# Investment Management And Factors

## Understand How To Invest Your Money Wisely

There are not many articles explaining investment management and its factors on medium, despite it being one of the most important fields in finance.

As a consequence, I have decided to write an article that focuses on investment management, its concepts along with the key factors which we should be familiar with so that the wider community can benefit from it. I will be aiming to explain everything from the basics.

Investment management can help us understand how to earn highest return from our investment by taking the least amount of risk

# Article Aim

This article will provide a thorough overview of the following topics:

- Explaining The Investment Problem
- Assets, Portfolio, Alpha, Beta & Benchmark
- What Is Factor Theory?
- Overview of CAPM and multifactor models
- Understanding what factors are

Please read FinTechExplained disclaimer. Always seek advice of a professional financial advisor before investing your money.

# 1. Let’s Understand The Investment Problem First

Let’s consider you have $10'000 of cash available and you are interested in investing it. Your aim is to invest the money for a year. Like any rational investor, you expect the final amount in a years time to be higher than the $10'000 amount you want to invest. The last thing you want is to lose the $10'000 you started your investment with.

**So far, so good!**

Now the research journey begins. You probably lookout for a number of investment opportunities which can earn you your highest return.

## Let’s Invest The Money

The most obvious investment option might be to invest in a fixed-term savings account of an AAA-rated bank.

The concept is simple. You invest x amount now and get x + interest in a year’s time. You might choose this option because of the fact that the investment option is easy to understand, *it is simple and it’s, well, pretty-much risk-free because you are guaranteed to get your return back.*

To elaborate, let’s assume that a bank named National Bank, is an extremely safe government bank and it is willing to give you a 2% return on your investment if you deposit the money for a year. **Let’s refer to this rate as the risk-free rate for now as you will get a 2% return without taking any risk.**

Therefore you will receive 10'200 = $10'000 x (100+2)% after a year.

*Usually, the rate offered on the Treasury Bills is the risk-free rate as it is the safest form of investment.*

## Let me now introduce the concept of risk-return trade-off

There are a couple of investment options, in potentially increasing order of risk, such as:

- Treasury Bills
- Government Bonds
- Bank Savings Account
- Investments In Developed Country
- Investments In Emerging Countries
- Equities & Company Shares In Stable Companies
- Equities & Company Shares In New Companies
- And so on

*The hypothetical chart above is indicating that the return you receive on your investment increases as you take more risk.*

Some of these investments are riskier than the others and these returns can help us gain higher returns. Hence, the point to note is that there exists a risk-return trade-off. As an investor, our sole aim might be to invest in the least risky investment option that yields the highest return. Let me explain this in a bit more depth!

What’s important to realise is that there is a tradeoff between risk and return. If an investor is expecting to invest in a riskier investment option than the risk-free rate then he/she is expecting to earn more in return. This is to compensate for the risk that the investor is taking. So far, it all makes sense!

An investor is willing to take more risk because he/she wants to earn more in return.

It is important to note that higher risk does not produce higher returns. Sometimes, investments with the lowest risk produced the highest returns as seen in 2011–2016 from iShares Edge MSCI Minimum Volatility USA ETF performance.

# 2. This Brings Us To The Concept Of Assets, Portfolio, Alpha, Beta & Benchmark

Up till now, we have realised that there is a risk-free rate. If we want to earn money above the offered risk-free rate that then we will have to take more risks.

## What Are Assets & Portfolio?

We might start our investment journey by buying equities of different companies, commodities, derivatives, and/or bonds etc. Let me refer to these transactions as ** assets **from now on. A

**groups/holds the assets together. Every time we change our portfolio by buying/selling an asset, we have to pay a transaction cost which could be a percentage of the transaction amount.**

*portfolio*There is also a theoretical market portfolio which holds every single asset that is available in the market.

As we start to add assets in our portfolio, we start realising that some of these assets are somewhat correlated with each other. The risk of an asset can be computed using a number of risk measures. One of these measures is the standard deviation which can inform us on how the price of an asset deviates from its mean. As an instance, some of the assets might be negatively correlated with each other, implying that as the value of the first asset moves down, the value of the negatively correlated asset increases. This shows us that the risk of a portfolio is not a simple sum of the risks of the individual assets.

Let’s understand it with an example

Consider an asset A. Its price fluctuates a lot. If we plot its daily price change, we can see that the asset is extremely volatile.

