returns: Computing expected returns and their covariance matrix
Description
Computing expected returns and their covariance matrix when the returns are lognormal.
Usage
returns(volvec, indexvol, beta)
Arguments
volvec
vector of volatilities
indexvol
volatility of the portfolio index
beta
vector of betas
Value
mean
vector of expected returns
cov
covariance matrix of returns
Details
The arguments are given in decimals. The single index model is used to compute the covariance matrix of a multivariate normal distribution. The mean vector is assumed to be zero. The properties of the log-normal distribution are then used to compute the mean vector and covariance matrix of the corresponding multivariate log-normal distribution.
References
Bodie, Kane, and Marcus (2014) Investments, 10th Global Edition, McGraw-Hill Education, (see Section 8.2 The Single-Index Model).