes on future accumulations often depends heavily on the type of account in which assets are held. Many countries have account structures with different tax profiles designed to provide some relief to the taxable investor. These structures are often intended to encourage retirement savings, but may also accommodate savings for health care and education. Most industrialized and developing countries have tax incentives to encourage retirement savings. An international survey of 24 industrialized and developing countries commissioned by the American Council for Capital Formation (ACCF) indicates that tax-advantaged savings accounts are offered to taxpayers by two-thirds of the countries surveyed, including Australia, Canada, Germany, Italy, the Netherlands, and the United Kingdom.11

#### Most types of investment accounts can be classified into three categories. The first type is taxable accounts. Investments to these accounts are made on an after-tax basis and returns can be taxed in a variety of ways as discussed in the previous section. A second class of accounts can be called tax-deferred accounts, or TDAs. Contributions to these accounts may be made on a pretax basis (i.e., tax-deductible), and the investment returns accumulate on a tax-deferred basis until funds are withdrawn at which time they are taxed at ordinary rates. As such, these accounts are sometimes said to have front-end loaded tax benefits. All but one of the countries in the ACCF study have some kind of retirement account that permits tax deductible contributions. In Canada they are called Registered Retirement Savings Plans (RRSPs), and in the United States some are called Individual Retirement Accounts (IRAs). In some countries, like Australia and Chile, individuals are mandated to contribute a fixed proportion of their income to these accounts. Many types of defined contribution pension plans, whether sponsored by the state or an employer, fall into this category. Argentina, for example, offers citizens the option to make contributions to a public pension fund company.

#### A third class of accounts has back-end loaded tax benefits. These accounts can be called tax-exempt (at least on a forward-looking basis) because although contributions are not deductible, earnings accumulate free of taxation even as funds are withdrawn, typically subject to some conditions. An example is the Roth IRA in the United States.

#### 4.1. Tax-Deferred Accounts

#### Assets held in a TDA accumulate on a tax deferred basis. Tax is owed when funds are withdrawn at the end of an investment horizon at which time withdrawals are taxed at ordinary rates or another rate, *Tn*, prevailing at the end of the investment horizon. The future after-tax accumulation of a contribution to a TDA is therefore equal to

**Equation (7)**

*FVIFTDA* = (1 + *r*)*n*(1 — *Tn*)

#### The form of Equation 7 is similar to the future value interest factor when tax is based entirely on capital gains that are recognized at the end of the investment horizon with a cost basis equal to zero (see Equation 3).

#### 4.2. Tax-Exempt Accounts

#### Tax-exempt accounts have no future tax liabilities. Earnings accumulate without tax consequence and withdrawals create no taxable event. Therefore, the future accumulation of a tax-exempt account is simply

**Equation (8)**

*FVIFTaxEx* = (1 + *r*)*n*

#### Potential insights are available in comparing Equations 7 and 8. First, we notice that *FVIFTDA* = *FVIFTaxEx*(1 − *Tn*), which means that future after-tax accumulation of assets held in a tax deferred account are less than the after-tax accumulation of the same assets when held in a tax-exempt account regardless of the type of asset (assuming equivalent returns). Put simply, assets in a TDA have a built-in tax liability whereas assets in a tax-exempt account do not. It can be shown that the value of an asset held in a TDA measured on an after-tax basis is therefore equal to (1 − *Tn*) times the value of the same asset held in a tax-exempt account. The taxing authority essentially owns *Tn* of the principal value of a TDA, regardless of the type of asset held in it, leaving the investor effectively owning only (1 − *Tn*) of the principal.

**EXAMPLE 10**

#### Comparing Accumulations of Account Types

#### Extending Examples 2 and 3, recall that Vladimir Kozloski lives in a tax jurisdiction with a flat tax rate of 20 percent which applies to all types of income. Kozloski expects to earn 7 percent per year on his investment over a 20 year time horizon and has an initial portfolio of €100,000. Assume that Kozloski has the following current investments:

**€100,000 invested in a taxable account earning 7 percent taxed annually**

**€100,000 invested in a taxable account earning 7 percent deferred capital gains (cost basis = €100,000)**

**€100,000 invested in a tax deferred account earning 7 percent**

**€100,000 invested in a tax exempt account earning 7 percent**

#### Compute the after-tax wealth for each account at the end of 20 years assuming all assets are sold and accounts liquidated at the end of 20 years and assuming a tax rate of 20 percent.

#### Solution to 1:

*FVIF* = €100,000[1 + 0.07(1 − 0.20)]20 = €297,357

#### Solution to 2:

*FVIF* = €100,000[(1 + 0.07)20(1 − 0.20) + 0.20] = €329,575

#### Solution to 3:

*FVIF* = €100,000[(1 + 0.07)20(1 − 0.20)] = €309,575

#### Solution to 4:

*FVIF* = €100,000[(1 + 0.07)20] = €386,968

#### 4.3. After-Tax Asset Allocation

#### The notion that a TDA is worth (1 − *Tn*) times an otherwise equivalent tax-exempt account has implications for after-tax asset allocation, which is the distribution of asset classes in a portfolio measured on an after-tax basis. Consider, for example, an investor with €1,500,000 worth of stock held in a TDA and €500,000 of bonds held in a tax-exempt account as displayed in Exhibit 6. Withdrawals from the TDA account will be taxed at 40 percent. A traditional view of asset allocation based on pretax values would suggest the investor has €2,000,000 of assets, 75 percent of which are allocated in stocks and 25 percent of which are allocated in bonds. In after-tax terms, however, the total portfolio is worth only €1,400,000 because the TDA has a built-in tax liability of €600,000, money the investor cannot spend. Moreover, because the investor is holding stock in the TDA, her after-tax equity exposure is less than a pretax analysis would suggest. Specifically, the after-tax equity allocation is only 64.3 percent rather than 75 percent.12

**Exhibit 6. Simple Example of After-Tax Asset Allocation**

**Account TypeAsset ClassPretax Market Value (€)Pretax Weights (%)After-Tax Market Value (€)After-Tax Weights (%)**TDAStock1,500,00075900,00064.3Tax-ExemptBonds500,00025500,00035.7 Total Portfolio2,000,0001001,400,000100

*Note*: Withdrawals at the end of the investment horizon are assumed to be taxed at a rate of 40 percent.

#### This simple example excludes taxable accounts and does not depend on an investor’s time horizon. However, the after-tax value of taxable accounts may depend on an investor’s time horizon, which can be difficult to estimate and may change over time. Therefore, estimating an investor’s time horizon presents a potential impediment to incorporating after-tax asset allocation in portfolio management. Another challenge is improving client awareness, understanding, and comfort with asset allocation from an after-tax perspective. Suppose an adviser increases pretax equity exposure to achieve a target after-tax asset allocation. Her client may have difficulty accepting the notion of after-tax asset allocation, especially in a bear market when the extra equity exposure would hinder performance.

#### 4.4. Choosing Among Account Types

#### A euro invested in a tax-exempt account always has a higher after-tax future value than a euro invested in a TDA, all else equal. Based on this, one may infer that it is always better to save in a tax-exempt account instead of a TDA. That conclusion would be premature, however, because the comparison overlooks the fact that contributions to TDAs are often tax-deductible whereas contributions to the tax-exempt accounts considered here generally are not.

