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To understand these ratios, let us first understand the types of risk of a fund. Total risk of a portfolio is measured by the standard deviation of its returns. The total risk actually consists of systematic risk and unsystematic risk. Systematic risk measures the volatility of a portfolio or a fund with respect to the market and is measured by beta (?). Systematic risk is that part of the total risk that is general to the economy or the market as a whole and hence cannot be diversified. Specific risk or unsystematic risk is that part of the total risk that is specific to the company or the industry and hence can be diversified.
Sharpe Ratio
Sharpe ratio evaluates the performance of a portfolio based on the total risk of a portfolio. It measures the excess return generated by a portfolio over the risk free rate in relation to the total risk or standard deviation of a portfolio.
Sharpe Ratio= (Rp - Rf)/σ
Where, Rp=return on the portfolio, Rf= risk free rate and ?= standard deviation of the return of the portfolio
Higher the Sharpe ratio, better is the fund.
Illustration: Consider two funds A and B. Let return of fund A be 30% and that of fund B be 25%. On the outset, it appears that fund A has performed better than Fund B. Let us now incorporate the risk factor and find out the Sharpe ratios for the funds. Let risk of Fund A and Fund B be 11% and 5% respectively. This means that the standard deviation of returns - or the volatility of returns of Fund A is much higher than that of Fund B.
If risk free rate is assumed to be 8%,
Sharpe ratio for fund A= (30-8)/11=2% and
Sharpe ratio for fund B= (25-8)/5=3.4%
Higher the Sharpe Ratio, better is the fund on a risk adjusted return metric. Hence, our primary judgement based solely on returns was erroneous. Fund B provides better risk adjusted returns than Fund A and hence is the preferred investment. Producing healthy returns with low volatility is generally preferred by most investors to high returns with high volatility. Sharpe ratio is a good tool to use to determine a fund that is suitable to such investors.
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.
Information Ratio
Information ratio is used to measure the performance of an active fund manager. It is expressed as the active return or alpha (α) of a portfolio divided by the tracking error. Active return or alpha return is the excess return generated by the fund over its benchmark. Tracking error measures the standard deviation of the alpha return.
Information ratio= (R-Rb)/σ= α/ω
Where R= return on the portfolio, Rb= Return on the benchmark σ= Standard deviation of the alpha return, α= alpha of the portfolio and ω= Tracking error
Information ratio is in other words nothing but risk adjusted alpha.
The ratio is similar to the Sharpe ratio, the difference being that instead of using risk free rate, the portfolio return is compared with the benchmark return here. Information ratio is a highly useful tool when one wants to evaluate the performance of an active fund manager. Alpha is the indicator of the stock picking ability of a fund manager. The ratio finds out the incremental return generated by the fund manager for the incremental risk undertaken by the manager to deliver the alpha returns. The higher the active return for the incremental risk undertaken over the benchmark portfolio risk, higher is the stock picking ability of a fund manager. Higher information ratio is therefore associated with superior skills of an active fund manager.
When looking at actively managed equity funds, we always look for alpha - the excess return over benchmark that the fund manager has produced. Alpha is widely regarded as the best metric to measure outperformance. In the Information ratio, we consider not only the alpha but also the degree of variability in the alpha that this fund manager has produced from time to time. If you find one fund with a higher overall alpha but a very large degree of fluctuations in the period-on-period alpha generated by the fund manager, it may just score lower in the Information ratio than another fund with a lower overall alpha but a more stable set of alpha numbers generated period-on-period by the other fund.
Information ratio is in other words nothing but risk adjusted alpha. In our market, since the vast majority of equity funds are actively managed and most of the money collected by fund houses is in various varieties of diversified equity funds, generating alpha has always been the focus of the fund managers. When alpha is a core focus area, it probably follows that the Information ratio should become increasingly a core focus area for analysts and advisors.
In conclusion
All three measures - Sharpe ratio, Treynor ratio and Information ratio - seek to measure risk adjusted returns. Many investors focus on highest absolute returns on the one hand but are unable to digest volatility on the other hand. The job of the advisor is to get investors to understand the notion of a risk adjusted return - in order to appreciate the virtues of consistency over flash-in-the-pan performances. These ratios are a very useful set of tools for advisors who want to go down the path of choosing consistent performance in funds they recommend to their clients.
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