Market timing benefit? Or just pure luck?
Market timing benefit? Or just pure luck?
Recently I'm bored and I played with numbers from Simba's backtesting spreadsheet, just for fun.
I observed something which is puzzling to me:
1. If I invested $1 in US stocks in 1970, it will grow to $112.66 by the end of 2017.
2. If I invested $1 in exUS stocks in 1970, it will grow to $59.39 by the end of 2017.
3. If I invested $0.5 each in US and exUS stocks in 1970, without rebalancing, it will grow to $86.02 by the end of 2017, which is the mean of $112.66 and $59.39.
4. If I invested $0.5 each in US and exUS stocks in 1970, rebalanced yearly, it will grow to $92.04 by the end of 2017, slightly higher than in scenario (3). This is not surprising because you usually expect a little bit of rebalancing benefit for asset classes with similar expected return.
5. This scenario is more tricky. I start with $0.5 each in US and exUS stocks in 1970 again. Instead of rebalancing yearly, I assume that I try to predict the market at the beginning of each year. If I predict that I will be better off rebalancing that year, then I rebalance. Otherwise I don't. However, the probability that I make a correct prediction is only 50%. Under this scenario with Monte Carlo simulation, the $1 invested will grow to about $94.9 on average by the end of 2017. The standard deviation is about $3.
I'm a bit puzzled why doing strategy (5) would lead to outperformance compared to strategy (4). Any explanation?
Off topic: Sorry for my bad English. I'm an international boglehead
I observed something which is puzzling to me:
1. If I invested $1 in US stocks in 1970, it will grow to $112.66 by the end of 2017.
2. If I invested $1 in exUS stocks in 1970, it will grow to $59.39 by the end of 2017.
3. If I invested $0.5 each in US and exUS stocks in 1970, without rebalancing, it will grow to $86.02 by the end of 2017, which is the mean of $112.66 and $59.39.
4. If I invested $0.5 each in US and exUS stocks in 1970, rebalanced yearly, it will grow to $92.04 by the end of 2017, slightly higher than in scenario (3). This is not surprising because you usually expect a little bit of rebalancing benefit for asset classes with similar expected return.
5. This scenario is more tricky. I start with $0.5 each in US and exUS stocks in 1970 again. Instead of rebalancing yearly, I assume that I try to predict the market at the beginning of each year. If I predict that I will be better off rebalancing that year, then I rebalance. Otherwise I don't. However, the probability that I make a correct prediction is only 50%. Under this scenario with Monte Carlo simulation, the $1 invested will grow to about $94.9 on average by the end of 2017. The standard deviation is about $3.
I'm a bit puzzled why doing strategy (5) would lead to outperformance compared to strategy (4). Any explanation?
Off topic: Sorry for my bad English. I'm an international boglehead
Last edited by greenhill on Tue Jul 17, 2018 8:39 am, edited 1 time in total.

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Re: Market timing benefit? Or just pure luck?
Suspect this is a product of momentum trend in underlying data?greenhill wrote: ↑Tue Jul 17, 2018 1:25 amRecently I'm bored and I played with numbers from Simba's backtesting spreadsheet, just for fun.
I observed something which is puzzling to me:
1. If I invested $1 in US stocks in 1970, it will grow to $112.66 by the end of 2017.
2. If I invested $1 in exUS stocks in 1970, it will grow to $59.39 by the end of 2017.
3. If I invested $0.5 each in US and exUS stocks in 1970, without rebalancing, it will grow to $86.02 by the end of 2017, which is the mean of $112.66 and $59.39.
4. If I invested $0.5 each in US and exUS stocks in 1970, rebalanced yearly, it will grow to $92.04 by the end of 2017, slightly higher than in scenario (3). This is not surprising because you usually expect a little bit of rebalancing benefit for asset classes with similar expected return.
5. This scenario is more tricky. I start with $0.5 each in US and exUS stocks in 1970 again. Instead of rebalancing yearly, I assume that I try to predict the market at the beginning of each year. If I predict that I will be better off rebalancing that year, then I rebalance. Otherwise I don't. However, the probability that I make a correct prediction is only 50%. Under this scenario with Monte Carlo simulation, the $1 invested will grow to about $94.9 on average by the end of 2017. The standard deviation is about $3.