#### Let’s compare after-tax future values of contributions of a *pretax* euro to a tax-exempt account and a TDA. Because contributions to a tax-exempt account are taxable, a pretax investment is reduced by taxes such that the after-tax investment is (1 − *T*0), where *T*0 is the tax rate applicable to the initial pretax contribution. The future value of a pretax dollar invested in a tax-exempt account is therefore (1 − *T*0)(1 + *r*)*n*. This expression reflects that taxes reduce the initial investment. The future value of a pretax dollar invested in a TDA is (1 + *r*)*n*(1 − *Tn*) because withdrawals are taxed at *Tn*. The only difference between the equations is the beginning and ending tax rates. The tax-exempt account is taxed at today’s rate, *T*0, while the TDA is eventually taxed at the tax rate in the withdrawal year, *Tn*. Therefore, comparing the attractiveness of the two types of accounts reduces to comparing the tax rate today to the expected tax rate when funds are withdrawn. If the prevailing tax rate when funds are withdrawn is less than the tax rate when they are invested, the TDA will accumulate more after-tax wealth than the tax-exempt account, and vice versa.

#### For example, consider an investor currently in the 40 percent tax bracket who is willing to forego €1,200 of spending this year. He could invest €2,000 pretax dollars in a TDA or €1,200 after taxes in a tax-exempt account. Both investments will reduce this year’s spending by €1,200 because the €2,000 TDA contribution would reduce this year’s taxes by €800. He invests in an asset that earns a 5 percent annual return for ten years. Assuming his tax rate is unchanged, in ten years, the TDA will be worth €2,000(1.05)10(1 − 0.40) = €1,955 after taxes. The tax-exempt account will be worth €1,200(1.05)10 = €1,955, the same as the TDA.

#### In this example, he could invest €2,000 in the TDA or €1,200 in the tax-exempt account; a contribution limit did not affect his choice of account type. However, annual contribution limits are usually expressed as a set amount whether the contribution is made with pretax or after-tax funds. A €2,000 contribution of after-tax funds to a tax-exempt account is effectively a larger contribution than a €2,000 contribution of pretax funds to a TDA. As a result, the tax-exempt account allows the investor to put more after-tax funds in a tax-sheltered account than a TDA, all else equal. Horan (2003, 2005) developed a more general approach that incorporates contribution limits in the balance of considerations.

#### Suppose, however, that the investor’s tax rate upon withdrawal will be 20 percent, which is lower than his current tax rate. The future value of the €1,200 contribution to tax-exempt accumulation is unchanged at €1,955, but the TDA accumulation increases to €2,606 or 2,000(1.05)10(1 − 0.20) making the TDA the better choice. The decision would be reversed if the tax rate at withdrawal exceeds the current tax rate.

**EXAMPLE 11**

#### Choosing Among Account Types

#### Bettye Mims would like to invest for retirement and is willing to reduce this year’s spending by €3,000. She will invest €3,000 *after taxes* this year and is in a 25 percent tax bracket, which is the top marginal tax rate in her jurisdiction. Mims is considering three types of accounts but would invest in the same portfolio which is expected to have a pre-tax return of 6 percent annually. If invested in a taxable account the income would be taxed each year at the same 25 percent rate.

#### Assuming Mims will make a single contribution today and withdraw all funds — paying any necessary taxes in 30 years — which of the following accounts will result in the largest after-tax accumulation?

*Account A*. A taxable account with an initial investment of €3,000.

*Account A*. A taxable account with an initial investment of €3,000.

*Account B*. A tax deferred account, where Mims can make a €4,000 tax deductible contribution (a €3,000 after tax cost to Mims).

*Account B*. A tax deferred account, where Mims can make a €4,000 tax deductible contribution (a €3,000 after tax cost to Mims).

*Account C*. A tax exempt account, where a €3,000 contribution is not deductible.

*Account C*. A tax exempt account, where a €3,000 contribution is not deductible.

#### Solution:

#### The taxable account would accumulate €11,236 after taxes:

#### For A, *FVIF* = €3,000[1 + 0.06(1–0.25)]30 = €11,236

#### The tax deferred account would accumulate €17,230 after taxes:

#### For B, *FVIF* = €4,000[(1 + 0.06)30(1–0.25)] = €17,230

#### The tax exempt account would also accumulate €17,230 after taxes:

#### For C, *FVIF* = €3,000[(1 + 0.06)30] = €17,230

#### Both B and C achieve the same after-tax accumulation assuming her tax rates in the contribution year and withdrawal year are the same.

#### 5. TAXES AND INVESTMENT RISK

#### It is fairly obvious that taxes reduce returns. Less obvious is the impact of taxes on investment risk. A fundamental premise regarding taxes and risk is that, by taxing investment returns, a government shares risk as well as return with the investor. Because the returns on assets held in TDAs and tax-exempt accounts are not currently taxed, investors bear all of the risk associated with returns in these accounts. Even in the case of TDAs in which the government effectively owns *Tn*of the principal, the variability of an investor’s return in relation to the current after-tax principal value is unaffected by the tax on withdrawals.13

#### Because the returns on assets held in taxable accounts are typically taxed annually in some way, investors bear only a fraction of the risk associated with these assets. Suppose asset returns are taxed entirely as ordinary income at a rate of *ti*. If the standard deviation of pretax returns is σ, returns are fully taxed at ordinary rates (and all investment losses can be recognized for tax purposes in the year they are incurred), then the standard deviation of after-tax returns for a taxable account is σ(1 − *ti*). That is, an investor bears only (1 − *ti*) of the pretax risk.

#### This concept is best demonstrated by way of example. Consider a €100,000 investment with an expected return of 10 percent, which is taxed annually at 40 percent. A three-state probability distribution of equally likely outcomes is presented in Exhibit 7. The standard deviation of pretax returns is 12.25 percent. The after-tax accumulations one year hence and the after-tax returns are presented in the last two columns.14

**Exhibit 7. Simple Example of Investment Risk and Taxes**

**OutcomeProb.Pretax Accumulation (€)Pretax Return (%)After-Tax Accumulation (€)After-Tax Returns (%)**Good1/3125,00025115,00015Average1/3110,00010106,0006Bad1/395,000−597,000−3Exp. Value110,00010106,0006Std. Dev. (σ)12.257.35

*Note*: Investment returns are assumed to be taxed at a rate of 40 percent in the year they are earned.

#### The standard deviation of after-tax returns equals 7.35 percent, which also equals 0.1225(1 − 0.40). In other words, taxes absorbed *toi* of the pretax volatility; the after-tax volatility is (1 − *toi*) of the pretax volatility. As a result, the taxes not only reduce an investor’s returns, but also absorb some investment risk. This concept has implications for portfolio optimization discussed below.

