Fund's Risk - Did You Break A Sweat

Risk can be defined in terms of short term fluctuations in expected value. Actually risk is something difficult to quantify. It relates to how much you can afford to lose without excessive damage to your wallet or your psyche. But a basic idea of volatility and it impact on returns can help an investor to select funds that suits his or her risk palate.

Volatality

While no single risk measure can predict with 100% accuracy how volatile a fund will be in the future, studies have shown that past risk is a pretty good indicator of future risk. In other words, if a fund has been volatile in the past, it's likely to be volatile in the future.

Standard Deviation

Standard deviation is probably used more often than any other measure to gauge a fund's risk. Investors like using standard deviation because it provides a precise measure of how varied a fund's returns have been over a particular time frame—both on the upside and the downside. With this information, you can judge the range of returns your fund is likely to generate in the future. For most funds, future monthly returns will fall within one standard deviation of its average return 68% of the time and within two standard deviations 95% of the time.

Caveat - Using standard deviation as a measure of risk can have its drawbacks. It's possible to own a fund with a low standard deviation and still lose money. In reality, that's rare. Funds with modest standard deviations tend to lose less money over short time frames than those with high standard deviations. The bigger flaw with standard deviation is that it isn't intuitive.

Beta

Beta, meanwhile, is a relative risk measurement, because it depicts a fund's volatility against a benchmark. Beta is fairly easy to interpret. The higher a fund's beta, the more volatile it has been relative to its benchmark.

Beta > 1.0 = Fund’s Volatility > Benchmark’s Volatility

e.g. If market goes up by 10% a fund with beta 1.1 will go up by 11%.

Beta < 1.0 = Fund’s Volatility < Benchmark’s Volatility

e.g. If market goes up by 10% a fund with beta .9 will go up by 9% but if market goes down by 10% it will just go down by 9%.

The biggest drawback of beta is that it's really only useful when calculated against a relevant benchmark. If a fund is being compared with an inappropriate benchmark, its beta is meaningless.

Beta and R-squared

R-squared, which you can find under the Ratings & Risk tab of a fund's report on Morningstar.com. The lower the R-squared, the less reliable beta is as a measure of the fund's volatility. The closer to 100 the R-squared is, the more meaningful the beta is. Unless a fund's R-squared against the index is 75 or higher, disregard the beta.

Treynor Ratio

A ratio that measures returns earned in excess of that which could have been earned on a riskless investment per each unit of market risk. Sometimes referred to as the return vs. volatility ratio the Treynor Ratio is a measure of the excess return per unit or risk

Treynor ratio= (Average Return of the fund – Risk Free return) /  Beta of the fund

In other words, the Treynor ratio is a risk-adjusted measure of return based on systematic risk. It is similar to the Sharpe ratio, with the difference being that the Treynor ratio uses beta as the measurement of volatility.

Risk Adjusted Returns

We've focused on yardsticks that tell you either how good or how volatile a fund's returns have been. But there are also measures that treat performance and risk together: risk-adjusted performance measures. Let’s look at them.

Alpha

Alpha is the difference between a fund's expected returns based on its beta and its actual returns. If a fund returns more than what you'd expect given its beta, it has a positive alpha. If a fund returns less than its beta predicts, it has a negative alpha.

Alpha= (Actual return – Risk free T-bill’s return) – Expected return based on Beta

e.g. Actual return = 30%; Beta=1.2; Risk Free Return=3%;

Bencmark’s return=20%; So based on Beta, Expected return=(20*1.2) 24%

Alpha = (30-3) – 24=3%

Because a fund's return and its risk both contribute to its alpha, two funds with the same returns could have different alphas. Further, if a fund has a high beta, it's quite possible for it to have a negative alpha. That's because the higher a fund's risk level (beta), the greater the returns it must generate in order to produce a high alpha. So, you would want to find high-alpha funds.

Inherent problems with Alpha –

1.      It's dependent on the legitimacy of the fund's beta. So, if a fund's beta isn't meaningful because its R-squared is too low (below 75), its alpha isn't valid, either.

2.      Alpha fails to distinguish between underperformance caused by incompetence and underperformance caused by fees.

3.      It's impossible to judge whether alpha reflects managerial skill or just plain old luck. Is that high-alpha manager a genius, or did he just stumble upon a few hot stocks? 

Sharpe Ratio

The Sharpe ratio uses standard deviation to measure a fund's risk-adjusted returns. The higher a fund's Sharpe ratio, the better a fund's returns have been relative to the risk it has taken on. Because it uses standard deviation, the Sharpe ratio can be used to compare risk-adjusted returns across all fund categories.

Sharpe ratio = (Fund’s return – risk free returns)/standard deviation

The higher a fund's Sharpe ratio, the better its returns have been relative to the amount of investment risk it has taken. If funds A and B both have same return of 25% but there Sharpe ratio is 1.09 and .74 then Fund A took less risk then fund B.

The higher a fund's standard deviation, the higher the fund's returns need to be to earn a high Sharpe ratio. Conversely, funds with lower standard deviations can sport a higher Sharpe ratio if they have consistently decent returns. A higher Sharpe ratio just means that the fund's risk/return relationship is more or optimal.

The lack of dependence on validity of beta is real advantage of Sharpe over Alpha. Moreover, it's easier to compare funds of all types using the standard-deviation-based Sharpe ratio than with beta-based alpha. But given no other information, you can't tell whether a Sharpe ratio of 1.5 is good or bad.


Sortino Ratio

The Sortino Ratio is an adjustment on the Sharpe Ratio in that it only penalizes downside volatility. This is done by creating a value known as downside deviation which is based on some minimum acceptable return (MAR) or hurdle rate which is a rate of return that an investor can set. This could be 3% annual risk free asset (unrealistic given current interest rates).

Sortino Ratio = (Fund’s Return – Risk Free investment’s Return)/Downside Deviation

The denominator of the Sortino ratio is calculated only with data from periods where performance was below the MAR. This differentiates the “positive” and “negative” volatiliy.

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