I'm a bit puzzled why doing strategy (5) would lead to outperformance compared to strategy (4). Any explanation?
i.e. returns are serially correlated, year on year?
Re: Market timing benefit? Or just pure luck?
Is this the same thing as saying you flip a coin Jan 1 and rebalance if it lands tails? I'm having trouble understanding how the whole 'prediction' part works. How do you program the decision to predict / time the market?greenhill wrote: ↑Tue Jul 17, 2018 1:25 am
5. This scenario is more tricky. I start with $0.5 each in US and exUS stocks in 1970 again. Instead of rebalancing yearly, I assume that I try to predict the market at the beginning of each year. If I predict that I will be better off rebalancing that year, then I rebalance. Otherwise I don't. However, the probability that I make a correct prediction is only 50%. Under this scenario with Monte Carlo simulation, the $1 invested will grow to about $94.9 on average by the end of 2017. The standard deviation is about $3.
If it's simply a 50% chance of rebalancing, maybe it's better to rebalance every 2 years instead of every year. Who decided rebalancing every year is the most optimal? Why not every 6 months or 18 months? Perhaps that is what your study is finding.
I think you may be on to something here.
"The one who covets is the poorer man, 
For he would have that which he never can; 
But he who doesn't have and doesn't crave 
Is rich, though you may hold him but a knave."  Wife of Bath tale
Re: Market timing benefit? Or just pure luck?
Yes, it is the same as flipping a coin if my predictive power is 50%.sjt wrote: ↑Tue Jul 17, 2018 6:30 amIs this the same thing as saying you flip a coin Jan 1 and rebalance if it lands tails? I'm having trouble understanding how the whole 'prediction' part works. How do you program the decision to predict / time the market?greenhill wrote: ↑Tue Jul 17, 2018 1:25 am
5. This scenario is more tricky. I start with $0.5 each in US and exUS stocks in 1970 again. Instead of rebalancing yearly, I assume that I try to predict the market at the beginning of each year. If I predict that I will be better off rebalancing that year, then I rebalance. Otherwise I don't. However, the probability that I make a correct prediction is only 50%. Under this scenario with Monte Carlo simulation, the $1 invested will grow to about $94.9 on average by the end of 2017. The standard deviation is about $3.
If it's simply a 50% chance of rebalancing, maybe it's better to rebalance every 2 years instead of every year. Who decided rebalancing every year is the most optimal? Why not every 6 months or 18 months? Perhaps that is what your study is finding.
I think you may be on to something here.
May not be that straight forward if my predictive power is some other random numbers, like 42% or 69%, though.
I suspected that it may be better to rebalance every 2 years as well. However, a 50/50 US/international portfolio rebalanced every 2 years will only grow to $92.48 by the end of 2017, still somewhat lower than the $94.9 in my scenario (5). That being said, I can't "prove" that strategy (5) is better than rebalancing regularly yet.
Perhaps it's just luck? Maybe the conclusion will be reversed if I rebalance on 13th June instead of 2nd January? Maybe just because I started the simulation from 1970? Or perhaps there is really some unknown benefits for the strategy? I have no answer myself as well...
Last edited by greenhill on Thu Jul 19, 2018 2:22 am, edited 1 time in total.
Re: Market timing benefit? Or just pure luck?
The first intention of rebalancing is risk management and ensure that the portfolio remains close to the chosen Asset Allocation.
Rebalancing can bring additional return or less.
Vanguard has published some good papers on this subject.
Rebalancing can bring additional return or less.
Vanguard has published some good papers on this subject.
BeBH65. (only an investment enthusiast, not a financial adviser, perform your due diligence).
Re: Market timing benefit? Or just pure luck?
US stocks outperformed exUS stocks over this time period, and strategy 5 held more US stocks than exUS stocks on average. Thus, even if there is no serial correlation between return differences, you might well come out ahead with strategy 5.greenhill wrote: ↑Tue Jul 17, 2018 1:25 amRecently I'm bored and I played with numbers from Simba's backtesting spreadsheet, just for fun.
I observed something which is puzzling to me:
1. If I invested $1 in US stocks in 1970, it will grow to $112.66 by the end of 2017.
2. If I invested $1 in exUS stocks in 1970, it will grow to $59.39 by the end of 2017.
3. If I invested $0.5 each in US and exUS stocks in 1970, without rebalancing, it will grow to $86.02 by the end of 2017, which is the mean of $112.66 and $59.39.
