Last night, my hometown team, the Los Angeles Dodgers, was defeated by the St. Louis Cardinals in the National League Championship series. The Cardinals will go on to the World Series for a chance at what could be their 20th world championship… while the Dodgers get to start their winter vacations.
After the game, legendary Dodgers broadcaster Vin Scully was quoted as saying something to the effect of, “Losing feels worse than winning feels good.”
When I heard this quote, it struck me that this applies to portfolio returns as well. Which is one of the points of one of the readings at the Expert Level of the CIPM curriculum: Reading 18 – How Sharp is the Sharpe Ratio.
One of the ideas that modern portfolio theory emphasizes is that we expect returns to fall in a symmetrical, normal distribution. In a way, the idea of efficient portfolios at least implies that this symmetry is desirable. One of the ideas of post modern portfolio theory, however, is that investors do not want symmetry in returns… investors definitely have a preference for the return history to have asymmetry to it.
Certain return statistics are referred to as “moments” in a distribution (history) of returns. These moments describe the shape of that history. In a return distribution:
- mean return is the first moment, describing the center of the distribution
- variance (or, alternatively, standard deviation) is the second moment, describing the range of the distribution
- skewness is the third moment, describing the tendency to have returns in the tails of the distribution
- kurtosis is the fourth moment, describing the flatness or peakedness of the distribution
Investors do not prefer symmetry. Rather, investors prefer:
- high mean returns
- low standard deviation (or variance)
- positive skewness (i.e., more returns in the right tail than a normal distribution would typically have)
- low kurtosis (a flatter distribution, which means more extreme returns (again, preferably on the right)
This reading makes the point that investors typically feel losses more painfully than they enjoy gains. Some of the risk statistics in this reading are designed specifically to focus on the number of extreme returns (painful losses or extreme wins).
The Adjusted Sharpe Ratio adjusts for skewness and kurtosis by using a penalty factor for negative skewness and excess kurtosis.
Downside deviation and downside potential focus on losing returns, while upside risk and upside potential focus on winning returns.
Omega ratio is upside potential divided by downside potential.
Conditional Value at Risk considers the size and shape of the tails of a return distribution, while Modified Value at Risk adjusts standard VaR for kurtosis and skewness. The Conditional Sharpe Ratio and Modified Sharpe Ratio are, then, modifications of the standard return to VaR formula that substitute either Conditional VaR or Modified VaR, respectively – in an attempt to focus on extreme losing returns.
This is just a sampling from your reading. Your focus for this reading is not the mathematics of these calculations, per se; rather, you should know the concepts behind why we want to measure extreme returns.
To summarize some differences between modern portfolio theory (MPT) thinking and post modern portfolio theory (post MPT) thinking:
- assumes normal distribution of returns
- tracking error (the standard deviation of excess returns) measures active risk
- returns above the mean and below the mean observation (of either absolute or relative return) are treated the same
- recognizes that investors prefer upside risk rather than downside risk
- hedge funds (and other post MPT portfolios) are designed to be asymmetric with (emphasis on) variability on the upside but not on the downside