TreynorRatio {PerformanceAnalytics} | R Documentation

## calculate Treynor Ratio of excess return over CAPM beta

### Description

The Treynor ratio is similar to the Sharpe Ratio, except it uses beta as the volatility measure (to divide the investment's excess return over the beta).

### Usage

    TreynorRatio(Ra, Rb, rf = 0, scale = 12, ...)

### 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
`scale` | number of periods in a year (daily scale = 252, monthly scale = 12, quarterly scale = 4)
`...` | any other passthru parameters

### Details

Equation:

frac{overline{(R_{a}-R_{f})}}{β_{a,b}}

### Value

Treynor ratio

### Author(s)

Peter Carl

### References

### See Also

`SharpeRatio` `SortinoRatio` `CAPM.beta`

### 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")

    TreynorRatio(data.zoo[,1], data.zoo[,2], rf=rf.zoo)

[Package PerformanceAnalytics version 0.9.5 Index]