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Treynor Ratio
Treynor ratio evaluates the performance of a portfolio based on the systematic risk of a fund. Treynor ratio is based on the premise that unsystematic or specific risk can be diversified and hence, only incorporates the systematic risk (beta) to gauge the portfolio's performance. The ratio can be expressed as excess return generated by the fund over the risk free rate divided by the systematic risk or beta.
Treynor ratio=(Rp-Rf)/β
Where, Rp=return on the portfolio, Rf= risk free rate and β= portfolio beta
The Treynor ratio considers the return (excess return generated over risk free return) of a fund in relation to the portfolio risk that the fund manager has taken (beta) in order to achieve that incremental return.
When comparing two funds, if you find a fund that has produced higher return, you would normally opt for that fund. But, if you were to take a risk-adjusted approach, you would consider not only the incremental return but also the incremental market risk that the fund manager took to achieve this higher return. That's where you look at the Treynor ratio in order to determine which fund to choose - on a risk adjusted basis.
A better fund would have a higher Treynor ratio.
In the illustration discussed earlier, beta of Fund A and B are 1.5 and 1.1 respectively,
Treynor ratio for fund A= (30-8)/1.5=14.67%
Treynor ratio for fund B= (25-8)/1.1= 15.45%
The results are in sync with the Sharpe ratio results.
Both Sharpe ratio and Treynor ratio measure risk adjusted returns. The difference lies in how risk is defined in either case. In Sharpe ratio, risk is determined as the degree of volatility in returns - the variability in month-on-month or period-on-period returns - which is expressed through the standard deviation of the stream of returns numbers you are considering. In Treynor ratio, you look at the beta of the portfolio - the degree of "momentum" that has been built into the portfolio by the fund manager in order to derive his excess returns. High momentum - or high beta (where beta is > 1) implies that the portfolio will move faster (up as well as down) than the market.
While Sharpe ratio measures total risk (as the degree of volatility in returns captures all elements of risk - systematic as well as unsystemic), the Treynor ratio captures only the systematic risk in its computation.
When one has to evaluate the funds which are sector specific, Sharpe ratio would be more meaningful. This is due to the fact that unsystematic risk would be present in sector specific funds. Hence, a truer measure of evaluation would be to judge the returns based on the total risk.
On the contrary, if we consider diversified equity funds, the element of unsystematic risk would be very negligible as these funds are expected to be well diversified by virtue of their nature. Hence, Treynor ratio would me more apt here.
It is widely found that both ratios usually give similar rankings. This is based on the fact that most of the portfolios are fully diversified. To summarize, we can say that when the fund is not fully diversified, Sharpe ratio would be a better measure of performance and when the portfolio is fully diversified, Treynor ratio would better justify the performance of a fund.
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