4. If I invested $0.5 each in US and exUS stocks in 1970, rebalanced yearly, it will grow to $92.04 by the end of 2017, slightly higher than in scenario (3). This is not surprising because you usually expect a little bit of rebalancing benefit for asset classes with similar expected return.
5. This scenario is more tricky. I start with $0.5 each in US and exUS stocks in 1970 again. Instead of rebalancing yearly, I assume that I try to predict the market at the beginning of each year. If I predict that I will be better off rebalancing that year, then I rebalance. Otherwise I don't. However, the probability that I make a correct prediction is only 50%. Under this scenario with Monte Carlo simulation, the $1 invested will grow to about $94.9 on average by the end of 2017. The standard deviation is about $3.
I'm a bit puzzled why doing strategy (5) would lead to outperformance compared to strategy (4). Any explanation?
Re: Market timing benefit? Or just pure luck?
Yes I think this at least explains the observation partially. The last 10 years is especially favorable to strategy (5) vs strategy (4), as US outperformed exUS in almost every year, sometimes by wide margins. One who didn't rebalance would be better off in the last 10 years.grabiner wrote: ↑Wed Jul 18, 2018 9:56 pmUS stocks outperformed exUS stocks over this time period, and strategy 5 held more US stocks than exUS stocks on average. Thus, even if there is no serial correlation between return differences, you might well come out ahead with strategy 5.greenhill wrote: ↑Tue Jul 17, 2018 1:25 amRecently I'm bored and I played with numbers from Simba's backtesting spreadsheet, just for fun.
I observed something which is puzzling to me:
1. If I invested $1 in US stocks in 1970, it will grow to $112.66 by the end of 2017.
2. If I invested $1 in exUS stocks in 1970, it will grow to $59.39 by the end of 2017.
3. If I invested $0.5 each in US and exUS stocks in 1970, without rebalancing, it will grow to $86.02 by the end of 2017, which is the mean of $112.66 and $59.39.
4. If I invested $0.5 each in US and exUS stocks in 1970, rebalanced yearly, it will grow to $92.04 by the end of 2017, slightly higher than in scenario (3). This is not surprising because you usually expect a little bit of rebalancing benefit for asset classes with similar expected return.
5. This scenario is more tricky. I start with $0.5 each in US and exUS stocks in 1970 again. Instead of rebalancing yearly, I assume that I try to predict the market at the beginning of each year. If I predict that I will be better off rebalancing that year, then I rebalance. Otherwise I don't. However, the probability that I make a correct prediction is only 50%. Under this scenario with Monte Carlo simulation, the $1 invested will grow to about $94.9 on average by the end of 2017. The standard deviation is about $3.
I'm a bit puzzled why doing strategy (5) would lead to outperformance compared to strategy (4). Any explanation?
The outperformance of strategy (5) is still observed in other time periods, though. Take the time period from 1970 to 2007 as an example,
$1 invested in US will grow to $49.39
$1 invested in exUS will grow to $49.33
$1 invested in strategy (4) will grow to $54.8
$1 invested in strategy (5) will grow to about $56.3 on average. SD is about $1.75.
Maybe rebalancing less frequently also did strategy (5) a favor.

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Re: Market timing benefit? Or just pure luck?
Just published is a simple framework for understanding the most basic math of market timing https://doi.org/10.1371/journal.pone.0200561. Among other things, the paper calculates boundaries for the past feasible set for market timing by making, with the benefit of hindsight, perfectly good market timing and perfectly bad market timing switches between asset classes. The paper looked at market timing with stocks and bonds, but there is matlab code in an appendix that you could easily adapt to explore your timing strategy with your chosen assets classes. The main principles in the paper probably apply to your scenario.
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Re: Market timing benefit? Or just pure luck?
Periods of benefit for US and for exUS in that series but more for US  so a strategy that rebalanced but not as often could on average take advantage of that but would still have more years with the dominant returning asset (US)  the fact that it is periods make Monte Carlo more complicated  but whether there is a ‘rebalancing bonus’ in such a set even with similar returns but uncorrelatrd is a function of the nature of the periods of benefit
G.E. Box "All models are wrong, but some are useful."
Re: Market timing benefit? Or just pure luck?
