Measures how widely a set of values varies from the mean. Standard deviation is a good historical measure of the variability of returns earned by an investment portfolio. In performance measurement, it is generally assumed that a larger degree of dispersion implies that greater risk was taken to achieve the return.
The Information Ratio is a measure of risk-adjusted return. The average excess return (over an appropriate benchmark or risk free rate) is divided by the standard deviation of these excess returns. The higher the measure, the higher the risk adjusted return. This ratio should not be confused with the Information Coefficient, which is the correlation of realized returns with forecasted returns.
Tracking Error measures the extent to which a portfolio tracks its benchmark. It is measured by dividing the squared variations around the average excess returns (of the portfolio over benchmark) by the number of observations. In this sense it is like an average error. The higher the tracking error, the higher the variability of the portfolio returns around the benchmark. The tracking error of an index portfolio should be lower than that of an active portfolio. The tracking error will always be greater than zero if the portfolio is anything other than a replication of the benchmark.
Variance is a measure of the volatility of return and is computed as an average squared deviation of return from the mean value of the return:
A measure of a portfolio's return in excess of the market return, after both are adjusted for risk. It is a mathematical estimate of the amount of return expected from a portfolio above and beyond the market return at any point in time. It is distinct from the amount of the return associated with high or low volatility, as measured by Beta. For example, an alpha of 1.25 indicates that a stock is projected to rise 1.25% in price in a year over the return of the market, or the return when the market return is zero. An investment whose price is low relative to its alpha is undervalued and considered a good selection. A security is under-priced if its alpha value is positive. A security is overpriced if its alpha value is negative. Investment managers who try to ‘beat the market’ hope to construct portfolios with positive alphas. Those who do not try to beat the market construct portfolios with zero alphas. Russell/Mellon and academic research has shown that alphas computed over historical returns are usually not predictive of future alphas.
A measure of the sensitivity of a portfolio's rate of return relative to changes in the market return. It is the coefficient measuring a stock’s relative volatility. The beta is the covariation of a stock in relation to the rest of the stock market. The broad market index, the Russell 3000® Index, has a beta coefficient with itself of 1. Any stock with lower beta can be expected to rise and fall more slowly that the market (these low beta stocks may also be referred to as defensive stocks). If a portfolio has a beta of 1.10, the portfolio’s return would be expected to rise 10% more than the market in an up-market and 10% worse in a down market. A conservative investor whose main concern is preservation of capital should focus on stocks with low betas, whereas one willing to take high risks in an effort to earn high rewards, should look for high-beta stocks. A good market timing manager will have high beta in an up market environment and low beta in a down market environment.
Correlation is a measure of association between market excess return and portfolio excess return. Correlation coefficients always lie between –1.0 and +1.0, inclusive. The former value represents the perfect negative correlation, and the latter, perfect positive correlation. Most cases lie somewhere in-between.
R-squared is a measure of how reliable, predictable, and valid the alpha and beta are.
R-squared indicates the proportion of a security’s total variance that is market-related or is explained by variations in the market. For example, if a portfolio has an R-squared of 0.8, that indicates that 80% of the portfolio return would be the result of market action (i.e., your portfolio return went up because the market went up, or your portfolio return went down because the market dropped). R-squared has a range limit of 0.00 to 1.0. An R-squared of 1.0 indicates perfect diversification and zero non-market risk. An R-squared of 0.0 indicates no diversification with a very high but unspecified non-market risk.
Standard error is a measure of the average error in predicting a portfolio’s return that cannot be explained by market fluctuations. A low standard error indicates that portfolio returns are closely correlated with market returns (as does R-squared).
The Sharpe Ratio measures the efficiency, or excess return per unit of volatility, of a manager's returns. It is the most widely used risk-adjusted performance measure. The Sharpe Ratio evaluates managers' performance on a volatility-adjusted basis. It is a portfolio's annualized return less the annualized risk-free rate (i.e., excess return), divided by the portfolio’s annualized standard deviation. Standard deviation is a commonly accepted measure of volatility. For a given return, the lower the standard deviation or volatility of returns, the higher the Sharpe Ratio. The higher the Sharpe Ratio, the more desirable the fund. A Sharpe Ratio greater than 1 indicates a good level of excess return relative to the volatility of the performance. A fund with a Sharpe Ratio approaching or less than 0 shows a poor rate of return per unit of volatility.
Like Sharpe’s, Sortino’s measure gives excess return per unit of risk, but uses downside semi-variance instead of total risk, the standard deviation of the portfolio. (See Chapter 9 of Harry M. Markowitz Portfolio Selection (Yale U. Press, New Haven, CT) 1959.) Where returns of a portfolio are not normally distributed, a better measure than standard deviation for measuring an investment’s risk is its downside semi-variance or downside semi-standard deviation. It is better because it takes into account only the downside size and frequency of returns and hence is a better idea of the return on the portfolio relative to undesirable downside variation. It measures the reward to negative volatility trade-off. Using Sharpe measures to compare and select among investment alternatives can be difficult because the measure of risk, portfolio standard deviation, penalizes the portfolio for positive upside returns as much as the undesirable downside returns.