The Use of Historical Averages

There are two uncontrolled, external parameters that significantly effect all retirement plans.

  • Inflation: increases in consumer prices.
  • Investment returns: dividends, interest and capital gains from invested assets.
Differences in modeling approaches have led to two different kinds of retirement calculators.
  • Deterministic: where future performance of these two parameters are estimated using historical averages.
  • Probabilistic (Monte Carlo): where the values of these two parameters are randomly generated to simulate the uncertainty of future values. [2]

This paper concentrates on the use of historical averages in deterministic models.

An historical average is computed for some measured value over a historical time period. This value is then applied to all time periods in the prediction time range of the model. Word has it that because of the importance of attaining this value, many consumer driven websites with quoting systems like advantage one are trying to incorporate automated calculators that may help obtain historical averages.

In the deterministic retirement calculator both inflation and rates of investment return are rates of change. Inflation is the annual percentage change in consumer prices. Investment return is the annual percentage returned on investments. Over a 25 year retirement the values will deviated from their averages but they will quickly return to their means and then swing to the other side -- regression to the mean. In other words their annual values will oscillate around their means and over time their historical averages are a good predictor of their future long term performance.


The rate of inflation is an external factor over which the retiree has no control and no real power to lessen its impact on the retirement portfolio. Inflation has a huge impact on the amount of money available for retirement spending as measured in today's dollars. Figure 1 illustrates the performance of inflation since 1970, when the Consumer Price Index was first compiled.

Figure 1: Inflation 1970 - 2007

Since 1970 inflation has gone through two separate and different phases. From 1970 to 1983 inflation was high due in part to mismanagement of the money supply by the Federal Reserve. By 1983 Fed Chairman Paul Volker's iron grip on the money supply took effect and inflation came down dramatically.

Table 1 shows the means and standards deviations for both periods and for the period as a whole.

YearsMeanStd Dev

Table 1: Inflation Summary Statistics

The choice of which average to use is up to the user. If the belief is that the economy is entering a new period of higher inflation the first period's average is to be used. If there is faith in the Federal Reserve to maintain it control of price changes, a task assigned to it by the Full Employment Act of 1946, then the second average is to be employed. The total average is irrelevant because prices never did oscillate about this mean.

Financial advisors have investment strategies available, such as investing in commodities or foreign currencies, to lessen the impact of inflation on retirement portfolios.

Investment Returns

Investment returns are the dividends, interest and capital gains that the retiree receives on her retirement portfolio. The retiree has a great deal of control over the performance of her retirement portfolio through the management of her portfolio.

A successful retirement portfolio must be actively managed. The investor has a number of tools available to lessen the impact of market fluctuations on her portfolio. A couple of retirement portfolio management techniques are noted here.

Portfolio Rebalancing

Establishing target asset allocations for the retirement portfolio and sticking to them is an effective way of leveling the fluctuations of the market. The sticking to them is the tricky part. Bryan Olsen provides an interesting discussion of emotions in the market and portfolio rebalancing.[3] Portfolio rebalancing has no tax consequences for IRAs and Roth IRA's and minimal consequences for the After-Tax account if it is done on an annual basis.

The Triple 40 Timing Model

Triple 40 is a simple and proven effective trend following, market timing model. . Triple 40 preserves capital by being totally out of the market when the market is going down and enjoying compounding when the market is going up. Those are noble sentiments but the trick is to believe the model when it issues a buy or sell signal. The Triple 40 Model uses these indicators.
  • 40 week moving average of the S&P 500 index.
  • 40 week moving average of 90-day T-Bill interest rate.
  • 40 week moving average of 10-year T-Bond interest rate.
They are computed weekly after Friday's market close.

A 40 week moving average is the average of the previous 40 weeks of the indicator values. Each Friday the oldest value is dropped, the latest is added to the list and the averages are recomputed. For those who would not go through the weekly hassle of updating the averages, commercially available 200 day moving averages serve as a reasonable substitute. However, none of the computational results done with 40 week moving averages have been replicated with 200 day moving averages.

The model buy and sell signals are made through the comparison of the moving averages:

  • Buy if the S&P 500 is above its moving average and at least one interest rate is below its moving average.
  • Sell if the S&P 500 is below its moving average or both interest rates are above their moving averages

Logic: we want to be in market when stocks are trending higher and interest rates are at least somewhat favorable (trending lower). (Interest rates are an inflation indicator.) The Triple 40 sell signal is logical inverse of its buy signal.

Considerable back testing has been done on the Triple 40 model. Table 2 compares the S&P 500 average to the Triple 40 results. When Triple 40 was in the market all of its funds were invested in SPY, the S&P 500 ETV fund which tracks the S&P 500 index.. When Triple 40 was out of the market all funds were in cash.

YearsS&P ReturnsTriple 40 Returns
1993-2002 7.3% 8.9%
1995-1999 26.2% 18.9%
2000-2002 -15.7%-3.9%

Table 2: Triple 40 Model Results

Table 3 gives an idea of the portfolio management results for Triple 40.

YearsS&P Triple 40
Max Draw down-49.1% -14.5%
Date of Draw down 10/9/2002 4/5/2002
Trades/Year - 2.05
% time in market 100% 51%

Table 3: Triple 40 Performance

The Triple 40 managed portfolio was off by at most 14.5% at its lowest point.

The central idea of Triple 40 is to keep the rate of return for the portfolio near its assumed average return as its value oscillates around its mean. The technique is to lop off the bottoms of the oscillations by exiting down markets while letting the tops grow in up markets. The price for employing this strategy is some reduction in portfolio performance during bull markets but the reward is portfolio stability in all economic environments.


Published material about retirement planning assumes that the retirement portfolio is passively managed, that the portfolio's investment return tracks the general market and that portfolio return will be victimized by an erratic rate of inflation.
  1. If the Federal Reserve does its duty under the Full Employment Act of 1946 then inflationary volatility will be minimal and an average figure will work just fine.
  2. If the retirement portfolio is actively managed then historical averages become an accurate projection into the future.
Monte Carlo enthusists[4] love to frighten their users by vividly illustrating the consequences of retiring into a down equity market. The key to avoiding these consequences is to begin managing retirement savings in the retirement mode a few years before actually retiring.

The fact is that if the inflation and asset return averages and the context in which they are being used are fully understood then they become a valuable tool for ORP.


  1. Market Timing: Why and How; Dr. Mark D. Pankin, Arlington, Virginia Library Lecture Series, March 8, 2003
  2. A Critique of Monte Carlo Retirement Calculators; James Welch, May 2008
  3. When to Go Against Your Gut ; Bryan Olsen; Schwab Investing InsightsŪ; August 21, 2008
  4. Flaws of Averages and What to Do About It. ; Dr. Sam Savage; Stanford University
August 21, 2008

© 2008, James S. Welch, Jr