It doesn't really make sense to say "the outperformance is observed" when you're talking about a random process. It can't outperform 100% of the time because you're relying on a coin flip. The coin could "flip wrong" and underperform, at least sometimes. You need to run the test many times and count the outcomes.
I did a quick test of running this 50 times and counting 40 subperiods per flip (19701971, 19701972, ..., 19702017) and I found that rebalancing based on coin flip won ~55% of the time on average but with a standard deviation of 25%. That is, 66% of the time it won somewhere between 30% and 80% of the subperiods I counted. There were plenty of times when it got crushed, as well; dramatically underperforming simple annual rebalancing. That's not a strategy I'd put my money into
Note that even this isn't perfect because I wasn't actually counting all subperiods, just ones starting in 1970. But it should be clear that:
 You can't talk about "outperformance" when using a random process unless you have lots of hedging and caveats, like "probabilistic outperformance" or whathaveyou
 Looking at different subperiods can give very different answers
 You can get very lucky and very unlucky whenever luck is involved
That makes me look at the 19701980 returns in more detail:
Year US Returns Intl Returns
1970 0.16 14.53
1971 15.96 31.53
1972 16.65 38.84
1973 18.19 11.55
1974 27.16 19.7
1975 38.53 30.78
1976 26.56 2.15
1977 4.41 15.93
1978 7.32 31.19
1979 22.42 9.22
1980 32.6 23.24
19761977 is an interesting year where you go from US +26/Intl +2 to the polar opposite: US 4/Intl +15. My hypothesis is that if the coin flip "picks wrong" here in an early year, then it will have an outsized impact on the final results. In my nonanalytical observation that's what I see: if the "coin flip" decides not to rebalance here, it has a difficult (but not impossible) time winning overall. If it chooses to rebalance, then it stays in the running.
Just eyeballing things in that first decade, it looks like there are plenty of times when Not Rebalancing was better. 19711972 when international crushed the US. 19751976 when the US outperformed substantially.
Anyway, overall I'd say the "rebalancing bonus" has mostly been disproved. If it exists, the effect is so fragile it rarely explains anything. We know that the momentum effect is often large and persistent. Then throw in compounding and it doesn't seem that hard to explain the very small 55/45 margin of victory for "rebalance less often".

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Re: Market timing benefit? Or just pure luck?
Actually if you are young and invest with a 80/20 portfolio, over a long time horizon it is best to never rebalance, but your asset allocation wont match your risk tolerance. If you are a young investor, rebalancing every 2 years is usually better than 1. If you are older and even retired, rebalancing every year around the same date is optimal.
Re: Market timing benefit? Or just pure luck?
Yes I made the conclusion too early.AlohaJoe wrote: ↑Thu Jul 19, 2018 4:36 amIt doesn't really make sense to say "the outperformance is observed" when you're talking about a random process. It can't outperform 100% of the time because you're relying on a coin flip. The coin could "flip wrong" and underperform, at least sometimes. You need to run the test many times and count the outcomes.
I did a quick test of running this 50 times and counting 40 subperiods per flip (19701971, 19701972, ..., 19702017) and I found that rebalancing based on coin flip won ~55% of the time on average but with a standard deviation of 25%. That is, 66% of the time it won somewhere between 30% and 80% of the subperiods I counted. There were plenty of times when it got crushed, as well; dramatically underperforming simple annual rebalancing. That's not a strategy I'd put my money into
Note that even this isn't perfect because I wasn't actually counting all subperiods, just ones starting in 1970. But it should be clear that:
What's more, due to compounding, I would expect that the "winner" is determined relatively early in any sequence. That is, whether flipping the coin wins or not will probably usually be determined by the results of the 19701980 period. And when I run the test repeatedly that's more or less what I see. It is uncommon for the winner to "switch" after the mid1980s. It is extremely rare to happen after the mid1990s. And I never saw it happen after 2000.
 You can't talk about "outperformance" when using a random process unless you have lots of hedging and caveats, like "probabilistic outperformance" or whathaveyou
 Looking at different subperiods can give very different answers
 You can get very lucky and very unlucky whenever luck is involved
That makes me look at the 19701980 returns in more detail:
Year US Returns Intl Returns
1970 0.16 14.53
1971 15.96 31.53
1972 16.65 38.84
1973 18.19 11.55
1974 27.16 19.7
1975 38.53 30.78
1976 26.56 2.15
1977 4.41 15.93
1978 7.32 31.19
1979 22.42 9.22
1980 32.6 23.24
19761977 is an interesting year where you go from US +26/Intl +2 to the polar opposite: US 4/Intl +15. My hypothesis is that if the coin flip "picks wrong" here in an early year, then it will have an outsized impact on the final results. In my nonanalytical observation that's what I see: if the "coin flip" decides not to rebalance here, it has a difficult (but not impossible) time winning overall. If it chooses to rebalance, then it stays in the running.
