Description Usage Arguments Details Author(s) References See Also Examples

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.

1 2 3 4 5 6 7 | ```
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 |

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.

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`

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