Using Risk-Adjusted Return

This example shows how to use the risk-adjusted return to shift the risk of a portfolio to match the risk of a market portfolio or 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 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)

MeanFund = 
0.0038

MeanMarket = mean(Market)

MeanMarket = 
0.0030

[MM, aMM] = portalpha(Fund, Market, Cash, 'MM')

MM = 
0.0022

aMM = 
0.0052

[GH1, aGH1] = portalpha(Fund, Market, Cash, 'gh1')

GH1 = 
0.0013

aGH1 = 
0.0025

[GH2, aGH2] = portalpha(Fund, Market, Cash, 'gh2')

GH2 = 
0.0022

aGH2 = 
0.0052

[SML, aSML] = portalpha(Fund, Market, Cash, 'sml')

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.