From Chapter 3
Posted: Sat May 15, 2004 7:32 am
In Chapter 3 of Common Sense on Mutual Funds, our featured book at the NoFeeBoards, John Bogle addresses asset allocation. His advice is worth reading. He goes into detail about risk, reward, cost and time.
I had originally wanted to address the basic concept of asset allocation and what it really provides. As in the past, I found a lack of clarity although John Bogle, to his credit, was very forthcoming in what he said.
Asset allocation, we have been told, explains a very large percentage of the variation in the returns among professional investors. But what does this mean? I don't know for sure. I think that it has to do with the variance (or standard deviation) of returns, but not with the returns themselves.
For example, if you had 100 fund manages investing only in the money market, their returns should be very close to each other. On the other hand, if you had 100 fund managers all invested totally in stocks, you would expect quite a bit of variation in their returns (along with a larger variance or standard deviation). If you had 100 fund managers all invested 50% in the money market and 50% in stocks, you would expect an intermediate amount of variation (i.e., an intermediate size of the variance or standard deviation). If you had 100 fund managers, each with his own allocation between the money market and stocks, the amount of variation would vary with the allocation percentages. Those with higher money market allocations would have very similar, tightly clustered returns. Those with higher stock allocations would have returns that differed from each other more and more as their stock allocations increased.
Notice that there is no mention of the typical or average returns, just the amount of variation.
Again, I am not sure. This is what I think people have actually discovered about asset allocation. This is far different from what many claim.
Instead, I will address the rebalancing bonus. Or, more precisely, the fallacy of a rebalancing bonus. What has actually been established is almost always misstated.
The Rebalancing Fallacy
I strongly recommend that you read Gummy's tutorial about the Rebalancing Bonus. It is an eye opener.
http://home.golden.net/~pjponzo/rebalancing-bonus.htm
This is what rebalancing actually does. If you start out with two investments and they produce annualized returns of P and Q and if you rebalance your portfolio to maintain a constant fraction x (of the overall portfolio amount) in the first investment and y in the other (with x + y = 1), the combined portfolio can provide a return bigger that [x*P+y*Q]. If it does, the improvement is called the rebalancing bonus. Whether there is a rebalancing bonus depends upon how well correlated the investments happen to be.
What rebalancing does not guarantee is a return bigger than what you would have had if you had not rebalanced. That is, if you start out with allocations of x and y and leave everything alone, you can end up with a much bigger return. The better investment would gradually increase its allocation percentage. Your final portfolio balance could be larger, much larger.
[In the special case that the two investments have the same annualized returns (statistically) and they are not perfectly correlated, an improvement can be guaranteed (in a statistical sense).]
In particular, it makes no sense to invest in an underperforming asset simply because it is uncorrelated with the rest of your portfolio. There can a good reason to do so such as an uncertainty as to when you will make withdrawals. The rebalancing bonus is not such a reason.
Rebalancing and Safe Withdrawal Rates
I have constructed tables of 30-Year Historical Database Rates for retirements beginning in 1871-1980 under four test conditions. One pair is for a portfolio consisting of 50% stocks and 50% commercial paper. I call them HDBR50N without rebalancing and HDBR50 with annual rebalancing. The other pair is for a portfolio consisting of 80% stocks and 20% commercial paper. I refer to them as HDBR80N without rebalancing and HDBR80 with annual rebalancing.
I collected data using my latest update of the Retire Early Safe Withdrawal Calculator version 1.61 from 7 November 2002. All of these conditions can be run on the unmodified calculator. It is just that data reduction would be harder.
In all cases the initial portfolio balance was $100 000 to reduce the effects of rounding errors. Expenses were 0.20%. Withdrawals were adjusted annually to match inflation according to the CPI. I left the other conditions at their default settings. A portfolio survived for the entire 30-Year period at the Historical Database Rate. It failed (became negative) before the end of the 30-Year period when withdrawals were increased by 0.1%.
Results
HDBR50N and HDBR50 produced similar results. On average, HDBR50N (without rebalancing) did slightly better than HDBR50 (with rebalancing). The mean difference was 0.12% with a standard deviation of 0.388% (with 109 degrees of freedom). The lowest Historical Database Rate for HDBR50N (without rebalancing) was 4.0% in 1966. The lowest Historical Database Rate for HDBR50 (with rebalancing) was 3.9% in 1937. The highest Historical Database Rate for HDBR50N was 9.3% in 1879. The highest Historical Database Rate for HDBR50 was 9.3% in the years 1871, 1872 and 1879.