#### To see how taxes affect after-tax risk in a portfolio context, consider an investor with 50 percent of her wealth invested in equities and 50 percent invested in fixed income, both held in taxable accounts. The equity has a pretax standard deviation of 20 percent and is relatively tax-efficient such that all returns are taxed each year at a 20 percent tax rate. The fixed income is also taxed annually but at a 40 percent rate with pretax volatility of 5 percent. If the two asset classes are perfectly correlated, the pretax portfolio volatility is 0.50(0.20) + 0.50(0.05) = 0.125 = 12.5 percent. On an after-tax basis, however, portfolio volatility is 0.50(0.20)(1 − 0.20) + 0.50(0.05)(1 − 0.40) = 0.095 = 9.5 percent. This example illustrates that annually paid taxes reduce portfolio volatility.15

#### Alternatively, suppose that the equity is held in a taxable account and the fixed income is held in a tax-exempt account like those described in the previous section. In this case, the investor absorbs all of the bond volatility in the tax-exempt account, and the new portfolio volatility is 0.50(0.20)(1 − 0.20) + 0.50(0.05) = 0.105 = 10.5 percent. After-tax volatility increased from the previous measure of after-tax volatility of 9.5 percent because one of the assets (bonds) became tax sheltered. The government therefore absorbed less investment risk through taxes, and the investor is left bearing more investment risk.

#### 6. IMPLICATIONS FOR WEALTH MANAGEMENT

#### The concepts introduced above have several important implications for financial analysts and portfolio managers. The value created by using investment techniques that effectively manage tax liabilities is sometimes called tax alpha. This section briefly discusses some opportunities for considering taxation in the management of individual’s portfolios and tax-planning opportunities to maximize the after-tax accumulation of wealth.

#### 6.1. Asset Location

#### In most tax regimes, a security’s asset class determines its tax profile when held in taxable accounts. Interest income on fixed income securities are often taxed differently from capital gains on stocks, for example. We have also seen how the account structure (e.g., TDAs or tax-exempt accounts) can override this tax treatment. Further, investments in TDAs and tax-exempt accounts are limited such that investors may not place all of their investments in these types of accounts. Investors, therefore, often have multiple types of accounts (e.g., taxable, TDAs, and tax-exempt) when tax advantaged accounts are permitted. An interaction exists between deciding what assets to own and in which accounts they should be held. The choice of where to place specific assets is called the asset location decision. It is distinct from the asset allocation decision. A well designed portfolio not only prescribes a proper asset allocation but simultaneously tells the portfolio manager the proper location for those assets. This section presents some valuable intuition and general guidance derived from the literature.

#### Much of the intuition is based on an arbitrage argument developed for corporate pension fund policy by Black (1981) and Tepper (1980). Suppose contributions to a pension plan are tax-deductible and the returns on pension assets are exempt from tax, much like a TDA for an individual investor. The basic idea behind the arbitrage argument is that a company should place assets that would otherwise be heavily taxed assets within the tax shelter of the pension fund, and locate more lightly taxed securities outside the pension fund. If this strategy causes the allocation of the heavily taxed asset held in the pension fund to be too high, an offsetting short position in the heavily taxed asset outside the pension fund can offset the excessive exposure in the pension fund.

#### For example, suppose bonds are more heavily taxed than equity. Moreover, suppose filling a company’s pension fund with bonds causes an excessive allocation to bonds. The company can borrow (i.e., short bonds) outside the pension fund and invest the proceeds in equities. In this way, lending (i.e., investing in bonds) in the pension fund offsets borrowing outside the pension fund, allowing the company to achieve the desired overall asset allocation. The exact amount of borrowing required to offset the fixed-income investment in the pension fund depends on the tax rate and how assets are taxed, but the concept remains the same.

#### This same logic applies to individual investors. That is, investors would place in TDAs and tax-exempt accounts those securities that would otherwise be heavily taxed if held in taxable accounts (e.g., securities subject to high tax rates and/or annual taxation). The taxable account would hold lightly taxed assets (e.g., securities subject to low rates and/or tax deferral). For example, suppose an investor has €100,000 in tax-deferred accounts and €25,000 in taxable accounts as in Exhibit 8. As suggested, the €100,000 of bonds is placed in the TDA, and €25,000 of stock is placed in the taxable account, creating a pretax bond allocation of 80 percent. Suppose that the target pretax allocation is 60 percent bonds and 40 percent stocks. The investor would borrow €25,000 and purchase additional stock in the taxable account for a total of €50,000 stock. The overall asset allocation is €75,000 bonds and €50,000 stock, which attains the target allocation of 60 percent bonds and 40 percent stock.16

**Exhibit 8. Simple Example of Asset Location**

**Account TypeAsset ClassExisting Pretax Market Value (€)Existing Pretax Allocation (%)Asset ClassTarget Pretax Market Value (€)Target Pretax Allocation (%)**TDABond100,00080Bond100,00080TaxableStock25,00020Stock50,00040Short Bond(25,000)(20)Total125,000100125,000100

#### There are limitations to this basic arbitrage argument. Investors may face restrictions on the amount and form of borrowing. For instance, the tax arbitrage argument assumes that investors can borrow and lend at the same rate in whatever amounts they wish. In reality, this is not the case. Investors are undoubtedly subject to borrowing costs that are greater than the yield on a bond of similar risk. At least a portion of the tax gains from the arbitrage are therefore consumed by this rate differential. Moreover, behavioral constraints can limit implementation because some investors are apprehensive about borrowing money (i.e., shorting bonds) to manage their retirement portfolio.

#### In addition, investors may face liquidity constraints (e.g., margin requirements or withdrawal penalties from TDAs and tax-exempt accounts) that would make the arbitrage strategy costly. For example, margin rules may preclude investors from borrowing as much as the arbitrage strategy would suggest or force them to borrow at rates in excess of the bond returns in the TDA. In some jurisdictions investors face penalties for withdrawing assets held in a TDA or tax-exempt account prior to a particular date. If the equity in a taxable account suffers a substantial decline in value, an investor may be forced to liquidate assets in the tax-deferred account to finance consumption, which may trigger an early withdrawal penalty for some investors. These constraints may make strictly executing the arbitrage strategy costly or impossible.

#### In these cases, asset location is still important. If there are constraints to borrowing in the taxable account then the investor may hold €25,000 in stocks in the taxable account. In the TDA, she could hold €75,000 in bonds and €25,000 in stocks in the TDA. This would achieve the target allocation, while following the location preference in the absence of borrowing.

#### Separately, suppose she has borrowing constraints and needs €5,000 as a cash reserve in her taxable account. She could hold €20,000 in stocks and €5,000 in cash in the taxable account. In the TDA, she could hold €70,000 in bonds and €30,000 in stocks, which would achieve her target asset allocation. In each example, she follows the asset location preference to the extent possible, while satisfying her other constraints and target asset allocation.

#### Some jurisdictions exempt municipal bond interest or other types of interest from taxes. In this case, it could conceivably make sense to place tax-free municipal bonds in a taxable account and more heavily taxed stock in the TDA. The yield on tax-free bonds, however, is generally much lower than those on taxable bonds so that in a well functioning market their after-tax returns are approximately equal. This yield concession is a significant disadvantage to placing low yielding tax-free bonds in a taxable account and equity in a TDA. In most instances the yield concession more than offsets the value of sheltering equity returns from taxes. As a result, it is generally better to follow the general strategy of locating bonds in TDAs and equity in taxable accounts.17

#### The tax regime governing the investor determines the relative importance of asset location. In a regime where all income is taxed annually (including unrealized capital gains) and at the same rates, asset location would not matter. As noted earlier, however, these regimes are rare. In most regimes the individual tax structure should be examined to determine which assets are taxed annually and highly versus those that are tax deferred or taxed lightly. Additionally, investment style impacts how an asset or asset class is taxed. For example, active management (discussed further below) or a covered call strategy for an equity portfolio may eliminate the ability to defer taxes.