Consider another asset B which exhibits similar behaviour as asset A. If we plot its daily returns, we can see that it also is highly volatile:

One might assume that buying both of these assets will not ba wise decision. However the opposite might be true. If I plot the daily returns of both of the assets, we can notice that the assets are perfectly negatively correlated with each other:

As a result, we end up diversifying the risk and thus the risk isn’t the sum of the risk of the individual assets anymore. Hence, we need to compute the comovement (covariance) of all of the assets with each other and then use it to compute the risk. This means that an investor can reduce the total risk and increase the return by choosing different assets with different proportions in a portfolio.

When we want to invest in a company, we need to understand its net worth per share to determine the value of a company share.

## Book Value Per Share

The net worth per share of a company is known as its book value per share. It is calculated as:

We also need to consider the price of the stocks into account to understand whether the share is a value or growth-share. Value shares are those shares that have a high book to market ratio and growth shares have a low book to market ratio. History informs us that the value stocks are positively correlated with each other and thus perform like each other.

We can start preparing a unique mixture of a large number of portfolios. An investor has his/her target return and risk profiles. Some of these portfolios will be more efficient than others. If we plot the risk-return of the portfolios on a scatter-chart then we will see a curve which will look like the image below.

*This is the set of efficient portfolios which yield the highest return for the lowest risk. I will explain in another article.*

**Note For Future: I am planning to demonstrate how we can compute the investment management theory by creating optimum and efficient portfolios using Python. This will then put the theory into practical action. I will also attempt to use advanced machine learning and data science concepts such as neural networks. So stay tuned and let me know if you are interested in the tool and the articles!**

## Alpha, Beta & The Benchmark

We understood that there is a risk-free rate investment which can give us a return on our portfolio without letting us take any risk. Before I explain Alpha, I need to quickly provide an overview of the benchmark index.

## Benchmark

Have you come across the famous indexes such as S&P 500, Russell 1000, FTSE 100, Nasdaq 100 indexes and so on? These indexes essentially provide us a way to measure the performance of the market as a whole. It is very difficult to assess the performance of every single company to understand how the market is behaving. As a result, these indexes provide a good overview. Essentially these are stock market indexes which represent the performance of top companies. This makes it simpler for investors to understand how the market is behaving. The concept is that a number of top companies are selected. As an example, Russell 1000 is an index of nearly 1000 largest companies in US equity market and S&P 500 is computed by considering 500 largest corporations by market cap that are listed on New York Stock Exchange. These indexes are highly diversified because some of the assets will be correlated with each other.

An investor can create his/her own portfolio and take the index as the benchmark which he/she has to beat!

Having said that, occasionally the risk-free rate is considered to be the benchmark. A large number of studies and methodologies have been implemented that select the appropriate benchmark for the investor.

For the sake of simplicity, we can think of these indexes as the average performance of the top companies in the market

Ok, so now we are pretty much there to understand what alpha is.

## Alpha

The index can be considered as a benchmark for the investor. And, the return that the investor earns in excess of a benchmark is known as the alpha!

Therefore, to carry on the risk-free rate example expressed above, if the risk-free rate is taken as the benchmark and an investor earns 5% return after investing in a large number of equities then in the simplest case, the alpha is 3% (5%-2%).

For the sake of avoiding confusion, I will explain and compute the risk-adjusted part of Alpha (Jensens Alpha) later on.

To be precise, alpha is the average performance of an investor in excess of the benchmark.

## Beta

Beta, on the other hand, helps us understand how risky an asset is by taking historical volatility into account. It measures how the asset moves when compared to a benchmark.

A beta is usually a Real number. As an instance, when an asset’s beta is -1 then it means that there is a true negative correlation between the asset and the benchmark index. As a result, it shows us that both the asset and the benchmark move in the opposite direction to each other.

The higher the beta, the riskier the asset.

To calculate the beta, we need to take the correlation of the asset with the benchmark along with their volatilities into account. The volatility is represented by the standard deviation of the asset prices.

## Let’s Combine Benchmark, Alpha & Beta Together

Let’s assume we invested $10'000 by buying gold. Let’s also consider our benchmark is the 2% savings account. The beta of gold with the benchmark is 1.75 which is calculated by taking the volatility of gold and the benchmark into account. This means that the volatility of gold is 75% greater than the volatility of the benchmark.