Just eyeballing things in that first decade, it looks like there are plenty of times when Not Rebalancing was better. 19711972 when international crushed the US. 19751976 when the US outperformed substantially.
Anyway, overall I'd say the "rebalancing bonus" has mostly been disproved. If it exists, the effect is so fragile it rarely explains anything. We know that the momentum effect is often large and persistent. Then throw in compounding and it doesn't seem that hard to explain the very small 55/45 margin of victory for "rebalance less often".
I think it's worth to test more different start/end date before arriving to any conclusion. I think it's worth to compare this strategy with rebalancing every 2 years, too. Maybe I'll try to do that on weekend.
Last edited by greenhill on Thu Jul 19, 2018 5:16 am, edited 1 time in total.
Re: Market timing benefit? Or just pure luck?
That's mostly because stocks as a more risky investment has higher expected return. However, if you are rebalancing 2 asset classes with similar risk/return structure, things may not be that trivial...averagedude wrote: ↑Thu Jul 19, 2018 4:55 amActually if you are young and invest with a 80/20 portfolio, over a long time horizon it is best to never rebalance, but your asset allocation wont match your risk tolerance. If you are a young investor, rebalancing every 2 years is usually better than 1. If you are older and even retired, rebalancing every year around the same date is optimal.
Re: Market timing benefit? Or just pure luck?
If you are a young investor with a long time horizon, 100% stock is mathematically optimal, and any strategy which increases your stock allocation, such as never rebalancing, is an improvement.averagedude wrote: ↑Thu Jul 19, 2018 4:55 amActually if you are young and invest with a 80/20 portfolio, over a long time horizon it is best to never rebalance, but your asset allocation wont match your risk tolerance.
But mathematics is not everything, as a lot of investors discovered in 20072009. I never recommend more than 80% stock unless you have already been through a bear market with a stockheavy portfolio and know how you react.
Re: Market timing benefit? Or just pure luck?
I ran the numbers again. Compared 10year, 20year and 30year returns with different starting dates. Rebalancing less frequently (more accurately: once every 2 years compared to once a year) gives better return in the last 40 years, so it's not surprising that the coin flip strategy outperformed yearly rebalancing during this period. It is worth to note that those who rebalanced more frequently in the early 1970s would be better off, though. Comparing the coin flip strategy with reblancing every 2 years gives mixed results. It is quite interesting to see that those who started their portfolio in the 1970s or 1980s would be better off by quite a bit if they choose to rebalance on odd years.
10year returns starting from different years
20year returns starting from different years
30year returns starting from different years
10year returns starting from different years
20year returns starting from different years
30year returns starting from different years
Re: Market timing benefit? Or just pure luck?
This shows the randomness with the starting point. For example, rebalancing after 2008 was a very good move, since the market crashed in 2008 and boomed in 2009. Therefore, strategies which rebalanced at the end of even years did much better than those which didn't. Rebalancing every two years starting in 2000 or 2002 got the benefit, rebalancing with a coin flip got the benefit half the time, and rebalancing every two yeas starting in 2001 or 2003 missed the benefit.greenhill wrote: ↑Fri Jul 20, 2018 1:17 amI ran the numbers again. Compared 10year, 20year and 30year returns with different starting dates. Rebalancing less frequently (more accurately: once every 2 years compared to once a year) gives better return in the last 40 years, so it's not surprising that the coin flip strategy outperformed yearly rebalancing during this period. It is worth to note that those who rebalanced more frequently in the early 1970s would be better off, though. Comparing the coin flip strategy with reblancing every 2 years gives mixed results. It is quite interesting to see that those who started their portfolio in the 1970s or 1980s would be better off by quite a bit if they choose to rebalance on odd years.
The right way to evaluate everytwoyear rebalancing is to consider rebalancing in the even and odd years (or, still better, in every one of the 24 possible rebalancing months) and average the returns.