More on Rebalancing
Posted: Thu Feb 17, 2005 12:52 pm
I continue to look at what the data show about rebalancing. My question is this: Is rebalancing portfolio allocations a good idea? In my earlier study, Hobby Stocks and Rebalancing, the answer was NO! except under the most stressful conditions. Rebalancing took away far more from the upside than it gave back in the form of downside protection.
This time I took matters to an extreme. I investigated the rebalancing of mirror portfolios. I looked at both the distribution and accumulation phases.
This is what I mean by mirror portfolios: Portfolio A had 80% stocks and 20% Treasury Bills while Portfolio B had 20% stocks and 80% Treasury Bills.
I rebalanced each individual portfolio annually.
I allowed the two portfolios to grow independently. I compared this to what happens if the two individual portfolios are rebalanced as well.
The Portfolios
Portfolio A consisted of 80% stocks and 20% Treasury Bills. It was rebalanced annually. Stocks were represented by the S&P500 index.
Portfolio B consisted of 20% stocks and 80% Treasury Bills. It was rebalanced annually. Stocks were represented by the S&P500 index.
The Conditions
I started with an initial balance of $100000. I set the investment expenses at 0.20%.
I allocated 50% of the initial balance to Portfolio A and 50% to Portfolio B.
For the distribution phase, I withdrew 3%, 4% and 5% of the initial balance (plus inflation) annually from the individual portfolios in proportion to their balances.
For the accumulation phase, I deposited 3%, 4% and 5% of the initial balance (plus inflation) annually to the individual portfolios in proportion to their balances. The calculator treats deposits as negative withdrawals.
I recorded balances of the combined portfolio at year 30 when I rebalanced Portfolios A and B and when I let them grow separately.
Calculator Conditions
I used the Gummy 04 version of the Deluxe Calculator V1.1A08 dated January 28, 2005. This calculator includes a complete set of Gummy's data, which can be entered separately as if they were stocks and commercial paper.
Portfolio A appears as stock holdings and Portfolio B appears as if it were commercial paper.
Here are the key entries:
Portfolio A: Entered as stocks
Portfolio B: Entered as commercial paper
Portfolio A: 80% S&P500 stocks and 20% Treasury Bills
Portfolio B: 20% S&P500 stocks and 80% Treasury Bills
Stock allocation: 50%
Fixed Income Series: commercial paper
Front end/back end?: 50%
Inflation: CPI
Investment expenses: 0.20%
Rebalance? NO!, the basic condition, and YES for making comparisons.
Others: Gummy's Algorithms 1 and 2: NO. Remove gains? NO.
Others: Reinvest Dividends? Yes, 100%. Reinvest Interest? Yes, 100%.
The calculator automatically rebalances the holdings within a portfolio. It offers a choice as to whether to rebalance between the two portfolios.
I examined 30-year historical sequences starting in 1921-1980. Gummy's data are for the years 1928-2000. I used Professor Shiller's S&P500 stock data prior to 1928. I used the stock returns of 2000 for the years 2001-2010. Be cautious about any conclusions based on sequences starting in years 1921-1927 and ending in 2001-2010. (Those 30-year sequences start in 1971-1980.)
Be especially careful about what happens after 2000. The calculator holds separate return sequences for Portfolios A and B. Portfolio A freezes at the year 2000 stock return while Portfolio B freezes at the year 2000 return for commercial paper.
Dollar Allocations
I set the initial balance equal to $100000.
I allocated 50% of this initial balance to portfolio A. This is $50000. I put 80% of this into the S&P500 index and 20% into Treasury Bills.
I allocated 50% of this initial balance to portfolio B. This is $50000. I put 20% of this into the S&P500 index and 80% into Treasury Bills.
Portfolio A started with $40000 in the S&P500 index and $10000 in Treasury Bills.
Portfolio B started with $10000 in the S&P500 index and $40000 in Treasury Bills.
The combination of the two portfolios started out with $50000 in the S&P500 index and $50000 in Treasury Bills.
Tables for the distribution phase
I am including tables of the balances at year 30 with withdrawal rates of 3%, 4% and 5% of the initial balance (plus inflation). All balances are in terms of real dollars. That is, after adjusting for inflation.
I have one table in which portfolios A and B are allowed to grow separately. I have another table in which the 50% / 50% allocation of portfolios A and B are maintained through annual rebalancing.
I have a third table in which I present the differences of the balances with and without rebalancing. Positive numbers indicate a rebalancing bonus. Negative numbers indicate a rebalancing penalty.
