CAPM.beta {PerformanceAnalytics} | R Documentation |

CAPM Beta is the beta of an asset to the variance and covariance of an initial portfolio. Used to determine diversification potential.

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

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)

`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 |

*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`

can 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.

systematic beta of an asset to the index, perhaps conditioned on positive or negative returns.

Peter Carl

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.

`BetaCoVariance`

`CAPM.alpha`

`CAPM.utils`

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 0.9.9-5 Index]