returns: Computing expected returns and their covariance matrix In RcmdrPlugin.RiskDemo: R Commander Plug-in for Risk Demonstration

Description

Computing expected returns and their covariance matrix when the returns are lognormal.

Usage

 `1` ```returns(volvec, indexvol, beta) ```

Arguments

 `volvec` vector of volatilities `indexvol` volatility of the portfolio index `beta` vector of betas

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.

Value

 `mean` vector of expected returns `cov` covariance matrix of returns

Author(s)

Arto Luoma <arto.luoma@wippies.com>

References

Bodie, Kane, and Marcus (2014) Investments, 10th Global Edition, McGraw-Hill Education, (see Section 8.2 The Single-Index Model).

Examples

 `1` ```returns(volvec=c(0.1,0.2,0.3),indexvol=0.2, beta=c(0.5,-0.1,1.1)) ```

Example output

```Loading required package: rgl
This is demography 1.22

Warning messages:
1: In rgl.init(initValue, onlyNULL) : RGL: unable to open X11 display
2: 'rgl_init' failed, running with rgl.useNULL = TRUE
call: fun(...)
4: no DISPLAY variable so Tk is not available
\$mean
[1] 0.005012521 0.020201340 0.046027860

\$cov
[,1]         [,2]         [,3]
[1,]  0.010151173 -0.002048581  0.023384248
[2,] -0.002048581  0.042476293 -0.004685185
[3,]  0.023384248 -0.004685185  0.103043079
```

RcmdrPlugin.RiskDemo documentation built on April 6, 2021, 5:06 p.m.