Monday, January 10, 2011

Risk-Adjusted Returns

Here is a trick question for you. Would you rather earn a 10% return with 10 units of volatility (don’t worry about how to measure the volatility units, I’m trying to make a point here), or would you rather earn an 8% return with 4 units of volatility? Clearly the second choice is the more efficient portfolio earning higher returns for each unit of volatility (two percent return per unit of volatility in the second choice versus one percent return per unit of volatility in the first choice). The correct answer is to choose the inefficient portfolio with the highest returns. Why? Because we know the return! In hindsight, volatility shouldn’t matter, even to the most risk adverse investors. If you know that portfolio A will earn 10% versus 8% for portfolio B, then you would cheerfully choose portfolio A even though it is 150% more volatile that Portfolio B. Volatility, as a measure of risk, is only meaningful in the context of uncertain returns. However, if you don’t know, with certainty, the future returns of Portfolio A or B, a condition that reflects the reality that investors face every day, then volatility as a measure of risk becomes very relevant. Perhaps Portfolio A is on the way to losing 10% instead of earning a positive return of 10%?

In bull markets it makes perfect sense that risk and volatility are undervalued. Why would anyone complain about too much upside volatility in their portfolio? It’s fun to imagine that phone call – “Ken. I’m calling you because my portfolio is making a lot more money than you said it would. You will be hearing from my attorney in the morning.” Hindsight is an amazing tool for diminishing the value of risk management of any kind in bull markets. Any strategy that reduces returns, or potentially reduces returns, has no value. Perhaps that’s why they coined the phrase, “you can’t eat risk-adjusted returns.” In bull markets, all that matters is the magnitude of the gains.

Professional investors have several tools to measure whether or not the amount of volatility in a portfolio is “worth it” considering the amount of portfolio return that is earned. Portfolio Alpha is a well known metric that measures the excess returns of a managed portfolio to a benchmark portfolio, and then divides the excess returns by the amount of beta of the portfolio (beta is the volatility of the portfolio compared to the volatility of the benchmark). A positive alpha means that the portfolio is earning more than you should expect for the amount of risk that you are taking. So, let’s go back to our first question. Portfolio A earns 10% with a negative alpha (very bad) and Portfolio B earns 8% with a positive alpha of 4.6 (very good). Which portfolio should you invest in? I already told you…Portfolio A. It made more money than portfolio B. Alpha only matters when you are trying to figure out what will happen in the future. If you get to make the decision with 20-20 hindsight (you never get this choice), then choose the highest return every time.