Wednesday, March 16, 2011

Long-Term Conservative Investors and Valuation-Based Asset Allocation Strategies

My thoughts and concerns are with everyone affected by the earthquake and tsunami in Japan. I live in Tokyo and would like to stay here and support Japan, but as my wife is 3-months pregnant and we have a 3-year old son, we decided it would be best to travel to the U.S. for a few weeks. I wish and pray that everything will be under control soon and and Japan can experience no further losses of life.  I hope I can contribute to helping Japan rise like a Phoenix once again.

I have been working on several research papers about valuations-based asset allocation, which I now realize I am not going to be able to finish properly until after I take the CFA Level 3 exam in June.  I had been rushing to try to finish them, but I should just take the time to do it right instead of rushing. Nonetheless, it is frustrating, as the figures and tables are all finished, I just don't have time to write up the results and theoretical background and caveats sufficiently now.  Posting this on my blog will help me to relax and forget about this subject until June when I can finish it properly.

So, I've decided to share some preliminary results now.  I can't provide a full write-up, but to better understand the tables, please see my research paper, "Revisiting the Fisher and Statman Study on Market Timing".

This study is about comparing fixed asset allocation strategies to valuation-based asset allocation strategies in the U.S.

Data is from Robert Shiller's webpage. The following figure shows the path of PE10 in the U.S. as well as the real equity premiums (real stock returns - real bill returns) for each year since 1881. This figure also shows the decision rule bounds for an investor using the "Graham and Dodd" strategy, which is to use their normal asset allocation (same as used by the fixed allocation portfolio) when PE10 is inside the bounds, and switch to low stocks when PE10 is high, and high stocks when PE10 is low.  Those bounds are 4/3 and 2/3 of the rolling medians PE10 values.



The next table compares a fixed 50/50 allocation to a number of different valuation-based strategies. Again, my research paper, "Revisiting the Fisher and Statman Study on Market Timing", explains what all these measures are.



Here is some explanation about what the abbreviations about strategies mean.


Cliff Strategy
The Cliff strategy, most of these strategies were named by Bennett (x), is the strategy frequently used in market-timing studies. There are two asset allocations, one for when markets are overvalued, and one for when markets are undervalued.  Market-timing studies tend to use 100/0 and 0/100 for these two allocations, but these values could be anything.  The high stock allocation will be used in years when the PE10 falls below its historical average (either the rolling mean or rolling median value) at the beginning of the year. The low stock allocation is used when PE10 is above this average.
High-Medium-Low (HML) Strategy The remainder of the decision rules use three allocation choices (high stocks, median stocks, and low stocks) instead of two. First, the high-medium-low strategy uses the distribution of past PE10 values up to each subsequent point in history, and determines that the market is over-valued when PE10 is in the top-third of this historical distribution at the beginning of the year, fairly valued in the middle third, and undervalued when in the bottom third. Asset allocation is set to the low, medium, and high stock allocations in these cases.
Interquartile Range (IQR) Strategy  I will also consider the evolving interquartile range of PE10 ratios between 1881 and each date in the historical period.  When PE10 enters the top quartile of for the historical data up to that point, the market is overvalued, and when PE10 falls into the bottom quartile, the market is undervalued.  It is fairly valued when in the middle two quartiles. This strategy causes the investor to spend more time with their medium asset allocation than the previous strategies.
Standard Deviation (SD) Strategy The market is considered as fairly valued when the start of year value of PE10 falls within one standard deviation of its fair value measure (rolling median or rolling mean) up to that point in history. When PE10 is more than one standard deviation from its average, the market is either undervalued (low PE10) or overvalued (high PE10). Figure 2 shows the SD strategy for rolling medians, and by 2010 the bounds for this strategy were PE10 values of approximately 9 and 22.
Graham and Dodd (G & D) Strategy Finally, Graham and Dodd (1940) suggested that the medium allocation be maintained as long as PE10 falls within a band between 2/3 and 4/3 of its historical average, and only switches to more extreme allocations when PE10 moves beyond these bounds. Again, a low stock allocation is used when PE10 rises high, and a high stock allocation is used when PE10 is low. Figure 2 shows that except for the last several years when the SD strategy overtook it, the Graham and Dodd strategy had the most extreme bounds, and therefore spent the most time at the medium allocation.
Halfway Rule Finally, the halfway rule is not a specific strategy, but rather an additional feature that may be used to modify any of the 3-allocation strategies. The strategies above would switch from a high or low allocation to the median allocation, whenever PE10 moved across the bound into the medium range. But with the halfway rule, the extreme allocation will be maintained until PE10 returned all the way to its average value (rolling mean or rolling median). This implies a stronger commitment to the idea of mean reversion, and it will cause the investor to maintain high or low stock allocations more frequently. It will also reduce the total number of asset allocation changes. This rule was a popular feature in the stock formula plans of the past as described by Jenkins (1961) and Tomlinson (x).