#### Of course, taxes are only one of many factors that go into the asset location decision. Others include behavioral constraints, access to credit facilities, age, time horizon, and investment availability. Another factor is planned holding period. If the investor has two accounts — a tax deferred account and a taxable account — that contain funds intended for retirement, then they would both have long term objectives and locating assets based on their taxation makes sense. However, if the tax deferred account contains retirement funds and the taxable account contains funds held for short term needs, it may not be appropriate to locate assets based strictly on their taxation. The asset allocation should be appropriate to the client’s time horizon for each account.

#### 6.2. Trading Behavior

#### The tax burden for many asset classes, such as equities when held in taxable accounts, depends on an investor’s trading behavior or that of the mutual fund held by an investor. Consider four types of equity investors. The first type is a *trader*who trades frequently and recognizes all portfolio returns in the form of annually taxed short term gains. This equity management style may subject investment returns to tax burdens similar to those applied to interest income thereby eroding possible tax efficiencies associated with equities. An *active investor*, who trades less frequently so that gains are longer term in nature, may receive more favorable tax treatment.18 The *passive investor* passively buys and holds stock. The *exempt investor* not only buys and holds stocks, but he never pays capital gains tax.19Optimal asset allocation and asset location for each of these investors is likely to differ.

#### For example, suppose these four individuals invest €1,000 in non-dividend paying stocks that earn 8 percent annually for 20 years. They live in a country that taxes capital gains realized within a year at 40 percent and gains realized after at least one year at 20 percent. The after-tax accumulations and accrual equivalent tax rates are listed in Exhibit 9.

**Exhibit 9. Future Accumulations for Different Types of Investors**

**Investor TypeFuture **

**Accumulation (€)Expression (€)Accrual Equivalent **

**Return (%)Accrual Equivalent **

**Tax Rate (%)**Trader2,5541,000[1 + 0.08(1 − 0.4)]204.840.0Active Investor3,4581,000[1 + 0.08(1 − 0.2)]206.420.0Passive Investor3,9291,000[(1.08)20(1 − 0.2) + 0.2]7.111.5Exempt Investor4,6611,000(1.08)208.00.0

#### Holding all else constant, the trader accumulates the least amount of wealth, and the tax exempt investor accumulates the most. The active and passive investors fall in between. This comparison illustrates that trading behavior affects the tax burden on stocks (and other assets that provide capital gain appreciation) when held in taxable accounts.

#### Research suggests that active managers must earn greater pretax alphas than passive managers to offset the tax drag of active trading.20 Other research suggests that mutual fund rankings change significantly depending on whether performance is measured on a pretax or after-tax basis.21 Therefore, it is important for the taxable investor to consider the impact of taxes on after-tax returns. Generally, for assets held in taxable accounts, portfolio turnover generates taxable gains that might otherwise be deferred. Because a number of countries have lower long-term capital gains tax rates for investment held beyond a particular holding period, higher portfolio turnover also foregoes preferential tax treatment associated with longer holding periods and lower turnover.

#### It is important to note that although locating highly taxed assets in tax sheltered accounts can add value for investors, a proper investment management strategy remains more important than the proper asset location strategy. That is, optimally locating assets in TDAs and taxable accounts cannot overcome the negative impact of a poor investment strategy that either produces a negative pretax alpha or is highly tax inefficient.22

#### 6.3. Tax Loss Harvesting

#### Although the previous section indicates that active management can create a tax drag, not all trading is necessarily tax inefficient. While jurisdictions allow realized capital losses to offset realized capital gains, limitations are often placed on the amount of net losses that can be recognized or the type of income it can offset (e.g., short-term capital gains, long-term capital gains, or ordinary income). Canada, for example, only allows tax deductible losses up to the level of realized taxable gains. Realized losses in excess of realized gains may be used to offset gains realized within the last three years. Realized losses beyond that point can be carried forward and applied against gain realized at some future date.

#### Regardless of the specific tax rules the opportunity to recognize a loss that offsets some kind of taxable gain in a given tax year can create value. The practice of realizing a loss to offset a gain or income — and thereby reducing the current year’s tax obligation — is called tax loss harvesting.

**EXAMPLE 12**

#### Tax Loss Harvesting: Current Tax Savings

#### Eduardo Cappellino has a €1,000,000 portfolio held in a taxable account. The end of the 2008 tax year is approaching and Cappellino has recognized €100,000 worth of capital gains. His portfolio has securities that have experienced €60,000 of losses. These securities have not yet been sold and their losses are therefore unrecognized. Cappellino could sell these securities and replace them with similar securities expected to earn identical returns.23The federal government taxes capital gains at 20 percent.

**Without making any further transactions, how much tax does Cappellino owe this year?**

**How much tax will Cappellino owe this year if he sells the securities with the €60,000 loss?**

**How much tax will Cappellino save this year if he sells the securities with the €60,000 loss?**

#### Solution to 1:

#### Capital gain tax = 0.20 × €100,000 = €20,000.

#### Solution to 2:

#### If Cappellino realizes €60,000 of losses, the net gain will be reduced to €40,000. New capital gain tax = 0.20 × (€100,000 − €60,000) = €8,000.

#### Solution to 3:

#### Tax Savings = €20,000 − €8,000 = €12,000.

#### It is important to understand that the tax savings realized in a given tax year from tax loss harvesting overstates the true gain. Selling a security at a loss and reinvesting the proceeds in a similar security effectively resets the cost basis to the lower market value, potentially increasing future tax liabilities. In other words, taxes saved now may be simply postponed. The value of tax loss harvesting is largely in deferring the payment of tax liabilities.24

**EXAMPLE 13**

#### Tax Loss Harvesting: Tax Deferral

#### In the previous example, the securities with an unrealized loss have a current market value of €110,000 and cost basis of €170,000 (an unrealized loss of €60,000). Cappellino could:

**Option A**

**Hold the securities with the unrealized loss, or**

**Option B**

**Sell the securities in 2008 and replace them with securities offering the same return.**

#### Next tax year (2009), the securities increase in value to €200,000 and the securities are sold regardless of which option Cappellino chooses.

**Calculate Cappellino’s 2009 tax liability if he holds the securities until year end 2009.**

**Calculate Cappellino’s 2009 tax liability if he recognizes the loss today in 2008, replaces them with securities offering the same return, and realizes the capital gain at year end 2009.**

**Compare the total two-year tax liability under both options using the 2008 tax liability computed in ****Example 12****, in which the 2008 tax liability was €20,000 if the loss was not realized and €8,000 if the loss was realized.**

#### Solution to 1:

#### Capital gain tax = 0.20(€200,000 − €170,000) = €6,000.

#### Solution to 2:

#### If Cappellino recognizes the loss in 2008 and replaces the securities, the basis will be reset to €110,000 from €170,000.

