Sharpe Ratio
This ratio measures the return earned in excess of the risk free rate (normally Treasury instruments) on a portfolio to the portfolio’s total risk as measured by the standard deviation in its returns over the measurement period. Nobel Laureate William Sharpe developed the model and the results of it indicate the amount of return earned per unit of risk. The Sharpe ratio is often used to rank the risk-adjusted performance of various portfolios over the same time. The higher a Sharpe ratio, the better a portfolio’s returns have been relative to the amount of investment risk the investor has taken. The major advantage of using the Sharpe ratio over other models (CAPM) is that the Sharpe ratio uses the volatility of the portfolio return instead of measuring the volatility against a benchmark (i.e., index). The primary disadvantage of the Sharpe ratio is that it is just a number and it is meaningless unless you compare it to several other types of portfolios with similar objectives.
S = Return portfolio - Return of Risk free investment Standard Deviation of Portfolio
Example: Let’s assume that we look at a one year period of time where an index fund earned 11% Treasury bills earned 6%
The standard deviation of the index fund was 20% Therefore S = 11-6/.20 = 25%
The Sharpe ratio is an appropriate measure of performance for an overall portfolio particularly when it is compared to another portfolio, or another index such as the S&P 500, Small Cap index, etc.
That said however, it is not often provided in most rating services.
Example: 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 judgment 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
This ratio is similar to the above except it uses beta instead of standard deviation. It’s also known as the Reward to Volatility Ratio, it is the ratio of a fund’s average excess return to the fund’s beta. 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. It measures the returns earned in excess of those that could have been earned on a riskless investment per unit of market risk assumed. The formula is typically used in ranking Mutual Funds with similar objectives.
T = Return of Portfolio - Return of Risk Free Investment
Beta of Portfolio
The absolute risk adjusted return is the Treynor plus the risk free rate.
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.
Example: In 2005 - 06 where Fidelity Magellan had earned about 18%. Many bond funds had earned 13 %. Which is better? In absolute numbers, 18% beats 13%. But if we then state that the bond funds had about half the market risk, now which is better? We don’t even need to do the formula for that analysis. But that is missing in almost all reviews by all brokers. For clarification we do not suggest they put all the money into either one- just that they need to be aware of the implications.
Jensen’s Alpha
This is the difference between a fund’s actual return and those that could have been made on a benchmark portfolio with the same risk- i.e. beta. It measures the ability of active management to increase returns above those that are purely a reward for bearing market risk. Caveats apply however since it will only produce meaningful results if it is used to compare two portfolios which have similar betas.
Assume Two Portfolios
A
B
Market Return
Return Beta
12
0.7
14
1.2
12
1.0
Risk Free Rate = 9%
The return expected = Risk Free Return + Beta portfolio (Return of Market - Risk Free Return) Using Portfolio A, the expected return = 0 .09 + 0.7 (0.12 - 0.09) = 0.09 + 0.021 = 0.111 Alpha = Return of Portfolio- Expected Return= 0.12 - 0.111 = 0.009
As long as “apples are compared to apples”- in other words a computer sector fund A to computer
sector fund b- it is a viable number. But if taken out of context, it loses meaning. Alphas are found in many rating services but are not always developed the same way- so you can’t compare an alpha from one service to another. However we have usually found that their relative position in the particular rating service is to be viable. Short-term alphas are not valid. Minimum time frames are one year- three year is more preferable.
Expense Ratio
The percentage of the assets that were spent to run a mutual fund. It includes things like
management and advisory fees, travel costs and consultancy fees. The expense ratio does not include brokerage costs for trading the portfolio. Also referred to as the Management Expense Ratio (MER)
Pay close attention to the expense ratio, it can sometimes be as high as 2-3% which can seriously undermine the performance of your mutual fund.
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