Imperfect Allocation Switching

Research on Safe Withdrawal Rates

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JWR1945
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Imperfect Allocation Switching

Post by JWR1945 »

This is a brief survey of what happens when switching allocations between stocks (i.e., the S&P500 index) and TIPS with a 2.0% interest rate depending upon P/E10 (i.e., the current price of the S&P500 index divided by the average of the last ten years of earnings).

This lets you know the penalty of buying high and selling low as well as the rewards of investing properly.

Procedure

I set up my latest Deluxe Calculator V1.1A07 (which is a modified version of the Retire Early Safe Withdrawal Calculator version 1.61 dated November 7, 2002) for switching allocations between stocks and 2.0% TIPS. I set the expense ratio at 0.20%. I rebalanced all portfolios annually. I selected the CPI for making inflation adjustments.

I determined the highest withdrawal rates that would have survived all 30-year sequences from 1921-1980. [Dummy data are used for 2002-2010.] The precision is 0.1%. That is, there always would have been at least one failure if the withdrawal rate were increased by 0.1%.

I set the P/E10 thresholds to 3-12-20-80. The thresholds of 3 and 80 eliminate the effects of allocations other than the three programmable selections. For the three programmable allocations I selected all possible combinations of 30%, 50% and 70%.

Results

Here are the results. The stock allocations are shown in the order of P/E10 below 12, P/E10 between 12 and 20 and P/E10 above 20. They are in percent although the percentage symbol is not included. The percentages shown are the historical surviving withdrawal rates (i.e., the highest withdrawal rates with no failures within 30-years).

30-30-30 4.3%.
30-30-50 4.1%.
30-30-70 3.7%.
30-50-30 4.1%.
30-50-50 3.8%.
30-50-70 3.5%.
30-70-30 3.8%.
30-70-50 3.5%.
30-70-70 3.2%.

50-30-30 4.5%.
50-30-50 4.4%.
50-30-70 4.3%.
50-50-30 4.3%.
50-50-50 4.2%.
50-50-70 4.1%.
50-70-30 4.1%.
50-70-50 3.9%.
50-70-70 3.8%.

70-30-30 4.7%.
70-30-50 4.6%.
70-30-70 4.5%.
70-50-30 4.5%.
70-50-50 4.4%.
70-50-70 4.3%.
70-70-30 4.2%.
70-70-50 4.1%.
70-70-70 4.0%.

Analysis

I made comparisons with allocations of X-Y-30, X-Y-50 and X-Y-70. In all cases, with X and Y equal to 30% or 50% or 70%, the historical surviving withdrawal rates were highest for X-Y-30, in the middle for X-Y-50 and lowest for X-Y-70. That is, reducing stock allocations always helped when P/E10 was above 20.

This is as expected.

I made comparisons with allocations of 30-X-Y, 50-X-Y and 70-X-Y. In all cases, with X and Y equal to 30% or 50% or 70%, the historical surviving withdrawal rates were lowest for 30-X-Y, in the middle for 50-X-Y and highest for 70-X-Y. That is, increasing stock allocations always helped when P/E10 was below 12.

This is as expected.

I made comparisons with allocations of X-30-Y, X-50-Y and X-70-Y. In all cases, with X and Y equal to 30% or 50% or 70%, the historical surviving withdrawal rates were highest for X-30-Y, in the middle for X-50-Y and lowest for X-70-Y. That is, reducing stock allocations always helped when P/E10 was between 12 and 20.

This is new information. It is consistent with previous results that have favored low stock allocations with P/E10 values in the middle range.

[The previously determined optimal stock allocations when including TIPS were 100-50-30-20-0% with P/E10 thresholds of 9-12-21-24.]

Using these results, I checked the results with the 70-30-30 allocation. It is, in fact, a global maximum, which is what we would expect.

I checked the results with the 30-70-70 allocation. It is, in fact, the global minimum, which is what we would expect.

I checked for interactions. Notice that the spread for allocations of 30-X-Y varies by 0.6% as Y varies from 30% to 70%. The spread for allocations of 50-X-Y varies by 0.2% to 0.3% as Y varies from 30% to 70%. The spread for allocations of 70-X-Y varies by 0.2% as Y varies from 30% to 70%.

This is the interaction:
A low stock allocation when P/E10 is low causes a wider than normal scatter in the results (i.e., historical surviving withdrawal rates).
A higher stock allocation when P/E10 is low produces more consistent results.

Comparisons

Here are the relevant buy-and-hold comparisons.

The allocation combination of 70-30-30 produced the best results. The historical surviving withdrawal rate was 4.7%.

A buy-and-hold allocation of 70% (i.e., 70-70-70) produced a historical surviving withdrawal rate of 4.0%.

A buy-and-hold allocation of 50% (i.e., 50-50-50) produced a historical surviving withdrawal rate of 4.2%.

