One way to produce an easily understood marriage of risk and return for funds and portfolios is to adjust the return for risk so that the return reported for all funds and portfolios assumes risk equal to that of a market benchmark. Funds and portfolios with volatility above the market benchmark will have their returns proportionally lowered, while funds and portfolios that are less risky (have lower volatility than their benchmark) will have their returns adjusted proportionally upward. The three-year risk-adjusted return uses that annual rate of return and the three-year standard deviation to measure volatility.
Standard deviation is a measure of price volatility (or return volatility) that helps investors better understand their market risk. Standard deviation is a measurement of the variation of a set of data points from its mean. For instance, an asset holding with returns consistently near the average return will have a low standard deviation, whereas an asset holding with returns consistently far from the average return (both above and below) has a high standard deviation. When calculating risk-adjusted returns, the standard deviation of a holding can be compared against that of the market. The return of a holding with a high standard deviation is adjusted downward to account for its above-average risk while the return of a holding with a low standard deviation is adjusted upward to account for its below-average risk.
The market benchmark used for return and risk is the Vanguard Total Stock Market Index Fund (VTSMX). The margin rate is being used as the risk-free rate of borrowing to leverage the fund or portfolio to match the risk of the market portfolio.
If 3-year returnasset > 3-year returnbenchmark:
Margin rate + (3-year standard deviationbenchmark/3-year standard deviationasset) × (3-year returnbenchmark/3-year returnasset)
If 3-year returnasset < 3-year returnbenchmark:
Margin rate + (3-year standard deviationasset/3-year standard deviationbenchmark) × (3-year returnbenchmark/3-year returnasset)