Working with a Riskless Asset

You can specify a riskless asset with the mean and covariance of asset returns in the AssetMean and AssetCovar properties such that the riskless asset has variance of 0 and is completely uncorrelated with all other assets. In this case, the Portfolio object uses a separate RiskFreeRate property that stores the rate of return of a riskless asset. Thus, you can separate your universe into a riskless asset and a collection of risky assets. For example, assume that your riskless asset has a return in the scalar variable r0, then the property for the RiskFreeRate is set using the Portfolio object:

r0 = 0.01/12;
m = [ 0.05; 0.1; 0.12; 0.18 ];
C = [ 0.0064 0.00408 0.00192 0; 
      0.00408 0.0289 0.0204 0.0119;
      0.00192 0.0204 0.0576 0.0336;
      0 0.0119 0.0336 0.1225 ];

p = Portfolio('RiskFreeRate', r0, 'AssetMean', m, 'AssetCovar', C);
disp(p.RiskFreeRate)

 8.3333e-004

Note

If your problem has a budget constraint such that your portfolio weights must sum to 1, then the riskless asset is irrelevant.