What this table suggests to me is that valuation-based strategies can still provide better risk-adjusted returns to a fixed 50/50 strategy that shares the same ex-ante average stock allocation. Risk aversion of 4 or 5 is typically assumed for conservative investors. For all these realistic risk aversion coefficients, the 12 valuation-based strategies provide superior risk-adjusted returns to the fixed 50/50 allocation. 

Even more, I will add my Table 1 below, which can be used to see that all 12 valuation-based strategies provide superior risk-adjusted returns compared to any fixed asset allocation strategies for risk aversion of 2, 3, 4, or 5.  Only the most aggressive investors with risk aversion of 1 would find some more aggressive fixed allocation strategies to be better.  But, one can easily design more aggressive valuation-based strategies to beat those.  The strategies in the table above are fairly conservative.  Again please see my  paper, "Revisiting the Fisher and Statman Study on Market Timing", explains what all these performance measures mean.



Finally, the next figure shows the results for rolling 30-year periods, which will be more important for actual investors than what happened over the whole time period.  This is important as well, because, valuation-based strategies performed very well during the Great Depression, and it is important that conclusions over the entire historical period are not based solely on this limited portion of the historical record. Obviously, people reducing stock allocations during the 1980s and 1990s would trail the fixed 50/50 allocation, but looking at the figure, it is hard to say that valuation-based strategies didn't work. 

 
Figure 4 presents results for the rolling periods analysis, comparing the 50/50 fixed allocation strategy to the valuation-based strategy of 25-50-75 using the Graham and Dodd decision rule based on rolling medians central values and without the use of the halfway rule. The first portion of the figure compares the wealth accumulations for the 110 rolling 30-year periods for careers beginning between 1871 and 1980, and ending between 1900 and 2009. VBA provides as much or more (defined as VBA provides more than 99 percent of the wealth provided by FA) in 99 of the 110 rolling periods.  As indicated in the figure, the years in which FA outperformed occurred from 1997 through 2007.
   
The second portion of the figure shows the time path for the asset allocation of each strategy. Between 1871 and 1914, both strategies shared the same allocation in every year except 1898. This explains why the wealth accumulations were so close during the early part of the historical period. Between 1915 and 1944, the asset allocation does change rather frequently, and often to the benefit of VBA as careers ending between the mid-1920s and 1960 show strong outperformance of VBA compared to the FA strategy. For 1944 through 1961, both strategies share the same allocation. For 6 years in the 1960s, VBA used a lower stock allocation, and from the mid-1970s to mid-1980s, VBA tended toward a higher stock allocation.  From 1985 through 1992, the allocations were again together, and then during the market boom of the 1990s, VBA used the lower stock allocation for all years between 1993 and 2008, except for 1995. Because the unprecedented market boom sent PE10 up to its highest levels ever in January 2000, and the VBA strategy used a lower stock allocation particularly in 1996-1999 when the difference between real stock and bill returns exceeded 10 percent for 4 consecutive years, this helps explain the underperformance for VBA in these years.

The third portion of Figure 3 shows the sorted distribution of outcomes from the FA strategy with the corresponding wealth provided by the VBA strategy in each case. Together with the top portion of the figure, this provides evidence that VBA was a less risk strategy as well over the rolling periods. In describing more generally about value stocks and growth stocks, Lakonishok, Schleifer, and Vishny (1994) argued, "To be fundamentally riskier, value stocks must underperform glamour stocks with some frequency, and particularly in the states of the world when the marginal utility of wealth is high." The figure shows precisely this. The instances in which FA outperformed tended to be cases when FA produces as much wealth as it ever had in the past, and the underperformance of VBA in this cases does not provide an indication that it is more risky, as it still provided more wealth than the FA strategy had in at least half of the historical cases. The underperformance of VBA in these can be thought of as a price paid for using a lower stock allocation at a time when the stock market continued to soar in spite of high valuations. But this figure does help alleviate the concern that the problem with valuation-based strategies is that an investor is hurt by being kept too long from the stock market. Importantly, VBA did not underperform in the years when both strategies were providing the lowest amounts of wealth, such as around 1920 and 1981.
   
