The five-year risk-adjusted returns for the period ended June 30 for the top quartile of equity funds beat all of the Russell Indexes on a risk-adjusted basis, although the returns ranged from 13% to 25%, as calculated by the Pension Research Institute.
This points out how important it was to be in the right sector of the market.
(You can plot your manager's return on the graph of the Frank Russell indexes shown above. The risk-adjusted return is a summary of downside risk and the nominal five-year return based on the PRI profile of an "average risk-averse investor.")
Notice in the chart on page 20 that 20th Century Ultra earned a higher risk-adjusted return than Keystone Small Company Growth, although it took less risk (9.6% vs. 10%). Is this a significant difference in risk? Not really. The main reason Ultra ranked higher is that it earned 90 basis points more in nominal return. The lower risk added only 20 basis points to the risk-adjusted return.
Fortunately, a growing number of services are calculating downside risk. Unfortunately, the procedure being used by some may mislead investors into thinking a portfolio has less downside risk than it actually does.
The example cited in this article uses the FT-Actuaries Japan Index from 1980 to 1990 and a minimal acceptable return of 10% annually (0.8% monthly).
One popular, but flawed, method is to calculate the deviations of each observed monthly return below 0.8%, and then convert the sum of these deviations to a monthly or annual percent. Technically, each time a return falls below the minimum acceptable return, the difference between the MAR and the return is squared, the sum of these squared differences is then divided by the number of observations, before taking the square root.
This "discrete time" method of calculating downside deviations assumes each bad outcome was the only return that could have occurred. Also, it assumes the worst return that occurred in the 23
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past is the worst that can occur in the future. At PRI, we believe it is essential to use a continuous probability distribution, i.e., recognize that each time a return occurred, there was a whole range of returns that could have occurred.
This is accomplished by fitting a curve to the data and using integral calculus to calculate the deviations below 10%. A simplistic approach would be to use a normal curve, but more precise procedures that allow the distribution to be skewed are available. We prefer the three parameter lognormal distribution.
If you have an aversion to the technical language of finance, remember, you don't need to understand the methodology for generating an MRI to know that it can do things an X-ray can't. Similarly, you should know there is a procedure for describing the shape of uncertainty of portfolio returns that goes beyond a bell-shaped curve. You should insist your consultant know the difference and know when another technique will expose data that can harm you financially.
Using the discrete time method, we get a monthly deviation of 2.74%, as opposed to 3.2% with the curve fitting method. The discrete method calculation is 27% less than the continuous time method.
If this monthly downside deviation is annualized in the traditional manner, multiplying by the square root of 12, the annualized downside deviation in discrete time (9.5%) becomes larger than continuous time method (7.5%). The monthly downside deviation in discrete time was smaller, but when annualized, the discrete downside deviation is larger.
What happened? It is incorrect to annualize downside deviations the way one annualizes standard deviations. Such analysis can lead to gross miscalculations of the downside risk. It has to do with something called end point of sensitivity.
We hope this article will give you enough information to ask your consultant some cogent questions, such as: Are you using a continuous probability distribution to make these calculations? Are you requiring the distribution to by symmetric?
PRI is willing to evaluate procedures for calculating downside risk at no charge; and if the procedure meets our standard, we will offer a letter of approval. Just send the documentation to: PRI, Suite 5, Fallon Place, San Francisco, Calif. 94133. We will also provide interested parties with a list of firms whose methodology has been approved.
Frank A. Sortino is director of The Pension Research Institute, (415) 323-6111. Details on PRI's methodology can be found in the fall issue of The Journal of Investing. A more detailed explanation of calculating downside risk will be in the Winter 1996 issue of the Journal of Portfolio Management.