[In making these calculations, I substituted zero for any negative balance. This prevents any big losses from distorting the results.]
The fourth table has a 1 whenever the money ran out by year 30 with rebalancing. The fifth table has a 1 whenever the money ran out by year 30 without rebalancing.
[These two tables turn out to be identical except in 1934, 1937, 1938 and 1965. At year 30, the rebalanced portfolios failed in 1934 and 1938, but not the portfolios that were allowed to grow independently. In year 20, the rebalanced portfolios failed in 1937 but not the portfolios that were allowed to grow independently. In contrast, in the 1965 sequence at year 20, the rebalanced portfolio combination still had a positive balance while the portfolios that had been allowed to grow independently were depleted.]
Tables for the accumulation phase
I am including tables of the balances at year 30 with annual deposits of 3%, 4% and 5% of the initial balance (plus inflation). That is, these annual deposits were $3000, $4000 and $5000 plus inflation. All balances are in terms of real dollars (i.e., after adjusting for inflation).
I have one table in which portfolios A and B are allowed to grow separately. I have another table in which the 50% / 50% allocation of portfolios A and B are maintained through annual rebalancing.
I have a third table in which I present the differences of the balances with and without rebalancing. Positive numbers indicate a rebalancing bonus. Negative numbers indicate a rebalancing penalty.
There was no need for the additional tables. There are no failures during accumulation.
Analysis
During the distribution phase, only a few conditions show a rebalancing bonus. Those with a bonus show only a small improvement. The sequences with a rebalancing bonus are those associated with high valuations and times of severe portfolio stress: a few years around 1929 and the entire decade of the 1960s.
Typically, there was a penalty for rebalancing. Typically, it was huge.
This is the same as we have seen before when looking at hobby stocks.
During the accumulation phase, all of the sequences favored leaving the two portfolios alone except for the years 1977-1980. This special behavior for the 1977-1980 sequences is probably an artifact of the calculator. These sequences end at year 30 in 2007-2010. The calculator returns for Portfolio A and Portfolio B have different dummy values in 2001-2010.
Conclusions
During distribution, the message remains unchanged. Except in times of severe portfolio stress, let the two portfolios grow independently.
This happens to be a time of severe portfolio stress. Today's valuations are higher than during the Great Depression and during the 1960s (and stagflation).
For those who are still in the accumulation phase, the message is simpler. Allow the two portfolios to grow independently.
Have fun.
John R.
This time I took matters to an extreme. I investigated the rebalancing of mirror portfolios. I looked at both the distribution and accumulation phases.
This is what I mean by mirror portfolios: Portfolio A had 80% stocks and 20% Treasury Bills while Portfolio B had 20% stocks and 80% Treasury Bills.
I rebalanced each individual portfolio annually.
I allowed the two portfolios to grow independently. I compared this to what happens if the two individual portfolios are rebalanced as well.
The Portfolios
Portfolio A consisted of 80% stocks and 20% Treasury Bills. It was rebalanced annually. Stocks were represented by the S&P500 index.
Portfolio B consisted of 20% stocks and 80% Treasury Bills. It was rebalanced annually. Stocks were represented by the S&P500 index.
The Conditions
I started with an initial balance of $100000. I set the investment expenses at 0.20%.
I allocated 50% of the initial balance to Portfolio A and 50% to Portfolio B.
For the distribution phase, I withdrew 3%, 4% and 5% of the initial balance (plus inflation) annually from the individual portfolios in proportion to their balances.
For the accumulation phase, I deposited 3%, 4% and 5% of the initial balance (plus inflation) annually to the individual portfolios in proportion to their balances. The calculator treats deposits as negative withdrawals.
I recorded balances of the combined portfolio at year 30 when I rebalanced Portfolios A and B and when I let them grow separately.
Calculator Conditions
I used the Gummy 04 version of the Deluxe Calculator V1.1A08 dated January 28, 2005. This calculator includes a complete set of Gummy's data, which can be entered separately as if they were stocks and commercial paper.
Portfolio A appears as stock holdings and Portfolio B appears as if it were commercial paper.
Here are the key entries:
Portfolio A: Entered as stocks
Portfolio B: Entered as commercial paper
Portfolio A: 80% S&P500 stocks and 20% Treasury Bills
Portfolio B: 20% S&P500 stocks and 80% Treasury Bills
Stock allocation: 50%
Fixed Income Series: commercial paper
Front end/back end?: 50%
Inflation: CPI
Investment expenses: 0.20%
Rebalance? NO!, the basic condition, and YES for making comparisons.
