## Measures of Risk

Several alternatives to the traditional measures of portfolio risk are commonly used when analyzing hedge funds.

Standard Deviation - Standard deviation is a measure of how dispersed the investment’s returns are from its arithmetic mean. It is derived by calculating the square root of the difference of the returns of the investment from its arithmetic mean. Volatility has historical precedence as one of the most commonly used risk measures.

Downside Deviation - It is the same as volatility, except downside deviation only measures the volatility of the investment returns that fall below the investor’s defined minimum acceptable return. For example, if the minimum acceptable return is 5%, the downside deviation would only measure the volatility of the returns falling below 5%. Investors prefer upside over downside volatility.

Drawdown - A drawdown occurs when an investment’s price falls below its last peak (high-water mark). Drawdown measures the investment’s cumulative drop in price from its previous high-water mark as a percentage of the peak price. Investors look at various statistics related to the measure of time regarding a drawdown. How long did it take to recover? (The period between the trough and the recapturing peak is called the recovery.) What was the average length of time a drawdown occurred? (This is called the length of the drawdown.) What is the worst drawdown? (This is the maximum drawdown and represents the greatest peak to trough decline over the life of the investment.)

Skewness - A return distribution that is not symmetrical is called skewed. The skewness for a normal distribution is zero.

Positively Skewed Distribution - characterized by many small losses and a few extreme gains and has a long tail on its right side. Relative to the mean return, positive skewness amounts to limited, though frequent, downside compared to a somewhat unlimited, but less frequent upside.

Negatively Skewed Distribution - characterized by many small gains and a few extreme losses and has a long tail on its left side. Relative to the mean return, negative skewness amounts to a limited, though frequent, upside compared with a somewhat unlimited, but less frequent downside.

 Positively Skewed Nagatively Skewed

Both return distributions have the same mean return and volatility. The one on the left is positively skewed. The one on the right is negatively skewed.

Kurtosis - Kurtosis characterizes the relative ‘peakedness’ or flatness of an investment’s return distribution compared with the normal distribution. The higher the kurtosis, the more peaked the return distribution is; the lower the kurtosis, the more rounded the return distribution is. A normal distribution has a kurtosis of 3.

Higher kurtosis indicates a return distribution with a more acute peak around the mean (higher probability than a normal distribution of more returns clustered around the mean) and a greater chance of extremely large deviations from the expected return (fatter tails, more big surprises). Investors view a greater percentage of extremely large deviations from the expected return as an increase in risk.

Lower kurtosis has a smaller peak (lower probability of returns around the mean) and a lower probability than a normal distribution of extreme returns.

 Lower Kurtosis:Lower peak, thinner tails Higher Kurtosis:Higher peak, fatter tails

Value-at-Risk - Unlike other risk metrics such as volatility that measure historical risk, VaR quantifies market risk while it is being taken. It measures the odds of losing money but does not indicate certainty.

Although we know a portfolio's current market value, we have no way of knowing what the portfolio can be expected to lose next month. VaR summarizes the amount of investment such that there is a given percentage probability of the portfolio losing less than that over the next trading period. VaR is typically stated using 90%, 95% and 99% confidence levels. For example, if a portfolio has a one year 90% VaR of \$10M, with a probability of 90%, the value of the portfolio will decrease by \$10M or less during the trading period, or in other words the investor can expect that with a probability of 10% (100% - 90%) the value of the portfolio will decrease by more than \$10M. The investor can expect the value of the portfolio will decrease by \$10M or less on 9 out of 10 trading periods, or by more than \$10M on 1 out of every 10 trading periods.