Finally, the bottom portion of the figure provides more detail about outperformance in rolling periods of lengths between 1 and 60 years. The two strategies are considered as "tied" when the difference in wealth accumulations between them is less than 1 percent of the value of the FA strategy's wealth accumulation. Because the strategies share the same asset allocation for large parts of the historical period, about 70 percent of the 1-year rolling periods produced "tied" results. This percentage gradually decreases as the length of the rolling periods increases, such that by 20 years about 25 percent of the rolling periods result in ties, and there are less than 10 percent ties for rolling periods of at least 37 years in length. As for strict outperformance, the FA strategy outperforms in about 10 percent of the cases regardless of the length of rolling periods between 1 and 60 years. Quite strikingly, the VBA strategy does as well or better in about 90 percent of cases regardless of the rolling period length.  Removing the "ties" and considering cases of strict outperformance by the VBA strategy, for 12-year rolling periods VBA strictly outperforms in about 50 percent of cases, and VBA strictly outperforms in about 75 percent of cases for 30-year rolling periods and in about 85 percent of cases for 40-year rolling periods.  Increasing the rolling period length leads to an increased probability that VBA has strictly outperformed FA. Again, the most striking feature of this bottom portion of the figure is that the FA strategy strictly outperforms in only about 10 percent of cases, and the length of rolling periods does not matter for this finding.

There are a lot of caveats for this research, which I will discuss in the full research paper. Much of the delay in producing a final paper, is that I am doing a lot of reading to properly explain caveats.

But the fact that this also worked in Japan does help cover some caveats.

Could Valuation-Based Asset Allocation Strategies Have Worked in Japan?

My thoughts and concerns are with everyone affected by the earthquake and tsunami in Japan. I live in Tokyo and would like to stay here and support Japan, but as my wife is 3-months pregnant and we have a 3-year old son, we decided it would be best to travel to the U.S. for a few weeks. I wish and pray that everything will be under control soon and and Japan can experience no further losses of life.  I hope I can contribute to helping Japan rise like a Phoenix once again.

I have been working on several research papers about valuations-based asset allocation, which I now realize I am not going to be able to finish properly until after I take the CFA Level 3 exam in June.  I had been rushing to try to finish them, but I should just take the time to do it right instead of rushing. Nonetheless, it is frustrating, as the figures and tables are all finished, I just don't have time to write up the results and theoretical background sufficiently now.  Posting this on my blog will help me to relax and forget about this subject until June when I can finish it properly.

So, I've decided to share some preliminary results now.  I can't provide a full write-up, but to better understand the tables, please see my research paper, "Revisiting the Fisher and Statman Study on Market Timing", and to better understand the rolling period figures, please see my blog entry, "Valuation-Informed Indexing - Preliminary Results."

Regarding valuation-based asset allocation strategies, I've seen a number of people say something to the effect of: Well, maybe the worked in the U.S., but what about some place like Japan that has experienced a much crazier roller-coaster ride regarding market valuations?

The point of this paper is to apply various valuation-based strategies that I first tested for the U.S. data, to the case of Japan.  Would valuation-based strategies have worked in Japan?

Though the results are not quite as impressive as with U.S., I think a fair assessment is that conservative investors who had a long-term horizon would have been fine by following valuation-based strategies using Japanese stock returns and Japanese short term bill returns.

Data is from Global Financial Data.  Data for P/E is available since 1956.  Using the stock index data as well, I backed out the data on Japanese earnings.  Then I used the price level data to compute real earnings and real stock index values, so that I could calculate PE10 for Japan in the same way as Shiller did for the US.  PE10 for Japan is available only since 1966 though. The following figure shows the path of PE10 in Japan (almost up to 100 by the start of 1990!) as well as the real equity premiums (real stock returns - real bill returns) for each year since 1966. This figure also shows the decision rule bounds for an investor using the "Graham and Dodd" strategy, which is to use their normal asset allocation (same as used by the fixed allocation portfolio) when PE10 is inside the bounds, and switch to low stocks when PE10 is high, and high stocks when PE10 is low.  Those bounds are 4/3 and 2/3 of the rolling medians PE10 values.



