AMSDP: Additive-Mean-Standard-Deviation Portfolio Utility Function

Description

Compute the utility function x %*% mp - gamma^theta * (t(x) %*% Cov %*% x)^(0.5 * theta) / theta for a portfolio x.

Usage

AMSDP(x, mp, Cov, gamma = 1, theta = 1)

Value

A scalar indicating the utility level.

Arguments

x: a numeric n-vector representing a portfolio.
mp: a numeric n-vector representing the mean payoff of each of the n assets.
Cov: the n-by-n covariance matrix of the payoff vectors of n assets.
gamma: a non-negative scalar representing the risk aversion coefficient with a default value of 1.
theta: a non-negative scalar with a default value of 1.

References

Danthine, J. P., Donaldson, J. (2005, ISBN: 9780123693808) Intermediate Financial Theory. Elsevier Academic Press.

Nakamura, Yutaka (2015) Mean-Variance Utility. Journal of Economic Theory, 160: 536-556.

Sharpe, William F (2008, ISBN: 9780691138503) Investors and Markets: Portfolio Choices, Asset Prices, and Investment Advice. Princeton University Press.

Xu Gao (2018, ISBN: 9787300258232) Twenty-five Lectures on Financial Economics. Beijing: China Renmin University Press. (In Chinese)

Examples

Run this code

# \donttest{
UAP <- matrix(c(
  0, 1, 1,
  0, 2, 1,
  1, 1, 1,
  1, 2, 1,
  2, 0, 1
), nrow = 5, byrow = TRUE)

portfolio <- c(1.977, 1.183, 3.820)

AMSDP(portfolio, colMeans(UAP),
  cov.wt(UAP, method = "ML")$cov,
  gamma = 1, theta = 1
)

AMSD(UAP %*% portfolio, gamma = 1, theta = 1)
# }