portalloc (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).

`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