When analyzing mutual fund performance, it is essential to use risk metrics to assess the influence of risk on fund returns. Popular risk metrics in modern portfolio theory (MPT) include R-squared and beta, while standard deviation and upside-downside capture ratios are also widely used to measure correlation and volatility. The Dodge & Cox International Stock Fund (“DODFX”) is closely correlated to its benchmark, the Morgan Stanley Capital International All Country World Index Ex-U.S, with slightly higher volatility.
Standard deviation is a measure of statistical variance in a data set. These calculations are frequently applied to the data of historical mutual fund returns to analyze the volatility of the portfolio's returns. High volatility investments are generally considered riskier. DODFX had three-, five- and 10-year standard deviation in returns of 15.6, 17.04 and 21.15 as of June 2016. The corresponding benchmark index's standard deviation values were 13.25, 15.54 and 19.15. DODFX was slightly more volatile than the benchmark over each period, so investors should expect higher returns to justify the extra risk assumed.
Beta is a statistical measurement of the correlation between a fund's returns and the returns of the broader market. Like standard deviation, beta provides information regarding volatility, but beta is specifically calculated relative to a benchmark. It is said to measure systematic risk, defined as risk inherent to the total market or market segment. Using the MSCI All Country World Index Ex-U.S. as the reference index, DODFX had beta values of 1.14, 1.06 and 1.08 over the three-, five- and 10-year periods ending March 2016. Instances of perfect correlation would have betas of exactly 1, with higher volatility and positive correlation sending this value higher. The beta values for DODFX indicate strong correlation and slightly higher volatility relative to the benchmark.
R-squared is a statistical measurement of correlation, and when applied to mutual fund historical returns, it shows what portion of the fund's gains or losses are attributable to wider market movements. Expressed as a percentage, an R-squared of 100% is perfect correlation and indicates a fund's returns are wholly the product of market fluctuations. High R-squared investments increase portfolio's exposure to market risk. DODFX has R-squared values of 93.56, 94.13 and 95.64% over the three-, five- and 10-year periods ending March 2016, relative to the MSCI All Country World Index Ex-U.S. These are exceptionally high values indicating sustained high correlation to the category index.
Upside and downside capture ratios measure the extent to which a fund's monthly returns reflect those of the underlying market, on average. The upside capture ratio only measures data for months in which returns were positive, while the downside ratio only concerns months in which losses were sustained. DODFX's upside capture ratios over the three-, five- and 10-year periods ending March 2016 were 119.2, 115.25 and 110.11%, so the fund has historically outpaced its benchmark through good market conditions. DODFX had downside capture ratios of 113.4, 109.95 and 108.33% over those periods, so the fund also sustained more extreme losses than its benchmark when the market tumbled.
Alpha and Sharpe Ratio
Alpha and the Sharpe ratio are two metrics that adjust fund returns based on the above risk metrics. Alpha is a measurement of returns over the benchmark, and is often used to represent the value added by a strategy or manager. Beta is one of the inputs used in the calculation of alpha, as it helps isolate expected returns based on benchmark performance. DODFX had alpha values of 1.18, 1.19 and 0.7 over the three-, five- and 10-year periods ending March 2016, indicating management modestly outperformed expected values based on benchmark returns.
The Sharpe ratio is calculated by dividing historical returns by standard deviation, thus adjusting fund performance for volatility risk. A fund's Sharpe ratios exceeds that of the benchmark if value is added by the strategy. DODFX had Sharpe ratios of 0.16, 0.16 and 0.17 over the three-, five- and 10-year periods, while the benchmark's corresponding values were 0.08, 0.09 and 0.14, supporting the view that fund management has driven modestly superior returns to those of the benchmark.