© Copyright 2000 Rogers Media. The following article first appeared in the June 2000 edition of BENEFITS CANADA magazine.

The Upside of Downside Risk

Downside risk is an accurate and customized tool for measuring risk. A growing number of investors are discovering its advantages.

By Neil Riddles

A lot of investors think they understand risk. In fact, it can be a deceiving concept that varies from case to case. Differing risk measurement techniques have more than a little to do with that.

The most widely ac-cepted measure of investment risk is standard deviation. When used to gauge performance risk, it measures the degree to which returns have been spread out around their historical average.

For example, a portfolio return of 15% annually over 10 years is generally good. But an investment style that returns 15% each and every year is more valuable than one which is up 100% one year and then down 75% another, even if it also averages 15% over a long period.

Investors look at returns to gauge the likelihood of future excess performance. Standard deviation measures how consistently that return was delivered. The more consistently a return occurred in the past, the more likely the investor will receive that return in the future.

The main advantages of this tool are that it's easily calculated, simple to manipulate and well un-derstood.

There are some drawbacks to using standard deviation as a measure of risk, however. It interprets any difference from the average, above or below, as bad. This runs contrary to the way most investors feel about returns. Few in-vestors fret about their portfolios doubling; most only worry about the downside--their returns being below average.

Downside risk, as the name implies, measures risk below a certain point. For example, if an investor is only worried about losing money, that point would be zero and the possibility of negative returns would be viewed as risky. If an investor needs to earn a 7% annual return in order to meet their goals, any return under 7% would be considered risky. This investment return floor, which serves as the dividing line between good and bad outcomes, is called the minimum acceptable re-turn (MAR).

Unlike standard deviation, downside risk accommodates different views of risk. Institutional investors often view investment risk as the possibility of underperforming the benchmark, whereas retail investors tend to regard risk in absolute terms as the possibility of loss.

Investors can customize the downside risk calculation using their own MAR. The institutional investor typically uses the benchmark rate as the minimum acceptable return while the retail investor often uses the risk-free rate. Since standard deviation can only measure how tightly distributed returns are around a mean, it cannot be customized for individual investors.

The amount of risk contained in a set of returns changes considerably when the MAR changes. For example, if Investor A needs an investment which returns 10% annually, any amount less than this will result in the underfunding of A's pension plan. Investor B wants a good return but doesn't want to incur losses. By raising the MAR from zero to 10%, a larger amount of the return distribution violates the MAR. This additional area--the amount between zero and 10%--is considered risk for Investor A but not for Investor B.

Another limitation to standard deviation lies with the underlying data. Most investors will recall normal distribution from their introduction to statistics course. This bell curve underlies all of the assumptions about standard deviation. If the underlying data is not normally distributed, then the standard deviation is likely to give misleading results. It's worth noting that a number of studies show that investment returns are not normally distributed.

The most accepted method of calculating downside risk begins with a standard log normal curve and adjusts it for three parameters. Basically, a log normal curve is stretched and compressed for a closer fit to the actual distribution. This custom fit provides a better indication of the true picture of the distribution.

A further enhancement to the calculation uses bootstrapping routines. This technique attempts to increase the explanatory ability of a limited amount of data. In this case, bootstrapping selects 12 months at random and links them to establish a one-year return. This process is repeated thousands of times resulting in a distribution with many observations instead of just a few.

Unfortunately, bootstrapping assumes that data is independent while empirical evidence shows that returns are not entirely independent. If one period's return influences another, then bootstrapping may create hypothetical annual returns that could never actually occur. The additional explanatory power gained by the increased number of observations must be weighed against the error introduced because returns are not entirely independent.

In spite of its potential drawbacks, many investors prefer to use bootstrapped data because they believe it offers a better indication of true distribution.

The Japanese market during the 1980s provides an example of bootstrapping's effectiveness. From 1980 to 1990, there was not one year in which the market was down. Based on this limited amount of data it appears that the Japanese stock market had no risk during that period. However, bootstrapping the monthly data produced a distribution that clearly indicated the potential for negative annual returns. This risk showed up in the early 1990s as the Japanese equity market suffered steep declines. Looking at the bootstrapped data might have alerted investors to the fact a sharp correction was indeed possible.

Downside risk calculations provide investors with more information than simply a downside deviation number. Additional statistics offer insight into the causes of the risk. They are:

• Downside frequency. Tells the user how often the returns violated the MAR, which helps investors accurately assess the likelihood of a bad outcome.
• Average downside deviation. Indicates the average size of unacceptable returns and helps judge the severity of the average bad return.
• Downside magnitude. This is the return at the 99th percentile on the downside--in other words, the worst-case scenario.
• Downside deviation. All of the risk statistics combined, including the size and the frequency of unacceptable returns.
• Risk-adjusted returns. One method of ranking investments is by their risk-adjusted returns. For downside deviation, the accepted risk-adjusted return is the Sortino ratio--the annualized return divided by the downside risk. Similar to the Sharpe ratio which uses standard deviation, the Sortino ratio measures how many units of return were received per unit of risk experienced.

