CAPM and Diversification
Everyone says that you should diversify your portfolio, but why?
This article will be more theoretical to start off with, but will undoubtedly lead to real value for you as an investor.
DISCLAIMER: This article references an opinion and is for information purposes only. It is not intended to be investment advice. Seek a duly licensed professional for investment advice.
Capital Asset Pricing Model
The Capital Asset Pricing Model, also known as CAPM, is a model used to define the theoretical relationship between an asset’s given risk and expected return. The model is built on the assumptions that every investor acts rationally, is naturally risk-averse, and some more perfect-world suppositions that we know not to be hard-and-fast rules in the real world. The model is by no-means made to be used by itself for investment decisions; If it were entirely accurate, generating returns over the market index would be impossible in the long-run. Before getting into the weeds, let’s review some key concepts and introduce some new ones.
Review
Alpha (α) refers to the return of an asset or portfolio above the related market index return. For example, if your portfolio appreciates by 20% over the course of a year whilst the stock market falls by 5% in the same time frame, your portfolio generated 25% alpha over that period. To be clear, α doesn’t mean much on a day-to-day basis, but is only considered true alpha over a sustained period.
Beta (β) refers to the sensitivity of a given asset’s return relative to the market index return, usually the S&P 500. High beta stocks (β>1) are more considered more volatile as they historically amplify market movements, and low beta stocks (β<1) are considered more stable as they historically suppress market movements. As you might expect, growth stocks and newer businesses operating in discretionary industries like tech are generally more volatile, whereas established companies operating in essential industries like waste management are more stable.
Illustrating Concepts
If we were to plot market returns x-axis against the returns of Apple stock on the y-axis for each month, and then graph a regression line through the data, this is what we would get.
If you remember the formula for a line from grade 9 math, it’s y=mx+b, where m is the slope of the line and b is the y-intercept. In this case, m is Apple stock’s β and b is Apple stock’s α (avg/expected monthly return). The way that CAPM quantifies risk is by defining it as the standard deviation of the data, calculated by square rooting the variance (VAR). Don’t worry about getting into the math; Both numbers will give us a number representing how far apart the data points are on the graph from the line. Either can be used so long as everything measured the same. The larger the variance or standard deviation, the greater the spread of the data relative to the regression line, and vice versa.
Covariance (COV) is the relationship between the movements of two separate asset prices. A highly positive covariance means that the stocks tend to move together very closely, and a highly negative covariance means that the stocks tend to move together inversely. A covariance close to zero means that they are not closely correlated.
The last key concept we will review is idiosyncratic risk and market risk. Idiosyncratic risk comes from an asset’s alpha, as it is the movement of the stock beyond that of the larger market. Apple’s supply chain breaking down would be an example of idiosyncratic risk. COVID-19 causing almost all supply chains to break down would be an example of market risk. Market risk affects all stocks, and thus comes from beta.
Efficiency Frontiers
The reason we are talking about CAPM today is the Efficient Portfolio Frontier. This is the curve we get if we use the annual expected returns of two or more assets and plot it against the standard deviation (risk) of a theoretical portfolio holding varying amounts of those assets. If that sounds complicated, just look at the Efficient Portfolio Frontier for stocks and bond and it should start to make sense.
Note: A portfolio of > 100% of an asset can be achieved through buying on leverage
The reason that risk decreases until the point of minimum variance is that diversifying a portfolio cancels out idiosyncratic risks (α) of individual assets within that portfolio. Beyond this point, the market risks (β) of the other asset take over. It’s important to realize that even at the point of minimum variance (25% stocks and 75% bonds), risk is not at 0%. This is because although idiosyncratic risk can cancel out to zero, market risk can never entirely be gotten rid of.
Risk
Looking at this chart, it may seem like everyone should be holding 25% stocks and 75% bonds, but this is is not the case. Although, this is the ratio that maximizes the expected return per quantity of risk, the goal of every investor is not to minimize absolute portfolio risk. For an investor who can stomach higher levels of risk, it can make complete sense to hold 100% stocks. The additional benefit exponentially diminishes, though it can be, and is still worth it for many investors.
