Analytical Toolbox: Know Your Risk
July 16, 2009
Financial risk is associated with both losses and gains that do not keep pace with rising costs. A first step towards managing risks you encounter in the stock market means knowing your risk. Ideally this translates to being able to quantify that risk.
Portfolio Returns
Identifying portfolio holdings as longer-term investments in this article, individuals can go down a variety of paths in an attempt to quantify expected returns. From a statistical standpoint, expected returns generally translate to average returns. Using the S&P 500 Index as proxy for a stock portfolio, two problems with such an approach are:
- The average annual return over the long-term is positive resulting in an approach that only compounds gains when using a simple average.
- Outlier events which include large annual gains or losses occur in the market (the “fat-tail” issue) and skew average values.
Rather than completely discarding a method that uses an average value, investors can incorporate it into one component of a scenario analysis.
A scenario analysis takes different approaches to a problem and assigns a probability to that particular approach. It then uses the approach or scenario to calculate an expected value and combines the outcomes based on the probability of each. The net probability for all scenarios taken together equals 1.0.
As an example, the investor may decide one of two scenarios has a 40% chance of occurring and the other has a 60% chance of occurring. Assuming returns of 6% for Scenario 1 and 9% for Scenario 2, the expected return using a scenario analysis is calculated as follows:
(0.40 x 0.06) + (0.60 x 0.09) = 0.078
Although a positive result is still compounded, it is slightly muted by the different techniques used to derive each result.
One scenario analysis to quantify returns for a portfolio that is positively correlated to the S&P 500 Index is described here. It is intended to provide a quantitative launching point for you to complete your own analysis. The advantage of creating your own scenario analysis, providing there are reasonable assumptions, is that it will provide a result that more closely tracks your situation. Everyone’s time horizon and portfolio balance vary.
Sample Scenario Analysis
The recent bear market has made it very apparent that bad years for the market can have a significant impact on reaching longer-term goals. The following four approaches for calculating annual stock market returns takes into consideration long-term results, the effect of bear markets, the effect of bull markets and actual returns.
Assuming a thirty-year holding period and using monthly results from January 1979 through December 2008, the scenario analysis is calculated using the following methods. Note that dividends, which can significantly impact returns, are not included in the data which was downloaded from Worden Brothers TeleChart 2007.
1. Average Returns
Use the basic approach of calculating an average return over a given period and determine what percentage of the actual returns were in the same bin when plotted in a histogram form. Rather than using annual returns, monthly returns are used then annualized.
The average value will be used as the methods scenario analysis value and the percentage of years satisfying the “reasonably close” requirement will be divided by the total number of years (30) for the method’s percent weight.
2. Returns from Best Years
Calculate the average return for the top ten years. This will represent 10/30, or 33% of the scenario analysis.
3. Worst Years Returns
Calculate the average return for the worst eight years. This will represent 8/30, or 27% of the scenario analysis. The lower number of years used for worst years versus best years may be considered conservative from the standpoint that the average value is closer to the worst value for the data set. It also reflects a market period with more up years than down years.
4. Actual Daily Returns
Assign the remaining percentage available for the scenario analysis to the geometric average of actual returns for the period.
Table 1 provides the average annual results and percentage weights for the four methods described.
Method | Annualized Return | % Weight |
1. | 8.7% | 26% |
2. | 27.2% | 27% |
3. | -17.5% | 20% |
4. | 7.8% | 27% |
Calculating the weighted average:
Weighted Average Returns = (8.7% * 0.26) + (27.2% * 0.27) + (-17.5% * 0.20) + (7.8% * 0.27)
Weighted Average Returns = 8.2%
Difference in ending value after 30 years ($100,000 initial balance):
30-year average: 1,221,479
30-year wtd. average: 1,063,697
The ending balance is approximately 13% less using the weighted average approach. The lower amount is actually better than the actual daily results for a 30-year buy and hold
What Can the Results Tell You?
If the expected returns you calculate do not outpace inflation or allow you to meet your longer-term goals, then simply having all of your assets in a buy-and-hold oriented portfolio is not effective. Some sort of timing system may be required, with less money allocated to equities when some objective filter provides a signal.
You may choose to allocate less money to the portfolio the month after the 50-day simple moving average [SMA] for the S&P 500 Index is below its 200-day SMA.
Using scenario analysis you would then need to determine what percentage of the time the condition was met during your test period and re-run your original scenario analysis for years when the condition was met as well as those when it wasn’t met. Returns for years with a lesser allocation can then combine the market returns from the scenario analysis with Treasury Bill or your broker’s money market returns.
Sound like a lot of work? Maybe initially, but guess what? Successful investing actually requires some work and having a method that can reduce your exposure during less favorable conditions is one way you can manage your risk.
Quick Look
A quick analysis of this approach exits the portfolio after the 50-day SMA moves below the 200-day SMA until the day after the 50-day SMA moves above the 200-day SMA. Not included in these costs are commissions, slippage and taxes if the funds are held outside a retirement account. A more realistic approach would set a longer-term interval to assess the filter, say one month. Since no partial allocation of the portfolio is identified, 0% returns are assumed when the portfolio is out of the market.
Using the actual daily values over the 30 year period, the ending portfolio value with the filter would have been $1,073,406 versus $963,300, or more than 11% higher. Even if the funds are in a retirement account and not effected by taxes, commission and slippage would surely have eaten away the advantage.
Transitioning to a monthly timing approach the investor would exit the market if the 50-day SMA is below the 200-day SMA at the end of the previous month (bullish) and entering the market again when the 50-day SMA is above the 200-day SMA at the end of the previous month (bearish). The ending portfolio value with the filter would have been $944,354 versus $856,862, or more than 10% higher. In the monthly approach bullish and bearish conditions actually persist for extended periods resulting in substantially reduced commissions and slippage.
Bottom line: you need to run the numbers. While the scenario analysis used with a buy and hold approach would not have prevented losses from the two most recent bears, it does provide a more realistic expectation for the portfolio. It acknowledges that returns are not some smoothed average value, but rather a mix of good years and bad years, sometimes extreme.
Summary
Longer-term investments are often earmarked as retirement dollars and completing a simple growth formula to it will suffer the most after a bearish period. Since we can expect bearish markets to continue to exist at different times over the next 30 years, the investor should take some time calculating realistic expected returns. The Scenario Analysis in this article was for sample purposes only, however, it was a relatively quick estimate that more closely tracked actual returns.
Figure 1 provides a histogram for actual monthly returns for the 30-year period. This is accomplished by specifying return intervals or ranges (i.e. 0.1% to 2.5%) and counting the number of months that fall into each range. While the right side displays a nice bell curve type result, the problems lay to the left of that where negative extremes occurred. Fat-tails do pose problems when it’s assumed the data is much more smooth and symmetrical.
Figure 1: Monthly Returns for the S&P 500 Index from Jan 1978 through Dec 2008
This approach addressed two primary issues regarding portfolio risk and expected returns:
- Expected returns for a portfolio given historical performance
- Potential fat-tail losses or historical outliers that could impact portfolio returns
Traders should not disregard investment risk. More next week.
Vive le Tour.
To access other articles written by Clare White, please click here.
Clare White
Contributing Writer and Options Strategist
Optionetics.com ~ Your Options Education Site
Questions for Clare? Visit the Optionetics.com Discussion Board
Email This Article
View Full HTML
Digg This
Delicious
Subscribe© Copyright 1995-2009 Optionetics. All rights reserved. This material is for personal use only. Republication and re-dissemination, including posting to newsgroups, is expressly prohibited without the prior written consent of Optionetics. Optionetics is a registered trademark of Optionetics, Inc.