After a year, let’s consider that the price of gold turned out to be $10'300. Therefore we have earned a return of 3%

If we invested $10'000 in a savings account, we would have earned $10'200. Therefore in the simplest case, our alpha is 1% (3%–2%).

Now we have built a strong foundation for us and I am sure we are realising how investment can be managed accurately.

Once we start to learn about investment management, we will come across various buzzwords such as the capital asset pricing model (CAPM) and multifactor models. These models are built on top of a theory that is widely known as the Factor Theory.

Let’s start by understanding what factor theory is.

# 3. Factor Theory

Consider a scenario that you want to buy some assets such as government bonds or equities (company shares). How will the assets behave if the economy slows down, or if the inflation increases, or if a war occurs or if a cure for a disease is found or whether the shares will increase in their value if a higher number of younger investors attempted to buy them all at once or how the assets will behave due to the introduction of a new monetary policy?

All of these questions are captured in factor theory

## Assets As Factor Risks

These assets in a portfolio are merely a group of factor risks. To understand it better, know that the behavior of the assets is dependent on the factors. Therefore, as an investor, it is crucial to map assets to the factors and then perform a thorough analysis of the factors.

## Good And Bad Times

We can think of good times as when we are gaining high returns, the economic outlook is positive, there is liquidity in the market, the inflation rate is low and there is a good balance of supply and demand in the market. The opposite can be considered as bad times.

There are many inefficiencies in the market. The most crucial analysis that an investor needs to perform is to determine whether an asset is valuable to hold in the current times. There is a cost associated with buying/selling an asset. As an instance, an investor might have to pay a transaction, agency, financing cost. Some researchers claim that an investor can beat the market by saving on transaction costs.

This brings us to the first key point:

Factor theory is about performing the analysis of the risks which are associated with the factors.

## Understanding Factor Risks

The price of an asset is changing on a timely basis. We can take the asset prices overtime to calculate their volatility (risk) and returns. An investor needs to be aware of the unexpected changes in the factors and needs to understand how they can impact the risk premiums and asset returns.

Some of these factors are at the macro level, whereas the other factors are at the micro-level. As an instance, factors such as the growth of the economy and the inflation rate are macro-factors. There could be other macro factors too, such as the market, interest rates and so on.

*There are not our company level statistical measures such as revenue, P/E ratios, EBIDTA, profit margin, return on assets, income, earnings, cash flows, dividends, payout ratio, beta, moving averages, share volume, credit quality and so on.*

Each factor exposes us to some form of risk but we might still invest in the asset due to the excessive premium it pays over the return of a safe riskless investment such as in treasury bill.

Investors usually assume that past growth rates will continue in the future. This behavior is known as overextrapolation.

This brings us to the second key point:

Factor risks are those risks which an investor is exposed to during bad times. These extra risks are rewarded with risk premium.

## 3 Principles Of Factor Theory

The theory is based on the three key principles:

- Don’t be concerned with what your exposure to an asset is. Rather concentrate on the exposure to the underlying factor.
- Group the assets into factors. This implies that your portfolio can contain 100s of assets but dependent on the asset types, the assets can be grouped into a handful of factors. Now the key to note is that some of the assets themselves are the factors such as equities, whereas some of the assets can contain multiple factors such as a corporate bond asset can contain interest rate to counterparty default risk factors.
- Not all investors have the same risk exposure profile and each investor can have different optimal exposures to the risk factors.

This brings us to the next topic of the article: CAPM and Multifactor Models

# 4. CAPM and Multifactor Models

A number of models have been implemented. This part of the article will briefly provide an overview of the concepts. *I am avoiding going in too much depth at the moment because I will be implementing a portfolio management tool which will explain everything with practical uses.*

## Let’s quickly review CAPM.

CAPM stands for Capital Asset Pricing Model. The model is essentially a mathematical formula that considers market portfolio to be the only risk factor. Therefore it is a single-factor model.

CAPM essentially states that the more risk you take, the more you can expect to earn.

It is based on a theory that the prices of the assets are dependent on the market and with each other. Therefore, we need to consider the covariance (comovement) of the asset with the market portfolio.

The covariance of the asset to the market portfolio is known as the beta of an asset.

As a result, the theory states that the assets with high beta yield high return.

