Risk Statistics and RiskAdjusted StatisticsMany investors approach manager selection and analysis with preconceived statistical prejudices based on a misunderstanding of statistics. In many cases, it is because they've been led to believe that a certain statistic measures something that it does not. Others encounter difficulties trying to use a predefined toolkit of investment statistics because they've been led to believe that those are the right statistics to choose. It is important to remember, however, that investors have different notions of risk. To some, risk is the uncertainty of achieving an expected return. To others, it is not achieving a minimal acceptable return (MAR). Still others define risk as flatout losing money. To illustrate this point, let's look at how many investors use standard deviation to help them identify "strong" investments. Standard DeviationInvestors sometimes begin a quantitative screening by stating that they want a fund with a "low risk." Because of the historical ties between risk and standard deviation in the world of traditional investments, they equate high standard deviation with high risk, and then use standard deviation as a comparative statistic. However, in truth, standard deviation is merely a statistic that measures predictability. A high standard deviation means that the fund is volatile, not that the fund is risky or will lose money, while a low standard deviation means a fund is generally consistent in producing similar returns. A fund can have extremely low standard deviation and lose money consistently, or have high standard deviation and never experience a losing period. One of the main differences between traditional return analysis and absolute return analysis is accepting the fact that volatility is good, provided it is on the upside. Indeed, most investors should be less concerned with upside volatility, and consider downside deviation as a better measure of a fund's ability to achieve its return goal. For this reason, investors should acquaint themselves with downside deviation. Downside deviation introduces the concept of minimum acceptable return (MAR) as a risk factor. If a retirement plan has annual liabilities of 8%, the plan's real risk is not earning 8%  not whether it has a high or low standard deviation. So, with standard deviation out of the equation, what statistics can we use to compare funds? While fund returns may seem useful, they do not consider the investment's risk. Therefore, investors should always use riskadjusted statistics such as the Sharpe, Sortino, Sterling or Calmar ratios. Sharpe RatioThe Sharpe ratio is the bestknown riskadjusted statistic. You calculate an investment's Sharpe ratio by taking the average period return, subtracting the riskfree rate, and dividing it by the standard deviation for the period. This calculation generates a number we can use to compare investments. Note that for meaningful comparisons, all comparative investment statistics must be calculated over the same time period. Sortino RatioSince upside volatility will decrease the Sharpe ratio of some investments, the Sortino ratio can be used as an alternative. The Sortino ratio is similar to the Sharpe ratio, however it uses downside deviation instead of standard deviation in the denominator of the formula, as well as substituting a minimum acceptable return for the risk free rate. In other words, the Sortino ratio equals the return minus the MAR, divided by the downside deviation. The Calmar and Sterling ratios provide additional comparative information for a riskadjusted assessment of drawdown analysis. Calmar RatioThe Calmar ratio is the annualized return for the last 3 years divided by the maximum drawdown during these years. Sterling RatioThe Sterling ratio is the annualized return for the last 3 years divided by the average of the maximum drawdown (in absolute terms) in each of the preceding 3 years, less an arbitrary 10%. An extra 10% is subtracted from the drawdown as one assumes that all maximum drawdowns will be exceeded. Benchmark RatiosBenchmark ratios are also useful in evaluating investments. These ratios provide information in a single number about a fund's performance relative to a benchmark. Obviously, the selection of an appropriate benchmark is critical. Active PremiumThe simplest benchmark ratio is the "active premium", which takes the fund's annualized return, and subtracts the benchmark's annualized return to yield the fund's gain/loss that is over/under the benchmark (i.e., the excess return). Positive active premium is good, while negative active premium is generally bad. Up and down capture ratios are also helpful when evaluating investments. Up Capture RatioThe up capture ratio is a measure of a fund's cumulative return when the benchmark was up, divided by the benchmark's cumulative return when the benchmark was up. The greater the value, the better. Down Capture RatioThe down capture ratio is a measure of a fund's cumulative return when the benchmark was down, divided by the benchmark's cumulative return when the benchmark was down. The smaller the value, the better. Up and Down Number RatiosUp and down number values measure the percentage of time that an investment moves in the same direction as the markets. For example, approximately 92% of the time the fund moves up and down with the benchmark. Unfortunately, this statistic doesn't yield much information about the fund's relative outperformance, so we combine these numbers with the proficiency ratios (up/down market percentage ratios) to glean more information about the fund. Up Market Percentage RatioThe up market percentage ratio is a measure of the number of periods that an investment outperformed the benchmark when the benchmark was up, divided by the number of periods that the benchmark was up. The larger the ratio, the better. For example, if the fund outperformed the index 54.5% of the time when the index was up. Down Market Percentage RatioThe down market percentage ratio is a measure of the number of periods that an investment outperformed the benchmark when the benchmark was down, divided by the number of periods the benchmark was down. The larger the ratio, the better. For example, if the fund outperforms the benchmark only 30% of the time when the benchmark was down. This would not be considered strong performance for a hedge fund manager.

