Apportioning Investments

in Proportion to Total Return

How to spread risk in a rational manner

Introduction

Total Return Prediction Results

Quoted total returns provide a way to statistically apportion fund (or stock) investments. While past performance is not a very good predictor of future performance, at least these statistics provide an indicator.

Some years ago, I did a statistical regression study that attempted to predict current performance of mutual funds based upon readily available data that was published six months earlier. In other words, I predicted six months ahead using data from six months earlier, and compared the predictions against the actual values I had from the present, rather than wait six more months to see how the prediction turned out.

Initial performance periods of one, six, twelve, and sixty months were used. The correlation of the prediction with actual results was poor for one, six, and 120 months, fair for twelve months, but best for sixty months. I have not repeated this experiment lately, but longer periods seem better suited for predicting long-term results. Clearly, ten-year performance was not as useful due to changes in the market, the manager, or the fund. I avoid data that contains history back to the Civil War (or even 1960); it is irrelevant to today's changing world.

Optimizing is difficult, since today's performance is not always strongly tied to future results. Published total return results are usually limited to "standard" periods. At least five-year performance is normally reported. At least one newspaper ("Florida Today" in Brevard County, FL) reports one-year, three-year, and five-year total returns recomputed each Tuesday, Wednesday, or Thursday. Your dividends must be used to repurchase shares for the fund total return values to be representative, as dividends are included in total return values that are published.

Apportioning Investments

Total return performance values are like taking two points on a semilog graph and drawing a line through them. (A semi-logarithmic plot has a linear scale for time and a compressed scale for the value, portraying constant rates of change as a straight line.) If slightly different end points are selected, the resultant slope will likely change, and the resultant total return rate will vary. This sensitivity of performance to the end point selection causes uncertainty in the estimate of the slope, which is the rate of return. A volatile equity will have a rapid change of N.A.V. (net asset value), and the rate of return will also be volatile.


A Fortune 500 Company Investment Savings Plan Example

Apportioning of funds to mirror fund total return performance offers a mechanistic approach to investing that is easy to implement. Here's an example of this allocation technique:

Suppose that a retirement savings plan offers an employee a choice of investment in several mutual funds. For certain reasons (reward vs. risk, philosophy), one chooses to use "Growth", "Indexed Equity", and "Equity Income" funds. Assume that the annualized performances over a 4.5-year period are quoted on 12/31/96 to be 11.2%, 16.9%, and 17.1%, respectively. (These are unofficial results; any copying or computation error is mine.)

(Do not apply this technique to negative returns; there would be no reason to invest in a fund that had a zero or negative total return over a long period of a rising market.)

The total of these values is 45.2%. The percentage of funds to be placed in each fund is found by division as

  • 11.2% / 45.2% = 24.7788% for "Growth",
  • 16.9% / 45.2% = 37.3894% for "Indexed Equity", and
  • 17.1% / 45.2% = 37.8319% for "Equity Income".

If the proportioned percentage of a fund falls significantly below the rest of the funds, it contributes little to your total results, but is just as hard to track for tax purposes. One probably should not carry funds that fall below five percent of your total investment. Probably three to six funds of varying volatility, investment type, and company are sufficient. The lowest performance fund should be considered for selling, while another high performing fund might be considered for buying.

If one were investing $100,000 in these three funds, rather than splitting it equally, one could apportion it by the total return performance values over the selected period. These values are then

  • $100,000 x 24.7788% = $24,778.80 for "Growth",
  • $100,000 x 37.3894% = $37,389.40 for "Indexed Equity", and
  • $100,000 x 37.8319% = $37,831.90 for "Equity Income".
These values can be periodically compared to the actual investment balances to make adjustments. In one company's investment savings plan, your changes submitted by the 25th day of a month will be effected by the company on the last working day of that month.

Since the reported performance values are not perfect estimators, the apportioned fund dollar estimates will continually change. Perhaps only a fraction (perhaps 0.3, or 30%) of the indicated adjustment should be rearranged each time. This approach provides a degree of filtering to avoid reacting to every change.

In practice, a fixed minimum dollar amount (perhaps $5000) and/or a percentage of the total could be chosen as a level to actually make changes. Only if the predetermined level is exceeded would the fund investments be changed. Since the strategy is mechanized in a computer algorithm, you may find it easier to go ahead with the changes without agonizing and delaying the decision. Now we'll do a follow-up calculation to see how to continue adjusting the assets spread.