People with lower tolerance to risk are willing to accept lower expected returns if there is also lower a beta (suppressed market risk). This is why many people hold gold in their portfolios, despite it having an annualized return of only 0.02% over the past 2000 years. Despite it offering very little return, gold acts as a counterweight in a portfolio during bear markets, oftentimes even having a negative beta value. To learn more about hedging investments, check out our article on risk and reward here.
Conclusions
Although it can make sense to be above the point of minimum variance, the most important takeaway from the CAPM is that it never makes sense to below that point. The reasoning is simply that for any point below the minimum variance, there exists a point directly above which offers the same level of risk with a higher expected return. Therefore, based on the above efficiency frontier, it never makes sense to hold less than 75% bonds in your portfolio with the rest, equities. Keep in mind, however, that this along with the following conclusions are entirely theoretical. Even still, they are useful to illustrate key investment concepts.
Looking at this new graph, the original may now seem misleading. For every point on the curve without oil, there exists some point on the curve with oil with the same expect return with a lower level of risk. With this new information, it now makes no sense to hold a portfolio with 0% exposure to oil. The key insight here is not that everyone should go and buy oil futures; the key insight is that I can continue to add additional curves to this graph with more and more assets that will allow for a portfolio with less risk and the same return. What you should takeaway from this is that your portfolio should have exposure to as many asset classes as you can, to varying degrees. Luckily, ETFs allow for every single investor to have easy access to virtually anything.
The conclusion that diversifying your portfolio can lead to lower risk with equal expected return comes with an asterisk; diversification works best when you hold assets with minimal covariance. If you hold shares of an oil company, oil futures, and a market ETF for a country mainly supported by oil, you’ve technically bought many different types of assets, but you haven’t really. Diversification only means something if your holdings don’t move in conjunction, thus are exposed to different inherent risks (α).
The mistake that many undisciplined investors make is looking at the return of specific holdings, getting worried, and then selling out of the worry that the asset will fall further. In reality, what matters is the risk and return of the entire portfolio of a prolonged period. You shouldn’t get caught up with the performance of one specific holding at one point in time.
Over-diversification
There’s one last caveat that comes with diversification, and that’s over-diversification. As you now know, diversification reduces risk and up to a certain point, can even increase expected return, but these benefits are subject to diminishing returns. At a certain point, it does not make sense to diversify further as you are simply diluting your returns.
Following the CAPM entirely would lead you to being an entirely passive investor based upon the Efficient Market Hypothesis Theory, but we are smarter than that. Generating real alpha is feasible, and taking key insights from CAPM into account makes it that much easier.
Please remember that the CAPM is based on a number of perfect-world assumptions and that risk and expected returns cannot truly be quantified.
Anyhow, hopefully this article helped illustrate to you the importance of diversification as well as its limits. If it did, please be sure to look over some key takeaways and at some next steps you can take to support us and further your learning!
Key Takeaways
- The Capital Asset Pricing Model is used to define the theoretical relationship between an asset’s given risk and expected return
- Alpha (α) refers to the return of an asset or portfolio above the related market index return, and Beta (β) refers to the sensitivity of a given asset’s return relative to the market index return.
- α is the source of Idiosyncratic risk, and β is the source of market risk.
- Risk is quantified through the spread of the data relative to the regression line, measured with either variance or standard deviation. Covariance measures the relationship of the returns of two separate assets
- The Efficient Portfolio Frontier is the curve when annual expected returns of two or more assets are plotted against the standard deviation (risk) of a theoretical portfolio holding varying amounts of those assets.
- It never makes sense to be at a point on the frontier below the minimum variance point, although it often does make sense for investors to be above it, depending on the tolerance for risk.
- Diversifying a portfolio to gain exposure to many different asset classes can reduce inherent risk whilst maintaining the same level of expected return within a portfolio, so long as the covariance of those assets is minimal.
- Diversification has diminishing marginal returns, and thus over-diversification can result in the dilution of returns with little to no change in a portfolio’s risk.
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