Others: Gummy's Algorithms 1 and 2: NO. Remove gains? NO.
Others: Reinvest Dividends? Yes, 100%. Reinvest Interest? Yes, 100%.
The calculator automatically rebalances the holdings within a portfolio. It offers a choice as to whether to rebalance between the two portfolios.
I examined 30-year historical sequences starting in 1921-1980. Gummy's data are for the years 1928-2000. I used Professor Shiller's S&P500 stock data prior to 1928. I used the stock returns of 2000 for the years 2001-2010. Be cautious about any conclusions based on sequences starting in years 1921-1927 and ending in 2001-2010. (Those 30-year sequences start in 1971-1980.)
Be especially careful about what happens after 2000. The calculator holds separate return sequences for Portfolios A and B. Portfolio A freezes at the year 2000 stock return while Portfolio B freezes at the year 2000 return for commercial paper.
Dollar Allocations
I set the initial balance equal to $100000.
I allocated 50% of this initial balance to portfolio A. This is $50000. I put 80% of this into the S&P500 index and 20% into Treasury Bills.
I allocated 50% of this initial balance to portfolio B. This is $50000. I put 20% of this into the S&P500 index and 80% into Treasury Bills.
Portfolio A started with $40000 in the S&P500 index and $10000 in Treasury Bills.
Portfolio B started with $10000 in the S&P500 index and $40000 in Treasury Bills.
The combination of the two portfolios started out with $50000 in the S&P500 index and $50000 in Treasury Bills.
Tables for the distribution phase
I am including tables of the balances at year 30 with withdrawal rates of 3%, 4% and 5% of the initial balance (plus inflation). All balances are in terms of real dollars. That is, after adjusting for inflation.
I have one table in which portfolios A and B are allowed to grow separately. I have another table in which the 50% / 50% allocation of portfolios A and B are maintained through annual rebalancing.
I have a third table in which I present the differences of the balances with and without rebalancing. Positive numbers indicate a rebalancing bonus. Negative numbers indicate a rebalancing penalty.
[In making these calculations, I substituted zero for any negative balance. This prevents any big losses from distorting the results.]
The fourth table has a 1 whenever the money ran out by year 30 with rebalancing. The fifth table has a 1 whenever the money ran out by year 30 without rebalancing.
[These two tables turn out to be identical except in 1934, 1937, 1938 and 1965. At year 30, the rebalanced portfolios failed in 1934 and 1938, but not the portfolios that were allowed to grow independently. In year 20, the rebalanced portfolios failed in 1937 but not the portfolios that were allowed to grow independently. In contrast, in the 1965 sequence at year 20, the rebalanced portfolio combination still had a positive balance while the portfolios that had been allowed to grow independently were depleted.]
Tables for the accumulation phase
I am including tables of the balances at year 30 with annual deposits of 3%, 4% and 5% of the initial balance (plus inflation). That is, these annual deposits were $3000, $4000 and $5000 plus inflation. All balances are in terms of real dollars (i.e., after adjusting for inflation).
I have one table in which portfolios A and B are allowed to grow separately. I have another table in which the 50% / 50% allocation of portfolios A and B are maintained through annual rebalancing.
I have a third table in which I present the differences of the balances with and without rebalancing. Positive numbers indicate a rebalancing bonus. Negative numbers indicate a rebalancing penalty.
There was no need for the additional tables. There are no failures during accumulation.
Analysis
During the distribution phase, only a few conditions show a rebalancing bonus. Those with a bonus show only a small improvement. The sequences with a rebalancing bonus are those associated with high valuations and times of severe portfolio stress: a few years around 1929 and the entire decade of the 1960s.
Typically, there was a penalty for rebalancing. Typically, it was huge.
This is the same as we have seen before when looking at hobby stocks.
During the accumulation phase, all of the sequences favored leaving the two portfolios alone except for the years 1977-1980. This special behavior for the 1977-1980 sequences is probably an artifact of the calculator. These sequences end at year 30 in 2007-2010. The calculator returns for Portfolio A and Portfolio B have different dummy values in 2001-2010.
Conclusions
During distribution, the message remains unchanged. Except in times of severe portfolio stress, let the two portfolios grow independently.
This happens to be a time of severe portfolio stress. Today's valuations are higher than during the Great Depression and during the 1960s (and stagflation).
For those who are still in the accumulation phase, the message is simpler. Allow the two portfolios to grow independently.
Have fun.
John R.