Financial Toolbox

portalloc

Optimal capital allocation

Syntax

• [RiskyRisk, RiskyReturn, RiskyWts, RiskyFraction, OverallRisk, 
  OverallReturn] = portalloc(PortRisk, PortReturn, PortWts, 
  RisklessRate, BorrowRate, RiskAversion)
  

Arguments

PortRisk	Standard deviation of each portfolio. A number of portfolios (NPORTS) by 1 vector.
PortReturn	Expected return of each portfolio. An NPORTS-by-1 vector.
PortWts	Weights allocated to each asset. An NPORTS by number of assets (NASSETS) matrix of weights allocated to each asset. Each row represents a different portfolio. Total of all weights in a portfolio is 1.
RisklessRate	Risk-free rate. A decimal number.
BorrowRate	(Optional) Borrowing rate. A decimal number. If borrowing is not desired, or not an option, set to NaN (default)
RiskAversion	(Optional) Coefficient of investor's degree of risk aversion. Higher numbers indicate greater risk aversion. Typical coefficients range between 2.0 and 4.0 (Default = 3).

Description

[RiskyRisk, RiskyReturn, RiskyWts, RiskyFraction, OverallRisk, OverallReturn] = portalloc(PortRisk, PortReturn, PortWts, RisklessRate, BorrowRate, RiskAversion) computes the optimal risky portfolio, and the optimal allocation of funds between the risky portfolio and the risk-free asset.

RiskyRisk is the standard deviation of the optimal risky portfolio.

RiskyReturn is the expected return of the optimal risky portfolio.

RiskyWts is a 1-by-NASSETS vector of weights allocated to the optimal risky portfolio. The total of all weights in the portfolio is 1.

RiskyFraction is the fraction of the complete portfolio allocated in the risky portfolio.

OverallRisk is the standard deviation of the optimal overall portfolio.

OverallReturn is the expected rate of return of the optimal overall portfolio.

Examples

Generate the efficient frontier from the asset data.

• ExpReturn = [0.1 0.2 0.15]; 
  
  ExpCovariance = [0.005   -0.010    0.004 
                  -0.010    0.040   -0.002 
                   0.004   -0.002    0.023];
  [PortRisk, PortReturn, PortWts] = portopt(ExpReturn,... 
  ExpCovariance);
  

Find the optimal risky portfolio and allocate capital. The risk free investment return is 8%, and the borrowing rate is 12%.

• RisklessRate  = 0.08;
  BorrowRate    = 0.12;
  RiskAversion  = 3;
  
  [RiskyRisk, RiskyReturn, RiskyWts, RiskyFraction, ... 
  OverallRisk, OverallReturn] = portalloc(PortRisk, PortReturn,... 
  PortWts, RisklessRate, BorrowRate, RiskAversion)
  
  RiskyRisk =
  
      0.1283
  
  RiskyReturn =
  
      0.1788
  
  RiskyWts =
  
      0.0265    0.6023    0.3712
  
  RiskyFraction =
  
      1.1898
  
  OverallRisk =
  
      0.1527
  OverallReturn =
  
      0.1899
  

See Also

frontcon, portrand, portstats

References

Bodie, Kane, and Marcus, Investments, Chapters 6 and 7.

pointfig

portcons