A buy-and-hold allocation of 30% (i.e., 30-30-30) produced a historical surviving withdrawal rate of 4.3%.

The allocation combination of 30-70-70 produced the worst results. The historical surviving withdrawal rate was 3.2%.

Notice that the average of the best and worst switching allocations is 3.95%. [That is, (4.7+3.2) / 2 = 3.95.] This is slightly worse than the historical surviving withdrawal rates of every one of the buy-and-hold choices.

Summary

Increasing allocations when valuations are favorable and reducing them when allocations are unfavorable produces a substantial benefit compared to maintaining a constant allocation. This is buying low and selling high.

Decreasing allocations when valuations are favorable and increasing allocations when allocations are unfavorable results in a substantial penalty compared to maintaining a constant allocation. This is buying high and selling low.

In the absence of other information, a buy-and-hold strategy produces slightly better results than varying allocations. This is more of a statistical observation than a practical result.

These results are in terms of historical surviving withdrawal rates. The general findings apply to Safe Withdrawal Rates as well. Avoid using these numbers by themselves before adjusting for valuations.

Have fun.

John R.
hocus2004
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Post by hocus2004 »

"The allocation combination of 70-30-30 produced the best results."

I am uneasy with the idea of putting forward a recommendation for an average investor to go with a 30 percent stock allocation at times of moderate valuations. I don't doubt that the numbers say what you report them to say. But I think we are at this point failing to take into account some significant emotional considerations. Stocks offer a strong value proposition at moderate valuation levels. So the possibility of suffering a feeling of regret for going with a 30 percent allocation at moderate valuation levels is not small. I am inclined to think that a 40 percent or 50 percent stock allocation is a better choice at moderate valuation levels. This is of course only a tentative conclusion. I of course remain open to changing my mind on this point as we examine the data from new perspectives. But my thought at this time is that a 30 percent allocation at times of moderate valuation is in at least some circumstances something less than "optimal" for the investor with typical goals and typical financial circumstances.

I am more comfortable with the 30 percent and 70 percent allocations for times of high valuation and low valuation. Depending on what future analyses show, I could imagine favoring allocations of as low as 60 percent at times of low valuation and as low as 20 percent at times of high valuation. There are some aspects of the question that I would like to see more data on. For now, though, my reaction is that the 30 percent and 70 percent allocations for high and low valuations are probably at least somewhere in the right ballpark. The 30 percent allocation for moderate valuations sounds off to me. Ultimately, we have to go with what the data says. But I question whether this number will stand up to intense analytical scrutiny (not because the calculations are wrong, but because there may be assumptions inherent in our current analytical framework that are not the most illuminating ones possible).

It might be interesting to take a look at whether moderate valuations produce better results when the trend in prices is upward rather than downward. Say that in a few years stock prices have gone down to moderate valuation levels. Would you feel confident putting a high percentage of your assets in stocks at that point? I certainly would have a significant stock investment if prices got to moderate levels, but it might be a mistake to go too high with one's allocation, given the historical data showing that extreme prices on the high side often are followed by extreme prices on the low side. Now say that you go a few more years out, and that stocks have hit extreme lows and then started a climb back up. At that point the moderate valuation levels might suggest greater long-term returns. There still would be the possibility of short-term price drops, of course. But if the general trend is upward, it might be that the likelihood of devastating price drops would not be so great.

It may be that the reason why you are getting such low numbers for moderate valuation levels is that your analytical framework is to look for worst-case scenarios and you are picking up worst-case scenarios from the few times in which stocks were coming down from extreme highs to extreme lows. Moderate valuation levels might support reasonable expectations of more appealing long-term results in circumstances in which a trend from extreme high valuations to extreme low valuations was not applicable.
JWR1945
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Post by JWR1945 »

Do not put too much emphasis on the allocations.

I used allocations of 30%-50%-70% simply because they are typical of what we would expect an informed investor to choose from. They are not meant to be optimal. They are meant to be reasonable.

It generally helps to have higher allocations when valuations are low and to cut back when allocations are high. The effects are gradual. It does not mean too much if you change allocations at the "wrong" P/E10 level. Of course, the "right" P/E10 level [going forward] is not known. We expect it to be close to what has happened in the past but not exactly the same.

The best allocations can depend upon a number of factors. The interest rate on the TIPS is one of them. When TIPS have higher interest rates, it makes sense to allocate a little bit more to them. When TIPS have very low interest rates, it make sense to put more money into stocks.

The main message that I was trying to convey is that the advantage of shifting allocations correctly (and against emotions) can be to increase withdrawal rates by 20%. The penalty for doing just the wrong thing (selling after stocks have collapsed) is around 20%. That is quite a swing.

The emotional factor is plus and minus 20% about what studies assume to be typical.

Have fun.

John R.
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