The return over the theoretical return of the CAPM return and the risk free rate is known as the alpha

There are a number of limitations of CAPM. As an instance, it is not realistic as it does not represent the true picture of the investment world. CAPM model does not work in inefficient markets where the same information is not available to all of the investors. As a consequence, multifactor models have been implemented.

## Let’s review Multifactor Models

There are a number of multifactor models. These models consider more than one factors into consideration. An example of such models is the arbitrage pricing theory (APT).

## APT

This model is very similar to CAPM because it describes the expected returns as a linear function of exposures to common risk factors. The issue with APT is that the expected returns might not be a linear function of exposures to common risk factors. As a result, to incorporate nonlinearity in the model, a number of superior multifactor models have been introduced which use a random stochastic discount factor (SDF) and it is represented as “m”. This random variable captures all bad times and the risk is measured by factor betas.

Therefore, in the multifactor model, a number of betas are computed, where each beta represents a factor. As an instance, we could have beta1 for inflation, beta2 for the investment strategy factor and so on.

One of the most famous models is the Fama-French model.

## Fama French Model

It is a three-factor model as it takes three dynamic factors into account. These factors are the market risk factor, the size factor and the value/growth effect factor. Each factor has its own beta coefficient. These explanatory factors can help us predict the alpha of an asset accurately. The size factor essentially captures the difference between the returns on small versus big stocks. Big stocks are those stocks with large market capitalisation. Furthermore, the value/growth factor captures the difference of returns between stocks that have a high book to market and low book to market values.

History has informed us that small stocks tend to outperform the large stocks once the beta for the firm is adjusted.

There are also other models such as dynamic stochastic general equilibrium model which take agents behavior along with technological changes into account. There are also overlapping generation models which take demographic factor into account. These models have helped us understand that we need to diversify the risks by investing in different factors.

# 5. Let’s Understand The Factors

So far, we have understood that the factors derive the risk premiums and the returns. Some of the factors are macro-level factors such as inflation, economic growth, and volatility. These factors can impact the risk premium and asset returns.

## Macroeconomic factors

There are a number of macroeconomic factors such as political risk to economic growth to inflation to demographic risk. Let’s understand the three most important macroeconomic factors

## 1. Economic Growth

Economic growth is measured by taking the GDP growth into account. The economic growth is a variable which usually performs stronger for a longer time.

It is vital to analyse the economic factor and invest accordingly. As an instance, some of the assets are riskier than others. History shows us that the riskier assets are not a wise choice to invest in during bad economic growth. To elaborate, equities are riskier than government bonds. During slow economic growth, riskier assets perform poorly when compared to the less risky assets. However, the returns are usually higher for riskier assets if an investor wants to invest for long-term.

We cannot easily hedge economic growth risk. Investors usually like gains more than they dislike losses. This behavioral theory is known as loss aversion and mental accounting.

## Inflation

The inflation rate is the rate at which the price of goods and products have increased in a country. It is measured periodically. The inflation rate is calculated by pricing a large number of common goods and services in a country and then taking the weighted average of them.

Government issues bonds to investors to raise its reserves. When inflation is high, interest rate increases and the value of the bonds decreases. As a result, the inflation rate can impact GDP Per Capita On PPP, foreign reserves and debts of a country. Additionally, when the price of goods is expensive, people tend to spend less on recreational activities. As a consequence, the overall well-being of a country decreases.

History teaches us that high inflation is bad for investors because both equities and bonds perform badly. Not only the risk increases, but the returns are also lowered. It is difficult to hedge against inflation risk.

## Volatility

VIX is a volatility index which represents the equity market volatility. When the volatility is high, the stocks perform badly and as a result, the market value of the equities fall. This is known as the leverage effect.

We can reduce the exposure to the volatility factor and hedge the volatility risk by investing in less risky assets such as bonds, or even better, consider investing in out of the money put options. These assets pay off during high volatility.

# Summary

Investment management is one of the most important fields in finance yet not many articles explain it in greater detail. In this article, I have attempted to explain the following key points:

- Explaining The Investment Problem
- Assets, Portfolio, Alpha, Beta & Benchmark
- What Is Factor Theory?
- Overview of CAPM and multifactor models
- Understanding what factors are

**I am planning to demonstrate how we can compute the investment management theory by creating optimum and efficient portfolios using Python. This will then put the theory into practical action. I will also attempt to use advanced machine learning and data science concepts such as neural networks. So stay tuned and let me know if you are interested in the tool and the articles!**