#### Capital gain tax in 2009 = 0.20(€200,000 − €110,000) = €18,000.

#### Solution to 3:

#### The two-year tax liability for both options is the same:

**2008 (€)2009 (€)Total (€)**Option A20,0006,00026,000Option B8,00018,00026,000

#### Although the two-year tax liability does not change, an advantage of tax loss harvesting is pushing a portion of the tax liability into subsequent years.

#### A subtle benefit of tax loss harvesting is that recognizing an already incurred loss for tax purposes increases the amount of net-of-tax money available for investment. Realizing a loss saves taxes in the current year, and this tax savings can be reinvested. This technique increases the amount of capital the investor can put to use.

**EXAMPLE 14**

#### Tax Loss Harvesting: Adding Net-of-Tax Principal

#### In the previous example, suppose Cappellino reinvests the 2008 tax savings if he sells the securities with an unrealized loss of €60,000. His two options are therefore:

**Option A**

**Hold the securities, or**

**Option B**

**Sell the securities, and reinvest the proceeds and the tax savings in nearly identical securities.**

#### In 2009, the securities experience an 81.81 percent increase regardless of which option Cappellino chooses.

**Calculate the securities’ pretax value next year if he holds the securities.**

**Calculate the securities’ pretax value next year if he recognizes the loss, and reinvests the proceeds and the tax savings in nearly identical securities.**

**What will the after-tax value be under both options if the securities are sold the next year?**

#### Solution to 1:

#### FV = €110,000(1.8181) = €200,000 (approximately).

#### Solution to 2:

#### If Cappellino replaces the securities and invests the tax savings of €12,000, the invested capital will become €110,000 + €12,000 = €122,000.

#### FV = €122,000(1.8181) = €221,808.

#### Solution to 3:

#### The new capital gain tax for Option B at the end of the next tax year is 0.20(€221,808 − €122,000) = €19,962.

**Pretax (€)Tax (€)After-Tax (€)**Option A200,0006,000194,000Option B221,80819,962201,846

#### Another advantage of tax loss harvesting is increasing the net-of-tax capital invested in the portfolio.

#### A concept related to tax loss harvesting is using highest-in, first-out (HIFO) tax lot accounting to sell a portion of a position. When positions are accumulated over time, lots are often purchased at different prices. Depending on the tax system, investors may be allowed to sell the highest cost basis lots first, which defers realizing the tax liability associated with lots having a lower cost basis.

#### Opportunities to create value through tax loss harvesting and HIFO are greater in jurisdictions with high tax rates on capital gains. Studies have shown that a tax loss harvesting program can yield substantial benefits. Although cumulative tax alphas from tax loss harvesting increase over time, the annual tax alpha is largest in the early years and decreases through time as deferred gains are ultimately realized.25The complementary strategies of tax loss harvesting and HIFO tax lot accounting have more potential value when securities have relatively high volatility, which creates larger gains and losses with which to work.

#### The previous section suggests that active trading creates a tax drag on portfolio performance. A certain amount of trading activity is required, however, to harvest tax losses if a portfolio contains unrealized losses. That is, tax-efficient management of stocks in taxable accounts does not require passive management. It requires passively allowing gains to grow unharvested, but actively realizing losses.

#### Harvesting losses is not always an optimal strategy. For example, in cases where an investor is currently in a relatively low tax rate environment and will face higher tax rates on gains in a subsequent period (either because her tax bracket will increase or because tax rates generally are increasing) the best strategy may be to defer harvesting losses. Doing so would offset gains that will be taxed relatively lightly compared to subsequent gains if tax rates will increase.26 Likewise, one might want to liquidate low basis stock (lowest in, first out or LIFO) if the current tax rate is temporarily low.

#### 6.4. Holding Period Management

#### The tax regime analysis earlier in the reading indicated that many jurisdictions encourage long-term investing (or equivalently discourage short-term trading) by reducing tax rates on long-term gains. The required holding period varies, of course. Depending on the magnitude of gain from waiting, short-term trading can be difficult to justify on an after-tax basis. If short-term gains are taxed at 40 percent and long-term gains are taxed at 20 percent, then 20 percent (i.e., 40 percent less 20 percent) of an investor’s gains are dictated by the holding period.

#### Exhibit 10 shows the relative benefit of gains subject to a lower tax rate. Using a twelve-month holding period requirement for a long-term capital gain tax of 20 percent versus a short-term capital gain tax of 40 percent, the table assumes that the entire return is taxed each year. For example, consider an 8 percent return over ten years. If returns are completely taxed each year as long term gains at 20 percent, €100 will grow to €100[1 + 0.08(1 − 0.20)]10 = €185.96. If returns are completely taxed as short-term gains at 40 percent, the accumulation is €100[1 + 0.08(1 − 0.40)]10 = €159.81. The ratio between the two figures is €185.96/€159.81 = 1.164. The benefit of realizing long-term gains in lieu of short-term gains is substantial, especially for long investment horizons and higher returns.

**Exhibit 10. Ratio of Future Accumulations: Accumulation Using Long-Term Capital Gains Tax Rate to Accumulation Using Short-Term Capital Gains Tax Rate**

**Investment Horizon in Years (***n*)*r*(%)51015202530354021.0201.0401.0611.0821.1041.1261.1481.17141.0401.0811.1241.1681.2151.2631.3131.36561.0591.1221.1891.2591.3341.4131.4961.58581.0791.1641.2551.3541.4611.5751.6991.833101.0981.2061.3241.4531.5961.7521.9242.112121.1171.2481.3941.5571.7391.9432.1702.425141.1361.2901.4661.6651.8922.1492.4412.773161.1551.3331.5401.7782.0532.3712.7383.162181.1731.3771.6151.8962.2242.6103.0623.593

*n*)

*r*(%)510152025303540

*Note*: Capital gains are assumed to be taxed each year. Short-term gains are taxed at a rate of 40 percent. Long-term gains are taxed at 20 percent.

#### The penalty associated with realizing short-term gains in this environment can be viewed from a different perspective. An investment earning a 10 percent pretax return subject to a long term rate yields 8 percent after-tax [i.e., 0.10 × (1 − 0.20)]. A 13.33 percent pretax return taxed as a short-term gain is necessary to produce the same result [e.g., 0.08/(1 − 0.40)]. In other words, the pretax return must be one-third greater to produce the same after-tax result. It can be quite difficult to generate enough pretax alpha to overcome the effect of taxes on short capital gains in these types of tax environments.

#### Another aspect of holding period management is more tactical in terms of which tax year the tax is due. If a taxpayer subject to taxation on a calendar year basis is contemplating an asset sale in December, it may be wise to defer the sale until January if there is a built-in capital gain or sell the asset in December if there is a built-in loss. Of course the timing of taxation is not the only consideration. The attractiveness of this investment relative to alternative investments must be considered.

**EXAMPLE 15**

#### Long-Term Gain

#### Gretel Hazburger is considering two different portfolio strategies. The first is a hyper-active market-timing trading strategy that is expected to yield a pretax return of 12 percent. All gains will be recognized each year and taxed at the short term capital gain rate of 50 percent. Alternatively, a less active tactical asset allocation trading strategy is expected to yield a pretax return of 10 percent. All gains will be recognized each year but classified as long term and taxed at 30 percent.

