PerformanceAnalytics (version 0.9.5)

CAPM.beta: calculate CAPM beta

Description

CAPM Beta 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 linear intercept model to achieve the same results as the symbolic model used by BetaCoVariance

Usage

CAPM.beta(Ra, Rb, rf = 0, digits = 4)

Arguments

Ra

a vector, matrix, data frame, timeSeries or zoo object of asset returns

Rb

return vector of the benchmark asset

rf

risk free rate, in same period as your returns

digits

number of digits to round results to

Value

• systematic beta of an asset to the index

Details

$$\beta_{a,b}=\frac{CoV_{a,b}}{\sigma_{a}}=\frac{\sum((R_{a}-\bar{R_{a}})(R_{b}-\bar{R_{b}}))}{\sum(R_{a}-\bar{R_{a}})^{2}}$$

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

References

Sharpe, W.F. Capital Asset Prices: A theory of market equilibrium under conditions of risk. Journal of finance, vol 19, 1964, 425-442. Ruppert, David. Statistics and Finance, an Introduction. Springer. 2004.

See Also

BetaCoVariance CAPM.alpha CAPM.utils

Examples

# First we load the data
data(edhec)
edhec.length = dim(edhec)[1]
start = rownames(edhec[1,])
start
end = rownames(edhec[edhec.length,])
edhec.zoo = zoo(edhec, order.by = rownames(edhec))
rf.zoo = download.RiskFree(start = start, end = end)
sp500.zoo = download.SP500PriceReturns(start = "1996-12-31", end = end)

# Now we have to align it as "monthly" data
time(edhec.zoo) = as.yearmon(time(edhec.zoo))
time(sp500.zoo) = as.yearmon(time(sp500.zoo))
time(rf.zoo) = as.yearmon(time(rf.zoo))
data.zoo = merge(edhec.zoo[,9,drop=FALSE],sp500.zoo)
time(data.zoo) = as.Date(time(data.zoo),format="%b %Y")
time(rf.zoo) = as.Date(time(rf.zoo),format="%b %Y")

CAPM.beta(data.zoo[, 1, drop=FALSE], data.zoo[, 2, drop=FALSE], rf = rf.zoo)