There was only one year that HDBR50N did worse than HDBR50 by as much as 0.3%. It was 1928 and the Historical Database Rates were 5.2% and 5.5%, respectively. The most that HDBR50N did better than HDBR50 was 1.5% in 1942. The Historical Database Rates in 1942 were 7.7% and 6.2%, respectively.
HDBR80N and HDBR80 produced similar results. On average, HDBR80N (without rebalancing) did slightly better than HDBR80 (with rebalancing). The mean difference was 0.04% with a standard deviation of 0.226% (with 109 degrees of freedom). The lowest Historical Database Rate for HDBR80N (without rebalancing) was 3.9% in 1966. The lowest Historical Database Rate for HDBR80 (with rebalancing) was also 3.9% in 1966. The highest Historical Database Rate for HDBR80N was 10.9% in both 1948 and 1950. The highest Historical Database Rate for HDBR80 was 10.4% in 1879.
There were only two years that HDBR80N did worse than HDBR80 by as much as 0.3%. They were 1926 and 1927. The Historical Database Rates for 1926 were 7.2% and 7.5% for HDBR80N and HDBR80, respectively. For 1927 they were 6.9% and 7.2% for HDBR80N and HDBR80, respectively. The most that HDBR80N did better than HDBR80 was 0.8% in 1942. The Historical Database Rates in 1942 were 9.8% and 9.0%, respectively.
Conclusions
In terms of the investment options examined on the calculator (stocks and commercial paper), annual rebalancing actually degraded Historical Database Rates (by several measures). It limited the growth of stock holdings when conditions were favorable. When rebalancing helped, it provided only a small improvement as seen in the Historical Database Rate comparisons.
Using Gummy's choice of words, we see Rebalancing Deficits, not bonuses.
There can be reasons for rebalancing in spite of these observations. The obvious situation is when stocks are greatly overvalued. The key is having a reliable method of identifying such a situation which also avoids trading excessively. John Bogle included a few remarks about such situations.
Have fun.
John R.
I had originally wanted to address the basic concept of asset allocation and what it really provides. As in the past, I found a lack of clarity although John Bogle, to his credit, was very forthcoming in what he said.
Asset allocation, we have been told, explains a very large percentage of the variation in the returns among professional investors. But what does this mean? I don't know for sure. I think that it has to do with the variance (or standard deviation) of returns, but not with the returns themselves.
For example, if you had 100 fund manages investing only in the money market, their returns should be very close to each other. On the other hand, if you had 100 fund managers all invested totally in stocks, you would expect quite a bit of variation in their returns (along with a larger variance or standard deviation). If you had 100 fund managers all invested 50% in the money market and 50% in stocks, you would expect an intermediate amount of variation (i.e., an intermediate size of the variance or standard deviation). If you had 100 fund managers, each with his own allocation between the money market and stocks, the amount of variation would vary with the allocation percentages. Those with higher money market allocations would have very similar, tightly clustered returns. Those with higher stock allocations would have returns that differed from each other more and more as their stock allocations increased.
Notice that there is no mention of the typical or average returns, just the amount of variation.
Again, I am not sure. This is what I think people have actually discovered about asset allocation. This is far different from what many claim.
Instead, I will address the rebalancing bonus. Or, more precisely, the fallacy of a rebalancing bonus. What has actually been established is almost always misstated.
The Rebalancing Fallacy
I strongly recommend that you read Gummy's tutorial about the Rebalancing Bonus. It is an eye opener.
http://home.golden.net/~pjponzo/rebalancing-bonus.htm
This is what rebalancing actually does. If you start out with two investments and they produce annualized returns of P and Q and if you rebalance your portfolio to maintain a constant fraction x (of the overall portfolio amount) in the first investment and y in the other (with x + y = 1), the combined portfolio can provide a return bigger that [x*P+y*Q]. If it does, the improvement is called the rebalancing bonus. Whether there is a rebalancing bonus depends upon how well correlated the investments happen to be.