**Which strategy is likely to produce a better after tax return?**

**What pretax return is required on the market timing strategy to produce the same after-tax return as the tactical asset allocation strategy?**

#### Solution to 1:

#### After-tax return to market timing = 0.12(1 − 0.50) = 0.06 = 6 percent.

#### After-tax return to tactical asset allocation = 0.10 (1 − 0.30) = 0.07 = 7 percent.

#### The tactical asset allocation strategy produces a better return.

#### Solution to 2:

#### Required return for market timing = 0.07/(1 − 0.50) = 0.14 = 14 percent.

#### 6.5. After-Tax Mean–Variance Optimization

#### We have seen how basic principles of measuring asset allocation in a pretax environment do not necessarily apply in a more economically relevant after-tax environment. The same is true for portfolio optimization techniques. That is, pretax efficient frontiers may not be reasonable proxies for after-tax efficient frontiers. It is beyond the scope of this reading to develop specific after-tax mean–variance optimization (MVO) methods. However, an important concept supporting those methods is that the same asset held in different types of accounts is essentially a distinct after-tax asset because it will produce different after-tax accumulations. In other words, an investor optimizing between two different asset classes (e.g., stocks and bonds) across two types of accounts (e.g., taxable and tax deferred accounts) has four different after-tax assets to allocate — stocks or bonds in each of the two accounts.

#### After recognizing that important insight, an important element in developing an after-tax MVO model is to substitute accrual equivalent returns, like those introduced above, for pretax returns in developing return expectations. Similarly, a portfolio manager would substitute the asset’s after-tax standard deviation of returns for pretax standard deviations in the optimization algorithm.

#### The optimization process must include some constraints. For example, an optimization algorithm cannot allocate more to a tax deferred account than the funds that are available in that account. Specific investment options may also be constrained in some types of accounts. For example, privatized retirement accounts in certain countries may limit investors’ options to certain types of securities. In sum, however, standard portfolio optimization practices can be adapted to consider the impact of taxes on investment returns and risk.

#### SUMMARY

#### Taxes can have a significant impact on investment returns and wealth accumulation, and managing taxes in an investment portfolio is one way advisers can add value. Taxes come in various forms and each country has its own tax code. Nonetheless, many jurisdictions share some common salient features, and many of those common elements can be identified. This allows one to define regimes that include countries with similar rules of taxation and to build models that capture the salient features of these regimes. That is the approach taken here and the resulting analysis suggests the following:

**Taxes on investments can take at least three primary forms as discussed here. They can be based on:**

**returns — accrued and paid annually;**

**returns — deferred until capital gains are recognized;**

**wealth — accrued and paid annually.**

**The impact of taxes on wealth accumulation compounds over time.**

**Deferred taxes on capital gains have less impact on wealth accumulation than annual tax obligations for the same tax rate.**

**An investment with a cost basis below its current market value has an embedded tax liability that may reduce future after-tax accumulations.**

**Wealth taxes apply to principal rather than returns and in consequence wealth tax rates tend to be much lower than returns-based tax rates.**

**Investments are typically subject to multiple forms of taxation. The specific exposure depends on the asset class, portfolio management style, and type of account in which it is held.**

**An accrual equivalent after-tax return is the tax-free return that, if accrued annually, produces a given after-tax accumulation.**

**An accrual equivalent tax rate is the annually accrued tax rate that, when applied to the pretax return, produces a given after-tax accumulation.**

**Sometimes the type of investment account overrides the tax treatment of an investment based on its asset class.**

**Tax-deferred accounts allow tax-deductible contributions and/or tax-deferred accumulation of returns, but funds are taxed when withdrawn.**

**Tax-exempt accounts do not allow tax-deductible contributions, but allow tax-exempt accumulation of returns even when funds are withdrawn.**

**By taxing investment returns, a taxing authority shares investment risk with the taxpayer. As a result, taxes can reduce investment risk.**

**The practice of optimally placing particular asset classes in particular types of accounts is called asset location.**

**Tax loss harvesting defers tax liabilities from current to subsequent periods and permits more after-tax capital to be invested in current periods.**

**When short-term gains are taxed more heavily than long-term gains, it can be difficult for a short-term trading strategy to generate enough alpha to offset the higher taxes associated with short term trading.**

**Traditional mean–variance optimization can be modified to accommodate after-tax returns and after-tax risk.**

**Otherwise identical assets held in different types of investment accounts should be evaluated as distinct after-tax assets.**

**An after-tax portfolio optimization model that optimizes asset allocation also optimizes asset location.**

#### PRACTICE PROBLEMS

#### © 2011 CFA Institute. All rights reserved.

#### The following information relates to Questions 1–7

#### Alan Jackson has a new client, Aldo Motelli, who expects taxable ordinary income (excluding investments) of €200,000 this tax year. Motelli currently has €250,000 in a taxable investment account for which his main objective is retirement in 15 years. He is considering making the maximum investment of €10,000 in a new type of tax deferred account permitted in his country of residence. The contribution would be deductible and distributions are expected to be taxed at a 20 percent rate when withdrawn. The income tax structure of his country is:

**Taxes on Ordinary IncomeTaxable Income (€)Tax on**

**Column 1 (€)Percentage on Excess**

**Over Column 1OverUp to**020,000–1020,00040,0002,0001540,00060,0005,0002060,00080,0009,0002580,000100,00014,00030100,00020,00035

**Taxes on Investment Income**Interest10% flat rateDividends10% flat rateRealized capital gains10% flat rate

**What is Motelli’s average tax rate on ordinary income?**

**22.5%.**

**27.5%.**

**35.0%.**

**If Motelli’s current investment account of €250,000 is invested in an asset which is expected to earn annual interest of 6.5 percent and no capital gains, what is his expected after tax accumulation in 15 years?**

**€578,664.**

**€586,547.**

**€642,960.**

**What is the accrual equivalent return assuming the facts in Question 2?**

**5.85%.**

**6.50%.**

**7.22%.**

**If Motelli’s current investment account of €250,000 is invested in an investment which is expected to earn a return of 7.5 percent, all of which are deferred capital gains, what is his expected after-tax accumulation in 15 years? The account’s market value is equal to its cost basis.**

**€640,747.**

**€665,747.**

**€690,747.**

**If Motelli’s current investment account of €250,000, has a cost basis of €175,000, and is invested in an investment which is expected to earn a return of 7.5 percent, all of which are deferred capital gains, what is his expected after tax accumulation in 15 years?**

**€673,247.**

**€683,247.**

**€690,747.**

**How much after-tax wealth would Motelli accumulate assuming the same facts as in Question 4 except that 50 percent of all capital gains are recognized each year?**

**€640,747.**

**€665,747.**

**€678,158.**

**Assuming an annual return of 7.5 percent, what would be the after-tax wealth accumulated in 15 years for a single current contribution to the TDA? Assume the contribution would be deductible but taxed at the end of 15 years at a 20 percent tax rate.**

