BetaCoVariance {PerformanceAnalytics} | R Documentation

## systematic beta of an asset to an initial portfolio

### Description

Beta covariance is the beta of an asset to the variance and covariance of an initial portfolio. Used to determine diversification potential. also called "systematic beta" by several papers.

This function uses a symbolic representation to achieve the same result as the linear intercept model used by `CAPM.beta`

### Usage

    BetaCoVariance(Ra, Ri, na.rm = FALSE)

### Arguments

`Ra` | return vector of asset being considered for addition to portfolio
`Ri` | return vector of initial portfolio
`na.rm` | TRUE/FALSE Remove NA's from the returns?

### Details

Systematic Beta BCoV(a,b)

BetaCoV=cov(a,b)/var(b)

Ruppert(2004) reports that this equation will give the estimated slope of the linear regression of Raon Rb and that this slope can be used to determine the risk premium or excess expected return (see Ruppert Eq. 7.9 and 7.10, p. 230-231)

### Value

systematic beta of the asset to the benchmark

### Note

### Author(s)

Brian G. Peterson

### References

Favre, L. and Renaldo, A.. How to Price Hedge Funds: From Two- to Four-Moment CAPM. October 2003. UBS and Edhec Business School. Equation [5] p 10 Ruppert, David. Statistics and Finance, an Introduction. Springer. 2004.

### See Also

`CAPM.beta`

### Examples

[Package PerformanceAnalytics version 0.9.5 Index]