Assume that the annualized performances over a 4.7-year period are quoted on 3/31/97 to be 9.3%, 16.6%, and 16.9%, respectively. (These are unofficial results; any copying or computation error is mine.)

The total of these values is 42.8%. The percentage of funds to be placed in each fund is found as

  • 9.3% / 42.8% = 21.7290% for "Growth",
  • 16.6% / 42.8% = 38.78504% for "Indexed Equity", and
  • 16.9% / 42.8% = 39.485981% for "Equity Income".

If the proportioned percentage of a fund falls significantly below the rest of the funds, it contributes little to your total results, but is just as hard to track for tax purposes. One probably should not carry funds that fall below five percent of your total investment. Probably three to six funds of varying volatility, investment type, and company are sufficient. The lowest performance fund should be considered for selling, while another high performing fund might be considered for buying.

If one were investing $100,000 in these three funds, the estimated values are then

  • $100,000 x 21.7290% = $21,729 for "Growth",
  • $100,000 x 38.78504% = $38,785 for "Indexed Equity", and
  • $100,000 x 39.485981% = $39,486 for "Equity Income".

Comparison of Results

Let's look at the changes that occur in three months (assuming the total investment remained constant):

"Growth" changed from 24.7788% to 21.7290%, or -3.050%.
"Indexed Equity" changed from 37.3894% to 38.78504%, or 1.396%,
"Equity Income" changed from 37.8319% to 39.485981%, or 1.655%.

From these changes, "Growth" appears to be yielding less total return, while "Equity Income" seems to be increasing. This suggests possibly changing the mix of funds if these trends continue.

A Selected Mutual Fund Example

A similar calculation can be done for direct mutual fund (or stock) investment:

In this example, I've picked a few typical, large volume, high growth funds from different investment companies for comparison. Note that the fund must have existed for five years to have five-year performance. Flash-in-the-pan funds are automatically excluded. One-year-wonder managers don't make it here.

Suppose these funds are American Century Ultra, Fidelity Asset Manager, Fidelity Contrafund, Fidelity Magellan, Mutual Series Shares, and Price Science & Technology. The annualized five-year total returns as of 12/12/96 were 16.5%, 12.5%, 20.1%, 17.1%, 19.7%, and 29.3%, respectively.

(If a long-term result is negative, don't even consider that fund!) When these percentages are added to get the total, the estimated allocation may be found by division:

  • 16.5% / 116.0% = 14.22474%,
  • 12.5% / 116.0% = 10.77586%,
  • 20.1% / 116.0% = 17.32759%,
  • 17.9% / 116.0% = 15.43103%,
  • 19.7% / 116.0% = 16.98276%, and
  • 29.3% / 116.0% = 25.25862%.
If one is apportioning $100,000 dollars by this method, the investment money spread is then
  • $14,225 in American Century Ultra,
  • $10,776 in Fidelity Asset Manager,
  • $17,328 in Fidelity Contrafund,
  • $15,431 in Fidelity Magellan,
  • $16,983 in Mutual Series Shares, and
  • $25,259 in Price Science & Technology.

adjusting to the nearest dollar.

Power Allocation Method

If selected funds are to receive investment allocations, the techniques above describe a direct allocation on the total returns you choose. When these are nearly equal, it doesn't matter that one was a percent or so greater than the rest. If they differ by ten percent, one might want to put somewhat more into the best performer. While the past total return reports may not be a perfect estimator of the future performance, slanting the allocation process may be desirable.

One way to do this is to raise the total return fraction to a power (exponent), and make the allocation percentages from these power results. This causes stronger funds (stocks) to receive a higher allocation while lower performers receive less.

The power used determines what the prorating effect will be. If the exponent is selected to be 1.0, there will be no different result than in the straight proration previously described. If one uses 10.0 as an exponent, the magnification effect will be so strong that a statistically insignificant difference in total return will cause an allocation to be almost entirely to the highest total return fund. At present, I suggest an exponent of 4.0, which provides some magnification, but not excessively so.

At a later time, I will insert a numeric example here. **********


From www.geocities.com/WallStreet/3298/apportioning.html

7/27/2004
1