The table tracks 16 years of monthly returns and provides an example of some downside risk statistics calculated on a portfolio and benchmark. These statistics were calculated with a MAR of zero, which means that any negative return is regarded as bad.

In this case study, the actively managed portfolio underperformed the benchmark by an annualized 70 basis points (15.6%­14.9%). The portfolio and the benchmark look similar on a risk-adjusted basis when using standard deviation as the measure of risk. The efficiency ratio (return/standard deviation) of the portfolio is 1.1 compared to the benchmark's 0.9.

However, the Sortino ratio (the return divided by downside deviation) is higher for the portfolio than the benchmark. An examination of the other statistics explains what happened.

Downside frequency tells us that the portfolio lost money half as often as the benchmark (10.7% of the time vs. 19.6%). The average downside deviation indicates that when the portfolio did suffer a loss, the loss was much smaller than the average loss suffered by the index (3.3% vs. 12.2%).

Clearly, an investor who is not willing to suffer losses would be better off in the active portfolio than with an index investment. On the other hand, a pension fund or other long-term investor might be more concerned with underperforming the benchmark than with the possibility of losses. In that case, an investment in an index fund might be more acceptable.

The chart (see "Downside risk distribution," page 69) shows the return distributions of the active portfolio and the index. The index curve extends further into negative territory than the active portfolio's curve which, while shifted a little lower than the index's curve, has much less of the curve in negative territory. If the MAR was shifted to about 10, then the risk of the portfolio would rise proportionately more than the index because the active portfolio's curve is so sharply peaked.

RELATIVE RISK

There are drawbacks to the present methods of calculating downside risk. Many investors define risk as underperforming a benchmark. Most downside risk software addresses this issue by allowing the investor to input the benchmark's return as the MAR, but this does not accurately reflect the investor's view of risk. If the index was up 10% over the period measured, then using it as the MAR would result in any portfolio with a return less than 10% being considered bad, when in fact, an investor concerned with performance relative to the index would look at an 8% return as quite good in a year when the benchmark was down 3%.

The first graph in the two-part chart (see "Risk of portfolio with index return as MAR," below) illustrates a bootstrapped distribution of returns for an active portfolio. The minimum acceptable return is 7.8%, the benchmark's return over the period. The downside risk is calculated at 14.9% over this period.

During the period measured, the portfolio outperformed the index five out of the eight years tracked. However, when the index's annualized return over the entire period is compared to the portfolio's return each year, the portfolio is seen as underperforming in five out of eight years. In one year the portfolio return was 0.4% and the benchmark was down 8.4%. Investors who are concerned with risk relative to the benchmark would consider this a successful year. Instead, using the index's annualized return as the MAR, the portfolio underperformed ­7.4% that year.

When following the distribution of the active returns (portfolio return minus the benchmark return) for the same portfolio and time period, any return below zero indicates the portfolio underperformed the benchmark (see "Risk of active return: portfolio ROR - Index ROR," below). Calculating downside risk in this manner results in a downside risk statistic of 7.3%, considerably lower than the other method's 14.9% statistic. This calculation leads to a different conclusion that is more of a realistic measure of risk for benchmark-sensitive investors.

While this is a non-standard way to calculate downside risk, it is a superior method for investors primarily concerned with underperforming a benchmark. For investors who have an actual set rate they need from their investments, or for investors who define risk as the possibility of loss, MAR adequately captures their risk preferences. However, determining the downside risk of the active returns is preferable for investors who are concerned with performance relative to a benchmark.

Why wasn't downside risk adopted earlier? Part of the reason may be that it requires more complex calculations.

Today, computing power and memory are relatively cheap commodities, and desktop software to calculate downside risk is readily available, even free, on the Internet (www.sortino.com.) Investors also have a healthy skepticism for new statistics, and for most investors downside risk is a new concept.

Another reason for the slow acceptance of downside risk is that investors are already using standard deviation, and they may be reluctant to adopt another measurement tool that could offer conflicting results.

However, it's prudent to embrace any valid new statistic that can provide additional insight into the risk profile of potential investments, and downside risk is slowly gaining acceptance in the financial community.

It's important to remember, however, that there are a number of ways to calculate downside risk and they are likely to yield different results. It is essential that individuals interpreting downside risk statistics understand the calculation methodology because downside risk statistics calculated using different assumptions are not comparable.

Neil Riddles is senior vice-president/director performance analysis at Templeton Global Investors Inc. in Fort Lauderdale, Fla.

The return distributions of the active portfolio and the index. The higher the curve, the more often the return occurred. The area under each curve and to the left of the MAR line is the amount of distribution considered as risk.

Tracking 16 years of monthly returns, here are some downside risk statistics calculated on a portfolio and benchmark. These statistics were calculated with an MAR of zero, and with any negative return regarded as bad.

The first chart, Risk of portfolio with index return as MAR (left), illustrates a bootstrapped distribution of returns for an active portfolio with a minimum acceptable return of 7.8%. The downside risk is calculated at 14.9%. The second chart, Risk of active return, depicts the distribution of active returns for the same portfolio and time period. Returns below zero indicate the portfolio underperformed the benchmark. Calculating downside risk in this manner results in a downside risk statistic of 7.3%, considerably lower than 14.9%.

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