**€23,671.**

**€23,965.**

**€29,589.**

**Sam Nakusi is managing a balanced portfolio of fixed income and equity securities worth £1,000,000. The portfolio’s pretax expected return is 6.0 percent. The percentage of return composed of interest, dividends and realized capital gain as well as the associated tax rates are listed below. Assume the portfolio’s cost basis equals market value.**

**Hypothetical Tax Profile and ExampleTax ProfileAnnual Distribution Rate (***p*)Tax Rate (*T*)Interest (*i*)20%35%Dividends (*d*)30%15%Capital gain (*cg*)40%25%

*p*)Tax Rate (

*T*)Interest (

*i*)20%35%Dividends (

*d*)30%15%Capital gain (

*cg*)40%25%

**What is the expected future accumulation in 15 years assuming these parameters hold for that time period?**

**£1,930,929.**

**£1,962,776.**

**£1,994,447.**

**In the previous question, recalculate the expected accumulation assuming the portfolio’s costs basis is equal to £700,000.**

**£1,373,943.**

**£1,962,776.**

**£1,887,776.**

**Gloria Vander is pursuing a buy-and-hold equity strategy on non-dividend paying stocks. She expects her €400,000 portfolio to experience no turnover over the next 10 years but expects to liquidate it at that time. The cost basis is currently equal to market value. If Vander expects an 8 percent pretax return and capital gains are taxed at 20 percent, what is her accrual equivalent return over that time period?**

**6.40%.**

**6.78%.**

**4.60%.**

**What is the accrual equivalent tax rate in the previous question?**

**15.25%.**

**20.00%.**

**84.75%.**

**Peter Cavuto lives in a country that imposes a wealth tax of 0.5 percent on financial assets each year. His €500,000 portfolio is expected to return 5 percent per year over the next twenty years. Assuming no other taxes, what is Cavuto’s expected wealth at the end of twenty years?**

**€1,200,100.**

**€1,205,857.**

**€1,326,649.**

**A client has funds in a tax deferred account and a taxable account. Which of the following assets would be ***most appropriate* in a taxable account in a Flat and Heavy Tax Regime, in which dividends and capital gains are taxed at ordinary rates and interest income is tax exempt? Assume that all assets are held in a client’s overall portfolio.

*most appropriate*in a taxable account in a Flat and Heavy Tax Regime, in which dividends and capital gains are taxed at ordinary rates and interest income is tax exempt? Assume that all assets are held in a client’s overall portfolio.

**Bonds.**

**Actively traded stocks.**

**High dividend paying stocks.**

**John Kaplan and Anna Forest both have €100,000 each split evenly between a tax deferred account and a taxable account. Kaplan chooses to put stock with an expected return of 7 percent in the tax-deferred account and bonds yielding 4 percent in the taxable account. Forest chooses the reverse, putting stock in the taxable account and bonds in the tax deferred account. When held in taxable account, equity returns will be taxed entirely as deferred capital gains at a 20 percent rate, while interest income is taxed annually at 40 percent. The tax rate applicable to withdrawals from the tax deferred account will be 40 percent. Cost basis is equal to market value on asset held in taxable account.**

**Kaplan’s and Forest’s Asset LocationTax ProfileKaplan (€)Forest (€)Taxable Account50,000bonds50,000stockTax deferred Account50,000stock50,000bonds Total (Before-tax)100,000100,000**

**What is Kaplan’s after-tax accumulation after 20 years?**

**€196,438.**

**€220,521.**

**€230,521.**

**In the previous question, what is Forest’s after-tax accumulation after 20 years?**

**€196,438.**

**€220,521.**

**€230,521.**

**What is the after-tax asset allocation for the following portfolio if withdrawals from the TDA will be taxed at 40 percent?**

**AccountPretax Market Value (€)Asset ClassTDA200,000BondsTax-exempt80,000Stock Total280,000**

**71.4% bonds; 28.6% stock.**

**50% bonds; 50% stock.**

**60% bonds; 40% stock.**

**Lorraine Newman is evaluating whether to save for retirement using a TDA or a tax-exempt account. The TDA permits tax-deductible contributions but withdrawals will be taxed at 30 percent. The tax-exempt account permits tax-free accumulation and withdrawals but contributions are taxable at a 40 percent tax rate. Assuming contribution limits do not affect Newman’s choice of accounts, which account should she choose?**

**TDA.**

**Tax-exempt.**

**The choices are the same.**

**Which of the following assets would be most appropriate to locate in a tax deferred account in a Heavy Interest Tax Regime assuming all assets are held in a client’s overall portfolio?**

**Low dividend paying stock.**

**Tax exempt bonds.**

**Taxable bonds.**

**Consider a portfolio that is generally appreciating in value. Active trading is most likely to be ***least* attractive in a:

*least*attractive in a:

**taxable account.**

**tax deferred account.**

**tax exempt account.**

**Jose DiCenzo has some securities worth €50,000 that have a cost basis of €75,000. If he sells those securities and can use the realized losses to offset other realized gains, how much can DiCenzo reduce his taxes in the ***current*tax year assuming capital gains are taxed at 30 percent?

*current*tax year assuming capital gains are taxed at 30 percent?

**€7,500.**

**€15,000.**

**€17,500.**

**In the previous question, suppose DiCenzo sells the securities in the current tax year and replaces them with securities having the same returns. He will then sell the new securities in the next tax year. What is the total tax savings assuming DiCenzo does ***not* reinvest the tax savings?

*not*reinvest the tax savings?

**€0.**

**€7,500.**

**€15,000.**

**Tax loss harvesting is most effective when:**

**there are few similar investment opportunities for the security with the loss.**

**the taxpayer is currently in a relatively high tax environment.**

**the taxpayer is currently in a relatively low tax environment.**

#### SOLUTIONS

**B is correct. Motelli’s tax liability on ordinary income is €20,000 (on the first €100,000, third column of table, last row) + (€200,000 − €100,000) × 0.35, or €55,000. The average tax rate on ordinary income is €55,000/€200,000, or 27.5 percent.**

**B is correct. The after tax wealth accumulation for annually taxable income is**

*FVIFi* = [1 + *r*(1 — *ti*)]*n*

*FVIFi*= [1 +

*r*(1 —

*ti*)]

*n*

**FV = €250,000 × ***FVIFi* = €250,000 × [1 + 0.065(1–0.10)]15

*FVIFi*= €250,000 × [1 + 0.065(1–0.10)]15

**= €586,547**

**A is correct. The accrual equivalent return is found by the following equation:**

**€250,000(1 + ***RAE*)15 = €586,547

*RAE*)15 = €586,547

*RAE* = 5.85%

*RAE*= 5.85%

**C is correct. The after tax wealth accumulation for deferred capital gains is**

*FVIFcg* = (1 + *r*)*n*(1 — *tcg*) + *tcg*

*FVIFcg*= (1 +

*r*)

*n*(1 —

*tcg*) +

*tcg*

*FVIFcg* = €250,000 × [(1 + 0.075)15(1–0.1) + 0.1] = €690,747

*FVIFcg*= €250,000 × [(1 + 0.075)15(1–0.1) + 0.1] = €690,747

**B is correct. The after tax wealth accumulation for deferred capital gains is**

*FVIFcg* = (1 + *r*)*n*(1 — *tcg*) + *tcg* — (1 — *B*)*tcg*

*FVIFcg*= (1 +

*r*)

