Most Popular ArticlesSome Additional Thoughts
September 8, 2009
I applied a number of different strategies, all of which involved annual rebalancing based on Shiller P/Es, and ran each strategy for overlapping 10-year periods beginning in 1928. The "base strategy" (1) on the chart is the one I used in the September 1 article. The particular algorithm involves holding 100% stocks at P/Es 7 or 8, 75% at 12, 50% at 17, 25% at 24, and zero above 33. The exact formula is: % Stocks = -.7213*(ln(P/E)-ln(17))+.4537. The formula uses logarithms to reflect the much larger historic range of above average values vs. below average values, and was calibrated so stock holdings would average 50%. Values are restricted to 0% - 100%.
Strategy 2 starts with the base strategy and simply moves all-the stock allocations higher so that the allocation to stocks averages 75% instead of 50%. Since stock returns are higher than bond returns, this increases expected returns, but also adds more than 1% to the 10-year standard deviation. The efficiency measure falls short of what we were able to achieve with the base strategy.
For strategy 3 I've tried an all-or-nothing approach—100% stocks when the P/E is below 16.5 and zero when it's above. The P/E 16.5 was chosen so that stock holdings would average 50% like in the base strategy, but the efficiency falls short of the base.
Strategies 4-7 try various approaches using a P/E of 12 as a break point. I chose 12 because it was significantly below the average P/E of 17, but not so low that it rarely occurred. Note that the 80% and 100% strategies did best on the efficiency measures. (The three strategies with the best efficiency ratings are shown in bold.) The 120% and 160% strategies, which would involve leveraging to boost stock holdings over 100%, did increase expected returns, but knocked down efficiency.
I could have tested using thresholds other than a P/E of 12 and likely found some improved results, but I would be suspicious of data mining effects. I expect that there are a number of strategies like numbers 1, 4 and 5 that can significantly raise expected returns (although not to the all-stock level) and keep the risk level close to the all-bond level. I doubt there are any viable "magic bullet" strategies that can dramatically raise returns without increasing risk.
These results are based on running strategies for 10-year periods. Shiller P/Es are more predictive of future returns over longer time horizons. These R-squared values show how much of the variation in return is explained by the beginning P/E: 1-year (.08), 5-year (.32), 10-year (.48), 20-year (.59). At one year the P/E explains less than 10% of the return, but by 10 years it's close to 50% and climbing
Planners should be mindful of the Shiller P/Es in making long-term investment recommendations, but there isn’t much to be gained by too much refinement in allocation strategies.
Chart 1:Asset Allocation Experiments Based on the Shiller P/Es
(using data from 1928-2008)
|
Allocation |
ROR |
10 Yr. Std. Dev. |
One Yr. Std. Dev. |
Added Return |
Added Risk |
Efficiency |
|
All Bond Portfolio |
5.16% |
3.30% |
7.61% |
0.00% |
0.00% |
0.00% |
|
All Stock Portfolio |
10.81% |
5.64% |
20.39% |
5.65% |
2.34% |
0.97% |
1 |
Base Strategy |
9.67% |
3.33% |
12.54% |
4.51% |
0.03% |
4.45% |
2 |
Raise Average Stock Allocation |
10.81% |
4.40% |
16.43% |
5.65% |
1.10% |
3.45% |
3 |
100% Stocks when P/E<16.5, |
10.15% |
4.83% |
16.35% |
4.99% |
1.53% |
1.93% |
4 |
80% Stocks when P/E<12, |
9.53% |
3.25% |
12.04% |
4.37% |
-0.05% |
4.47% |
5 |
100% Stocks when P/E<12, |
10.16% |
3.57% |
13.32% |
5.00% |
0.27% |
4.46% |
6 |
120% Stocks when P/E<12, |
10.75% |
4.22% |
15.13% |
5.59% |
0.92% |
3.75% |
7 |
160% Stocks when P/E<12, |
11.76% |
6.02% |
19.77% |
6.60% |
2.72% |
1.16% |
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