portalloc (Financial Toolbox)

Optimal capital allocation.

Syntax

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

Arguments


`PortRisk`	Variance of each portfolio. A number of portfolios (`NPORTS`)-by-`1` vector.
`PortReturn`	Expected return of each portfolio. A number of portfolios (`NPORTS`)-by-`1` vector.
`PortWts`	Weights allocated to each asset. A number of portfolios (`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`	Borrowing rate. A decimal number. If borrowing is not desired, or not an option, set to `NaN` (default)
`BorrowRate`
`RiskAversion`	Coefficient of investor's degree of risk aversion. Higher numbers indicate greater risk aversion. Typical coefficients range between `2.0` and `4.0` (`3` = default).

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 variance of the optimal risky portfolio.

RiskyReturn is the expected return of the optimal risky portfolio.

RiskyWts is a 1-by-number of assets (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 variance of the optimal overall portfolio.

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

Example

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