*n*(1 —

*tcg*) +

*tcg*— (1 —

*B*)

*tcg*

*FVIFcg* = €250,000 × [(1 + 0.075)15(1–0.1) + 0.1 — (1–0.70)(0.10)] = €683,247

*FVIFcg*= €250,000 × [(1 + 0.075)15(1–0.1) + 0.1 — (1–0.70)(0.10)] = €683,247

**C is correct.**

*r** = *r*(1 — *pcgtcg*)

*r** =

*r*(1 —

*pcgtcg*)

**= 0.075(1 — (0.5)(0.10)) = 0.075(1–0.05) = 0.07125**

*T** = *tcg*(1 — *pcg*)/(1 — *pcgtcg*)

*T** =

*tcg*(1 —

*pcg*)/(1 —

*pcgtcg*)

**= 0.10[(1–0.5)/(1–0.5 × 0.10)] = 0.052632**

*FVIFTaxable* = (1 + *r**)*n*(1 — *T**) + *T** — (1 — *B*)*tcg*, *B* = 1

*FVIFTaxable*= (1 +

*r**)

*n*(1 —

*T**) +

*T** — (1 —

*B*)

*tcg*,

*B*= 1

*FV* = €250,000 × [(1 + 0.07125)15(1–0.052632) + 0.052632]

*FV*= €250,000 × [(1 + 0.07125)15(1–0.052632) + 0.052632]

**= €678,158**

**A is correct.**

*FVIFTDA* = (1 + *r*)*n*(1 — *Tn*)

*FVIFTDA*= (1 +

*r*)

*n*(1 —

*Tn*)

*FVIF* = €10,000[(1 + 0.075)15(1–0.20)] = €23,671

*FVIF*= €10,000[(1 + 0.075)15(1–0.20)] = €23,671

**B is correct.**

*r** = *r*(1 — *pdtd* — *piti* — *pcgtcg*)

*r** =

*r*(1 —

*pdtd*—

*piti*—

*pcgtcg*)

**= 0.06*[1 — (0.30)(0.15) — (0.20)(0.35) — (0.40)(0.25)]**

**= 0.0471 or 4.71 percent**

*T** = *tcg*(1 — *pd* — *pi* — *pcg*)/(1 — *pdtd* — *piti* — *pcgtcg*)

*T** =

*tcg*(1 —

*pd*—

*pi*—

*pcg*)/(1 —

*pdtd*—

*piti*—

*pcgtcg*)

**= ***tcg*(1–0.30–0.20–0.40)/[1 — (0.30)(0.15) — (0.20)(0.35) — (0.40)(0.25)]

*tcg*(1–0.30–0.20–0.40)/[1 — (0.30)(0.15) — (0.20)(0.35) — (0.40)(0.25)]

**= 0.0318**

*FVIFTaxable* = £1,000,000[(1 + *r**)*n*(1 — *T**) + *T**]

*FVIFTaxable*= £1,000,000[(1 +

*r**)

*n*(1 —

*T**) +

*T**]

**= £1,000,000[(1 + 0.0471)15(1–0.0318) + 0.0318]**

**= £1,962,776**

**C is correct.**

*B* = £700,000/£1,000,000 = 0.70

*B*= £700,000/£1,000,000 = 0.70

*FVTaxable* = £1,000,000[(1 + *r**)*n*(1 — *T**) + *T** — (0.25)(1–0.70)]

*FVTaxable*= £1,000,000[(1 +

*r**)

*n*(1 —

*T**) +

*T** — (0.25)(1–0.70)]

**= £1,000,000[(1 + 0.0471)15(1–0.0318) + 0.0318–0.075]**

**= £1,887,776**

**B is correct.**

*FVcg* = €400,000[(1 + *r*)*n*(1 — *tcg*) + *tcg*]

*FVcg*= €400,000[(1 +

*r*)

*n*(1 —

*tcg*) +

*tcg*]

**= €400,000[(1 + 0.08)10(1–0.20) + 0.20]**

**= €770,856**

**Solving for the rate set equates €770,856 with its present value of €400,000**

**€770,856 = €400,000(1 + ***RAE*)10

*RAE*)10

*RAE* = 0.0678 or 6.78 percent

*RAE*= 0.0678 or 6.78 percent

**A is correct.**

*r*(1 — *TAE*) = *RAE*

*r*(1 —

*TAE*) =

*RAE*

**0.08(1 — ***TAE*) = 0.0678

*TAE*) = 0.0678

*TAE* = 0.1525 or 15.25 percent

*TAE*= 0.1525 or 15.25 percent

**A is correct.**

*FVIFw* = [(1 + *r*)(1 — *tw*)]*n*

*FVIFw*= [(1 +

*r*)(1 —

*tw*)]

*n*

*FV* = €500,000[(1.05)(1–0.005)]20 = €1,200,100

*FV*= €500,000[(1.05)(1–0.005)]20 = €1,200,100

**A is correct. Tax-exempt assets are not appropriate for tax deferred accounts. In a Flat and Heavy Tax Regime, dividends and capital gains are taxed at ordinary rates and are not the best choices for taxable accounts.**

**A is correct. The taxable account will accumulate to**

*FVi* = €50,000[1 + *r*(1 — *ti*)]*n*

*FVi*= €50,000[1 +

*r*(1 —

*ti*)]

*n*

**= €50,000[1 + 0.04(1–0.4)]20**

**= €80,347**

**The tax deferred account will accumulate**

*FVTDA* = €50,000(1 + *r*)*n*(1 — *Tn*)

*FVTDA*= €50,000(1 +

*r*)

*n*(1 —

*Tn*)

**= €50,000(1.07)20(1–0.40)**

**= €116,091**

**Total = €196,438**

**C is correct. The taxable account will accumulate to**

*FVcg* = €50,000[(1 + *r*)*n*(1 — *tcg*) + *tcg*]

*FVcg*= €50,000[(1 +

*r*)

*n*(1 —

*tcg*) +

*tcg*]

**= €50,000[(1.07)20(1–0.20) + 0.20]**

**= €164,787**

**The tax deferred account will accumulate**

*FVTDA* = €50,000(1 + *r*)*n*(1 — *Tn*)

*FVTDA*= €50,000(1 +

*r*)

*n*(1 —

*Tn*)

**= €50,000(1.04)20(1–0.40)**

**= €65,734**

**Total = €230,521**

**C is correct. The after-tax value of the TDA account is €200,000(1 − 0.40) = €120,000. The after-tax value of the tax-exempt account is €80,000. The total after-tax value of the portfolio is €200,000. Stock represents €80,000/€200,000 = 40 percent of the total, whereas bonds represent €120,000/€200,000 = 60 percent of the total.**

**A is correct. The future accumulation of the TDA is (1 + ***r*)*n*(1 − 0.30), whereas the future accumulation of the tax-exempt account is (1 + *r*)*n*(1 − 0.40). Therefore, the TDA will accumulate more wealth.

*r*)

*n*(1 − 0.30), whereas the future accumulation of the tax-exempt account is (1 +

*r*)

*n*(1 − 0.40). Therefore, the TDA will accumulate more wealth.