## Honing in on the Sharpe Ratio – Part I

I’ve been reading that investment professionals still use the Sharpe Ratio to evaluate fund performance which led me to ask the question of some of my peers as to what they consider to be a “good” Sharpe Ratio. The answers I received were unexpectedly all over the map; some considered anything over 1 to be good. Others thought that only double digit Sharpe Ratios were worth bothering with while still others said that the Sharpe Ratio had no impact on their investment decisions.

This left me even more confused and I decided to explore the Sharpe Ratio in detail so that I could make my own informed decision concerning its validity. To help me in my investigation, I called on Professor Pat as he’s the resident StockMarketCookBook expert on all things related to portfolio theory.

In only two days, he presented me with an exceptional treatise on the subject of the Sharpe Ratio. The only problem I had with it was the length which I felt was too long for one blog so I broke it up into three distinct parts which will be run over the next few days. What follows is essentially his writing with some of my own thoughts tossed in.

Definition of The Sharpe Ratio
The Sharpe Ratio is named after William Sharpe, a 1990 Economics Nobel Laureate who won it for his work on the Capital Asset Pricing Model (known as CAPM) which shows how the market prices individual securities in relation to their asset class. Here the discussion is focused on the Sharpe Ratio which for a particular investment is a direct quantitative measure of reward to risk.

Sharpe devised the ratio which he called the ‘reward to variability ratio’ in 1966. It later became known as the Sharpe ratio as other economists and financial professionals attributed the ratio to him. It is a measure of how much excess return an investment provides over and above a riskless investment (e.g., T-bills) considering the additional risk (σ, the standard deviation of the returns on the investment under evaluation) that is entailed. It is mathematically defined as the following:

Sharpe Ratio = [Investment Rate of Return – Risk-free rate of return] / σ

The Sharpe ratio is there used to assess how well an investment compensates an investor for assuming additional risk. Higher values of the Sharpe ratio are considered to be better than lower ones. The investment community generally considers values over 1.0 to be good, over 2.0 to be very good, and over 3.0 to be excellent, but these can vary depending on the current financial climate. [Note: As of this writing, the risk-free rate is almost zero which means that the Sharpe Ratio is essentially just the investment return rate divided by the investment risk.]

Riskless Investment Returns
The measure used in calculating the rate of return of a riskless investment is typically short-term (90-day or less) U.S. Treasury Bills. This investment is considered to be as safe an investment as you can possibly find, and will exhibit no variation in base value during the holding period. Only the rate of interest will change as the bonds mature and are rolled over.

Other measures of what is considered “risk-less” can produce significantly different Sharpe Ratios. Long-term government bonds are not an appropriate measure for a risk-less security as market interest rate changes can significantly alter their values and in some cases can drive down the total return to very small levels or even produce losses.

Hedge Funds and the Sharpe Ratio
Implicit in the Sharpe Ratio is the assumption that returns on the investment follow a normal distribution (i.e., the bell-shaped curve). While this is a very good assumption for equity based stock index funds that are large and liquid it is not so good for strategically managed hedge funds that employ dynamic trading techniques, illiquid investments, or highly leveraged instruments such as options. For example, a hedge fund strategy that sells deep out-of-the-money options will show a higher than average Sharpe ratio–that is, until the market unexpectedly moves counter to the prevailing trend and the fund is hit with large losses.

Because of the Sharpe Ratio’s mathematical nature, high values must either employ a high return and/or a low risk. As history has shown, high return/low risk situations can’t be sustained for long periods of time.

Here’s an actual example of a supposedly stable fund with a high Sharpe Ratio whose demise nearly destabilized the global financial markets.

In the 1990’s, Long Term Capital Management, the bond arbitrage hedge fund touted as mathematically safe due to the supposed low probability of incurring significant overall losses on its massive portfolio, showed a very high Sharpe Ratio of 4.35. The fund managers employed highly leveraged strategies to make money on small arbitrage spreads. A financial crisis in Russia caused by defaults on government bonds and a resultant flight to quality resulted in massive losses for the fund which controlled nearly 5% of the world’s fixed income market.

Unable to make the loan payments on the huge debt incurred to finance its leveraged positions, they faced collapse. Had they gone into default it would have caused a worldwide financial meltdown. They were bailed out by the Federal Reserve and other creditors and taken over in 1998. So, what else is new?

Hedge fund illiquidity also works to distort the Sharpe Ratio. Investments in real estate, private equity, or mortgage backed securities for which there is no ready market can appear to be less volatile which helps their Sharpe Ratios. Fund managers tend to price these securities in a way that is, of course, favorable to the fund’s statistics and can produce an artificially high value for the Sharpe Ratio.

[Note: Illiquidity relates to how assets are valued. When there is no ready market how do you determine what something is worth? The recent mortgage crisis is an example where fund managers were valuing their own assets arbitrarily. The rate of return on an investment is related to how its value fluctuates. If it does not fluctuate then the standard deviation is low and the Sharpe Ratio is high. If that lack of fluctuation is artificial then the Sharpe Ratio is also artificial.]

Summary
Many hedge funds that currently report a high Sharpe Ratio may be employing strategies that are manageable at their current size but as they grow those same techniques may prove impractical and the Sharpe Ratio could drop dramatically. As a result, the Sharpe Ratio may not always be a good measure for evaluating a hedge fund’s risk/reward relationship.

To get a better picture of a fund’s risk/reward profile, investment professionals look at other aspects of performance including maximum portfolio draw-down and statistical measurements such as kurtosis and skewness. The Sortino Ratio, a modification of the Sharpe Ratio, focuses on downside volatility. Some think that it’s a more accurate representation of hedge fund risk but it, too, is subject to many of the same criticisms as the Sharpe Ratio. As one professor of risk management so aptly said, “Risk is one word, but it is not one number.” [Ref. 1]

Tomorrow we’ll look at the Sharpe Ratio in the context of Modern Portfolio Theory, so dust off your propeller hats!

References
1. “The Sharpe Ratio can oversimplify risk,” Investopedia.com.
2. “Risk gets riskier,” Hal Lux, Institutional Investor, October 2002.

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