CAPM.beta {PerformanceAnalytics} | R Documentation

## calculate single factor model (CAPM) beta

### Description

The single factor model or CAPM Beta is the beta of an asset to the variance and covariance of an initial portfolio. Used to determine diversification potential.

### Usage

    CAPM.beta(Ra, Rb, Rf = 0)

    CAPM.beta.bull(Ra, Rb, Rf = 0)

    CAPM.beta.bear(Ra, Rb, Rf = 0)

    TimingRatio(Ra, Rb, Rf = 0)

### Arguments

`Ra` | an xts, 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

### Details

This function uses a linear intercept model to achieve the same results as the symbolic model used by `BetaCoVariance`

beta = cov(Ra,Rb)/var(R)

Ruppert(2004) reports that this equation will give the estimated slope of the linear regression of Ra on Rb 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).

Two other functions apply the same notion of best fit to positive and negative market returns, separately. The `CAPM.beta.bull` is a regression for only positive market returns, which can be used to understand the behavior of the asset or portfolio in positive or 'bull' markets. Alternatively, `CAPM.beta.bear` provides the calculation on negative market returns.

The `TimingRatio` may help assess whether the manager is a good timer of asset allocation decisions. The ratio, which is calculated as

Timing Ratio = beta+/beta-

is best when greater than one in a rising market and less than one in a falling market.

While the classical CAPM has been almost completely discredited by the literature, it is an example of a simple single factor model, comparing an asset to any arbitrary benchmark.

### Author(s)

Peter Carl

### 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.
Bacon, Carl. Practical portfolio performance measurement and attribution. Wiley. 2004.

### See Also

`BetaCoVariance` `CAPM.alpha` `CAPM.utils`

### Examples

    data(managers)
        CAPM.alpha(managers[,1,drop=FALSE],
    			managers[,8,drop=FALSE],
    			Rf=.035/12)
        CAPM.alpha(managers[,1,drop=FALSE],
    			managers[,8,drop=FALSE],
    			Rf = managers[,10,drop=FALSE])
        CAPM.alpha(managers[,1:6],
    			managers[,8,drop=FALSE],
    			Rf=.035/12)
        CAPM.alpha(managers[,1:6],
    			managers[,8,drop=FALSE],
    			Rf = managers[,10,drop=FALSE])
        CAPM.alpha(managers[,1:6],
    			managers[,8:7,drop=FALSE],
    			Rf=.035/12)
        CAPM.alpha(managers[,1:6],
    			managers[,8:7,drop=FALSE],
    			Rf = managers[,10,drop=FALSE])
        CAPM.beta(managers[, "HAM2", drop=FALSE],
    			managers[, "SP500 TR", drop=FALSE],
    			Rf = managers[, "US 3m TR", drop=FALSE])
        CAPM.beta.bull(managers[, "HAM2", drop=FALSE],
    			managers[, "SP500 TR", drop=FALSE],
    			Rf = managers[, "US 3m TR", drop=FALSE])
        CAPM.beta.bear(managers[, "HAM2", drop=FALSE],
    			managers[, "SP500 TR", drop=FALSE],
    			Rf = managers[, "US 3m TR", drop=FALSE])
        TimingRatio(managers[, "HAM2", drop=FALSE],
    			managers[, "SP500 TR", drop=FALSE],
    			Rf = managers[, "US 3m TR", drop=FALSE])
        chart.Regression(managers[, "HAM2", drop=FALSE],
    			managers[, "SP500 TR", drop=FALSE],
    			Rf = managers[, "US 3m TR", drop=FALSE],
    			fit="conditional",
    			main="Conditional Beta")

[Package PerformanceAnalytics version 1.5.3 Index]