“In an effort to give our clients a look under the hood of our firm, please see the first write up of our series on risk and return from our financial analyst and investment committee member Griffin Sheehy.” – Mark Shone CFP®
This series aims to address the relationship between taking risk and properly being compensated for taking that risk. There are a multitude of statistics for measuring the risk-reward relationship for an investment and they are all related to some degree yet have slightly differing interpretations. It is important to understand the underlying similarities as well as the differences in how they are derived, calculated, and ultimately interpreted. Without this knowledge an investor runs the risk of comparing a portfolio of apples to that made of oranges and thinking they are inherently the same when this couldn’t be further from the truth. An example of this would be should a portfolio of globally diversified equity be compared to a benchmark consisting only of the S&P 500? The answer to this question is a hard and emphatic NO! Specifically talking in terms of this question, the answer is a simple one. It’s simple because the orange in this discussion (global equity) consists of domestic stock as well as international stock in both developed and emerging markets. The apple (S&P 500) however, consists only of the 500 largest domestic stocks. It doesn’t take rigorous analysis at this point to think they may have differing risk-return profiles knowing that. It also doesn’t take much rigor to think this comparison may lead to dubious investment decisions if acted upon. Sometimes the answers aren’t this easy to uncover because other asset classes, like bonds for example, may be included in the portfolio. This leads us to the need for more in depth analysis from a statistics standpoint to truly understand how a portfolio’s risk characteristics drive its returns.
Intro to Modern Portfolio Theory and the Capital Asset Pricing Model (CAPM)
In a little known article first published in 1952, Harry Markowitz formalized the relationship between risk and reward. Until that time, the anecdotes of “don’t put all your eggs in one basket” and “nothing ventured, nothing gained” dominated Wall Street with good old-fashioned common sense. His research culminated in an article titled “Portfolio Selection” and later became the founding father of Modern Portfolio Theory. With this work, Markowitz was one of the first to empirically test these assumptions by involving multiple asset classes. For example, on one end of the spectrum are low risk-low reward investments like short term bonds and on the other are high risk-high reward assets like stocks. Between these are investors trying to balance the highest gains with the lowest risk. His theory is often interpreted as choosing the right risk tolerance based on an acceptable level of volatility and matching that to a specific portfolio expected return. The goal in this is to find a portfolio that is efficient, or the one that maximizes gains per unit of risk taken. William Sharpe (and others) took these findings and ran with them to develop other groundbreaking works in the field of finance such as the CAPM. The CAPM is a simple linear relationship derived from the work of Markowitz and looks like this:
r = Rf + β x ( Km – Rf )
r is the expected return rate on a security;
β is the volatility of the security, relative to the asset class; Rf is the rate of a “risk-free” investment, i.e. cash; Km is the return rate of the appropriate asset class.
This equation has certain implications and consequences. First off, it allows us to easily calculate something called the efficient frontier (more on that next time). Second, is that it shows investors require higher expected returns for taking higher risk (just like what Markowitz says). One way to think about this equation is as a function of beta, where you can predict the rate of return investors require if you know that particular security’s beta.
For example, Proctor and Gamble (PG) has a beta of 0.67 with the S&P 500. We can interpret this as saying that we’d expect PG approximately to have 67% of the volatility compared to the largest 500 stocks in the US. Because of this we can also expect it to have 67% of the expected return (above the risk free rate, usually treasuries) as well, both positive and negative. The eyes may glaze over when discussing this example but in terms of importance within finance, Modern Portfolio Theory and CAPM form the backbone. Understanding it or being somewhat familiar with it is key to being a successful investor because metrics such as alpha, beta (which we discussed a little bit), standard deviation, etc. depend on it. Not to mention more sophisticated techniques involved in forecasting and portfolio management like regression and factor analysis are built on its foundation (which will be a future subject). As investors we’ve always been told about the benefits of diversification, but with the introduction to these topics it is possible to show the math that answers diversification’s most important question: Why?