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# How to define risks and rewards

May 17, 2010 12:04 IST

Sharpe and Treynor ratios are important. However, there is no guarantee that future performance will resemble the past.

From the 1950s onwards, serious attempts were made to measure the intuitive concept of higher reward for higher risk. The Sharpe ratio (SR) and the Treynor ratio (TR) are among the more popular tools that quantify reward divided by risk.

The two define risks and rewards differently or rather, measure different risks and rewards. SR is all about absolute risk, while TR is about risk relative to the stock market. In both cases, the return is defined as return minus a risk-free return but again, the definition of "risk-free" differs.

The interpretation is obviously different and both ratios are used for mutual fund ratings, as well as by some commodity traders and equity investors. Hedge funds and private equity players also use these. They are widely quoted and understanding them can help in investment decisions.

Take the SR first, since it's simpler. The risk is conceptualised as the volatility of return, and calculated by using standard deviation, (always positive). An ideal SR has a high return (minus risk-free return, which is usually assured debt), divided by a relatively low standard deviation.

In practice, the Nifty has an annualised SR of about 0.4 and few diversified funds will outscore that by much. Negative SR occurs only if the return is lower than the risk-free return, which makes investment a poor proposition.

Problems arise when returns are not normally distributed. In such cases, standard deviation is a poor measure. If the distribution includes long-tails (large gains or losses) or some other peculiarity, the SR may be very misleading.

TR uses a stock-market index as the benchmark. The index's return is assumed "risk-free". It can be received by a passive investor, who's assuming minimum risk that cannot be diversified away.  The TR numerator of return minus index return is also called "alpha". For example, a stock that returns 20 per cent versus an index return of 13 per cent has an alpha of +7.

TR uses Beta as the risk-denominator. Beta compares the volatility of an asset to the index. It is the ratio of the given asset's movement for every unit of index movement. For example, a stock that moves 1.2 per cent for every 1 per cent Nifty movement has a beta of 1.2.

The directional correlation can be positive (in the same direction as the index) or negative. A beta greater than 1 means the asset is highly-correlated to the index and more volatile. A positive beta of less than 1 shows an asset correlated to the index but less volatile than the index.

A negative beta is counter-cyclical  the asset  moves in the opposite direction. Zero-beta is something like assured debt return  it has no index correlation. TR can have a much wider range of numeric values in practice than SR because beta can be a very small number.

Since both TR denominator and numerator can be negative, interpretation is complex. A high positive TR can mean an asset that yields good returns, if beta is positive. But, a high TR can also mean an asset with negative returns and a negative beta.

A negative TR occurs if the return is positive and beta negative. This is a highly desirable hedge. Sugar companies, for example, had negative TR during the 2008-09 bear market, giving positive returns in a bear market.

But, a negative TR can also mean an asset with returns lower than the index, and positive beta. Even such cases of negative alpha (returns lower than index) are sometimes worth considering.

The return may be higher than assured debt, absolute risk may be low and the asset may be low-beta. The dividend yields of mature FMCGs can fall in this category. These are low beta assets with, low risks of dividend cuts. The returns may be more than assured debt but less than the market.

TR seems to offer the most useful insights when used on a narrow portfolio or a single asset, which is why hedge funds like it so much. SR works for both diversified assets as well as single assets.

Used together, SR and TR ratios are complementary. If the asset has positive SR, the undesirable TR cases are unlikely (though not impossible). In practice, few diversified funds have negative beta  but sometimes speciality sector funds do.

Apart from conceptual issues, both SR and TR measure historical average performances. There are no guarantees the future will resemble the past. Both ratios and their elements change over time. So, they must be used with caution.

Devangshu Datta in New Delhi
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