# Documentation

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## Using Risk-Adjusted Return

### Introduction

Risk-adjusted return either shifts the risk (which is the standard deviation of returns) of a portfolio to match the risk of a market portfolio or shifts the risk of a market portfolio to match the risk of a fund. According to the Capital Asset Pricing Model (CAPM), the market portfolio and a riskless asset are points on a Security Market Line (SML). The return of the resultant shifted portfolio, levered or unlevered, to match the risk of the market portfolio, is the risk-adjusted return. The SML provides another measure of risk-adjusted return, since the difference in return between the fund and the SML, return at the same level of risk.

Given our example data with a fund, a market, and a cash series, you can calculate the risk-adjusted return and compare it with the fund and market's mean returns

```load FundMarketCash Returns = tick2ret(TestData); Fund = Returns(:,1); Market = Returns(:,2); Cash = Returns(:,3); MeanFund = mean(Fund) MeanMarket = mean(Market) [MM, aMM] = portalpha(Fund, Market, Cash, 'MM') [GH1, aGH1] = portalpha(Fund, Market, Cash, 'gh1') [GH2, aGH2] = portalpha(Fund, Market, Cash, 'gh2') [SML, aSML] = portalpha(Fund, Market, Cash, 'sml') ```

which gives the following results:

```MeanFund = 0.0038 MeanMarket = 0.0030 MM = 0.0022 aMM = 0.0052 GH1 = 0.0013 aGH1 = 0.0025 GH2 = 0.0022 aGH2 = 0.0052 SML = 0.0013 aSML = 0.0025```

Since the fund's risk is much less than the market's risk, the risk-adjusted return of the fund is much higher than both the nominal fund and market returns.