The next table compares a fixed 50/50 allocation to a number of different valuation-based strategies. Again, my research paper, "Revisiting the Fisher and Statman Study on Market Timing", explains what all these measures are.


Here is some explanation about what the abbreviations about strategies mean. Please note, this is from my U.S. paper, so 1881 is replaced by 1966 in Japan's case.  Also, the mentions of figures are about the US, but I won't edit that now.

Cliff Strategy
The Cliff strategy, most of these strategies were named by Bennett (x), is the strategy frequently used in market-timing studies. There are two asset allocations, one for when markets are overvalued, and one for when markets are undervalued.  Market-timing studies tend to use 100/0 and 0/100 for these two allocations, but these values could be anything.  The high stock allocation will be used in years when the PE10 falls below its historical average (either the rolling mean or rolling median value) at the beginning of the year. The low stock allocation is used when PE10 is above this average.
High-Medium-Low (HML) Strategy The remainder of the decision rules use three allocation choices (high stocks, median stocks, and low stocks) instead of two. First, the high-medium-low strategy uses the distribution of past PE10 values up to each subsequent point in history, and determines that the market is over-valued when PE10 is in the top-third of this historical distribution at the beginning of the year, fairly valued in the middle third, and undervalued when in the bottom third. Asset allocation is set to the low, medium, and high stock allocations in these cases.
Interquartile Range (IQR) Strategy  I will also consider the evolving interquartile range of PE10 ratios between 1881 and each date in the historical period.  When PE10 enters the top quartile of for the historical data up to that point, the market is overvalued, and when PE10 falls into the bottom quartile, the market is undervalued.  It is fairly valued when in the middle two quartiles. This strategy causes the investor to spend more time with their medium asset allocation than the previous strategies.
Standard Deviation (SD) Strategy The market is considered as fairly valued when the start of year value of PE10 falls within one standard deviation of its fair value measure (rolling median or rolling mean) up to that point in history. When PE10 is more than one standard deviation from its average, the market is either undervalued (low PE10) or overvalued (high PE10). Figure 2 shows the SD strategy for rolling medians, and by 2010 the bounds for this strategy were PE10 values of approximately 9 and 22.
Graham and Dodd (G & D) Strategy Finally, Graham and Dodd (1940) suggested that the medium allocation be maintained as long as PE10 falls within a band between 2/3 and 4/3 of its historical average, and only switches to more extreme allocations when PE10 moves beyond these bounds. Again, a low stock allocation is used when PE10 rises high, and a high stock allocation is used when PE10 is low. Figure 2 shows that except for the last several years when the SD strategy overtook it, the Graham and Dodd strategy had the most extreme bounds, and therefore spent the most time at the medium allocation.
Halfway Rule Finally, the halfway rule is not a specific strategy, but rather an additional feature that may be used to modify any of the 3-allocation strategies. The strategies above would switch from a high or low allocation to the median allocation, whenever PE10 moved across the bound into the medium range. But with the halfway rule, the extreme allocation will be maintained until PE10 returned all the way to its average value (rolling mean or rolling median). This implies a stronger commitment to the idea of mean reversion, and it will cause the investor to maintain high or low stock allocations more frequently. It will also reduce the total number of asset allocation changes. This rule was a popular feature in the stock formula plans of the past as described by Jenkins (1961) and Tomlinson (x).


What this table suggests to me is that valuation-based strategies can still provide better risk-adjusted returns to a fixed 50/50 strategy that shares the same ex-ante average stock allocation, even in the roller coaster ride of Japan over the last 50-60 years. All 12 valuation-based strategies provided lower standard deviations, higher Sharpe ratios, lower maximum drawdowns, lower downside deviations, higher Sortino ratios, and higher risk-adjusted returns for the utility-based performance measures for all investors except the most aggressive one.  Risk aversion of 4 or 5 is typically assumed for conservative investors.They didn't always provide higher total wealth, and many have a lower information ratio for a comparison with 50/50 as the benchmark.  

Finally, the next figure shows the results for rolling 20-year periods in Japan, which will be more important for actual investors than what happened over the whole time period.  Obviously, people reducing stock allocations during the 1980s run-up would trail the fixed allocation, but looking at the figure, it is hard to say that valuation-based strategies didn't work.