What rebalancing does not guarantee is a return bigger than what you would have had if you had not rebalanced. That is, if you start out with allocations of x and y and leave everything alone, you can end up with a much bigger return. The better investment would gradually increase its allocation percentage. Your final portfolio balance could be larger, much larger.
[In the special case that the two investments have the same annualized returns (statistically) and they are not perfectly correlated, an improvement can be guaranteed (in a statistical sense).]
In particular, it makes no sense to invest in an underperforming asset simply because it is uncorrelated with the rest of your portfolio. There can a good reason to do so such as an uncertainty as to when you will make withdrawals. The rebalancing bonus is not such a reason.
Rebalancing and Safe Withdrawal Rates
I have constructed tables of 30-Year Historical Database Rates for retirements beginning in 1871-1980 under four test conditions. One pair is for a portfolio consisting of 50% stocks and 50% commercial paper. I call them HDBR50N without rebalancing and HDBR50 with annual rebalancing. The other pair is for a portfolio consisting of 80% stocks and 20% commercial paper. I refer to them as HDBR80N without rebalancing and HDBR80 with annual rebalancing.
I collected data using my latest update of the Retire Early Safe Withdrawal Calculator version 1.61 from 7 November 2002. All of these conditions can be run on the unmodified calculator. It is just that data reduction would be harder.
In all cases the initial portfolio balance was $100 000 to reduce the effects of rounding errors. Expenses were 0.20%. Withdrawals were adjusted annually to match inflation according to the CPI. I left the other conditions at their default settings. A portfolio survived for the entire 30-Year period at the Historical Database Rate. It failed (became negative) before the end of the 30-Year period when withdrawals were increased by 0.1%.
Results
HDBR50N and HDBR50 produced similar results. On average, HDBR50N (without rebalancing) did slightly better than HDBR50 (with rebalancing). The mean difference was 0.12% with a standard deviation of 0.388% (with 109 degrees of freedom). The lowest Historical Database Rate for HDBR50N (without rebalancing) was 4.0% in 1966. The lowest Historical Database Rate for HDBR50 (with rebalancing) was 3.9% in 1937. The highest Historical Database Rate for HDBR50N was 9.3% in 1879. The highest Historical Database Rate for HDBR50 was 9.3% in the years 1871, 1872 and 1879.
There was only one year that HDBR50N did worse than HDBR50 by as much as 0.3%. It was 1928 and the Historical Database Rates were 5.2% and 5.5%, respectively. The most that HDBR50N did better than HDBR50 was 1.5% in 1942. The Historical Database Rates in 1942 were 7.7% and 6.2%, respectively.
HDBR80N and HDBR80 produced similar results. On average, HDBR80N (without rebalancing) did slightly better than HDBR80 (with rebalancing). The mean difference was 0.04% with a standard deviation of 0.226% (with 109 degrees of freedom). The lowest Historical Database Rate for HDBR80N (without rebalancing) was 3.9% in 1966. The lowest Historical Database Rate for HDBR80 (with rebalancing) was also 3.9% in 1966. The highest Historical Database Rate for HDBR80N was 10.9% in both 1948 and 1950. The highest Historical Database Rate for HDBR80 was 10.4% in 1879.
There were only two years that HDBR80N did worse than HDBR80 by as much as 0.3%. They were 1926 and 1927. The Historical Database Rates for 1926 were 7.2% and 7.5% for HDBR80N and HDBR80, respectively. For 1927 they were 6.9% and 7.2% for HDBR80N and HDBR80, respectively. The most that HDBR80N did better than HDBR80 was 0.8% in 1942. The Historical Database Rates in 1942 were 9.8% and 9.0%, respectively.
Conclusions
In terms of the investment options examined on the calculator (stocks and commercial paper), annual rebalancing actually degraded Historical Database Rates (by several measures). It limited the growth of stock holdings when conditions were favorable. When rebalancing helped, it provided only a small improvement as seen in the Historical Database Rate comparisons.
Using Gummy's choice of words, we see Rebalancing Deficits, not bonuses.
There can be reasons for rebalancing in spite of these observations. The obvious situation is when stocks are greatly overvalued. The key is having a reliable method of identifying such a situation which also avoids trading excessively. John Bogle included a few remarks about such situations.
Have fun.
John R.