- Risk is one of the most important factors to consider while building an investment portfolio.
- Risk can be moderated or adjusted using the Modern Portfolio Theory and the Capital Asset Pricing Model.
- Nothing is perfect, especially economic theories, how come?
As a newbie in the financial world, it’s very easy to get confused. There are countless financial instruments available, a lot of different markets, and a lot of types of investments. But for sure the first thing mentioned no matter what finance topic is being discussed is diversification. An investment must be part of an investment portfolio, and every allocation must be adjusted according to a range of factors. Between these factors we find personal information, geographic position, capital amount and attitude toward risk. Just being aware of this means being part of the small fraction of young investors who are looking for an exit from the social media – financial gurus – mainstream media loop.
Today the focus will be on why risk and returns are expected to be correlated and, most importantly, how a basic knowledge of the correlation between assets and markets could be crucial to effectively diversify an investment portfolio. As a valid source and help for this research, I recall the intriguing pages of the latest edition of “A Random Walk Down Wall Street” by B.G. Malkiel, as well as other online resources that can be found at the end of this article.
Why am I talking about risk? The answer is simple: out of the factors mentioned above, attitude toward risk plays a huge role both in investing results as in people’s mental health: risk is what discourages people from investing, keeps them awake at night, and is blamed instead of the irresponsibility of the investor. Seems fair that assuming more risk means expecting higher returns on the investment, otherwise no one would increase their portfolio risk factor. For these reasons, analyzing risk is important.
Nobel Prize winner H. Markowitz elaborated the Modern Portfolio Theory (MPT) during the 1950s in his book “Portfolio Selection” assuming that all investors are quite like my mum, so basically risk-averse and very skeptical about investments. His thesis was that a portfolio of risky stocks might be put together in such a way that the portfolio as a whole could be less risky than the stocks that it contained. It evolves around the basic idea of diversification, which aims to minimize idiosyncratic risk by holding assets that are not perfectly positively correlated. Please note that idiosyncratic risk is the inherent risk involved in investing in a specific asset, such as a stock. It’s the opposite of systematic risk, which affects every investment in a specific asset class. The key factor is the correlation between the assets, also known as the covariance: it’s a number between 1 and -1 with 1 meaning that the investments move pretty much together, and -1 the opposite. With a negative covariance of -1, all idiosyncratic risks can be eliminated. In today’s global world is quite difficult to find such assets, but that’s not even necessary: with a correlation coefficient just below 1 some moderate risk reduction is possible. And, to be honest, the covariance is not that difficult to calculate: it involves the standard deviation (the measure of the dispersion of data from its average) and it’s expressed with the formula “Correlation=ρ= Cov(X,Y)/ σXσY”. Of course, a proper advantage can be obtained with around fifty different stocks, and according to Malkiel “The paradoxical result of this analysis is that overall portfolio risk is reduced by the addition of small amount of riskier foreign securities”: his analysis found out that the portfolio with the least risk was composed by 18% of foreign securities and 82% of U.S. securities, with an average annual total return of about 8,87% and a volatility of returns of about 0.163 between 1970 and 2017, outscoring the S&P 500 in both categories (source: Bloomberg).
Despite being a great, if not dreamy, theory, the MPT has a big problem. It doesn’t consider that returns are not only determined by the specific risk of every stock. Between a group of securities with high specific risk and another with low specific risk (assuming the same systematic risk between the two), the total risk is higher in the first group. That is the fundamental thesis of the Capital-Asset Pricing Model (CAPM) by Nobel prize winner W. Sharpe with J. Lintner and F. Black. Their view on the risk-return narrative starts by pointing out that diversification is not able to eliminate all risks as we were in a fantastic world. Thus, to get a higher average long-run rate of return you need to increase the risk level of the portfolio that cannot be diversified away. This vast majority of the remaining risk is the systematic one, which can be valued by a factor called β. Beta is the measure of the volatility of the investment compared to the relative market: the higher the β is, the higher the expected returns must be.
In the main formula, an investment’ beta is multiplied by the market risk premium, which is the return expected from the market above the risk-free rate. The risk-free rate is then added to the product of the stock’s beta and the market risk premium. The result should give an investor the required return or discount rate that they can use to find the value of an asset. In fact, the aim of the CAPM model is to evaluate whether a stock is fairly valued when its risk and the time value of money are compared with its expected return. It is a simple way to determine the expected returns from investment volatility, in order to buy if the investment’s current price is undervalued, as in the popular Firm-Foundation Theory.
Being curious, I wanted to apply the CAPM to the crypto market. Why not? Don’t you like rollercoasters? Well, apparently, it’s not a great idea. The CAPM may be easy to comprehend but not as effective. The main problems with it are that it assumes that volatility is synonymous with risk and, more importantly, it considers correlation and beta between assets are predictable in the long run using historical data. In a 1992 study, E. Fama and K. French divided stocks based on their betas and compared them with the respective average monthly return during the 1963-1990 period: no relationship was found between riskier stocks and highest returns. These two economists then integrated the CAPM with two more factors to describe risk: the size of the company (market capitalization) and the relation of its market price to its book value. The Fama-French three-factor model was later adapted to include two other factors: profitability (companies reporting higher future earnings have higher returns in the stock market) and investment (companies directing profit towards major growth projects are likely to experience losses in the stock market). The FF5F model (French-Fama 5 factor) can describe that smaller company stocks produced the highest returns, even with the same beta levels. An article published in 2020 analyzing empirically the efficiency of the model demonstrated that big-size portfolios have statistically insignificant HML (relation between market price and book value, also known as B/M ratio) and RMW (profitability).
Economists and academics will go on forever studying and analyzing data, creating new models, and testing them. The key lesson summarizing this long article is that everything has its risk and that the creation of a portfolio can be way more difficult than it seems. But, 100% sure, I can guarantee you that if you talk about it with my mother, you better just spend your time listening to financial gurus.
Sources:
https://seekingalpha.com/article/4108577-high-risk-high-reward-think-again#comments
https://mba.tuck.dartmouth.edu/pages/faculty/ken.french/Data_Library/f-f_5_factors_2x3.html
https://crypto.com/university/portfolio-management-like-a-pro-the-capital-asset-pricing-model
https://www.investopedia.com/terms/c/capm.asp#toc-what-is-the-capital-asset-pricing-model
“An empirical investigation of the Fama-French five-factor model” by Oleksandr Paliienko, Svitlana Naumenkova and Svitlana Mishchenko (2020), Business Perspectives, Sumy (Ukraine): https://www.businessperspectives.org/images/pdf/applications/publishing/templates/article/assets/13210/IMFI_2020_01_Paliienko.pdf
“A random walk down Wall Street: the time-tested strategy for successful investing” by Burton G. Malkiel (2019), Norton, New York (USA)
The Bear Street Journal. 
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