We calculate Treynor's performance measure which takes into account the systematic risk (or beta) and the average return when assessing the overall risk adjusted performance of a portfolio.
A double equal to Treynor's measure of the risk-adjusted performance of a portfolio.
The Treynor measure differs from the SharpesRatio measure in that the return per unit measure of `risk' in standardized by uses the beta of the portfolio rather than the standard deviation of the price.
The Beta of a Portfolio
The beta of a portfolio measures the sensitivity of a portfolios return
to some underlying market index (for example, the S&P500, FT100 etc). That is,
if the underlying index increase by x
percent then the Portfolio
increase by ax
percent then the beta of the portfolio
against this index is said to be a
. Care should be taken that the
time period used in measuring the return of the portfolio and market index are
the same. Moreover, there are good grounds for using the same the time period
of the same length as the time period over which the average return and risk free
interest rate are quoted.
Remark: An effective means by which to estimate the beta is by applying the least squares regression line from regression analysis.
Selection of a suitable Market Index to measure the Portfolio's Beta against
The market index used in order to measure the portfolios performance with respect to Treynor's measure such reflect the range of asset from which the portfolio can be constructed or is benchmarked against. For example, for a fund which can select investments form the S&P500 and is benchmarked against the S&P500, then S&P500 should be the market index used in the evaluation of the beta of the portfolio. If on the other hand the fund invests in Eastern European Stocks then a more natural benchmark could be Barrings European European Benchmark.
Applying Treynor's Measure
Suppose an US stock investment gives a return over a given year of 10 percent and the rate available from a risk free Treasury Bond over the same year is 6 percent. Then the reward for taking on the higher level of `risk' (as measured by the beta of the portfolio) of the stock investment over the risk free Treasury bond investment is 4 percent. Say the risk (i.e. standard deviation) of the stock over the year is 2 percent. Then the excess return of the stock over the Treasury per unit of risk (i.e. per 1 percent of standard deviation) is 2 percent. That is, the Sharpe's ratio here is 2 percent.
Application of Treynors Measure
The Treynor measure allows you to compare the performance of portfolios which invest within similar market sectors. It also help in differentiation of skill of a fund manager from the performance of the sector in which he often is obliged to invest it. Below we describe two instances when this can be particularly helpful:
PerformanceEvaluation Class | WebCab.Libraries.Finance.Portfolio Namespace