The Effects of Missing the Best Months of the S&P500, 1945 - May, 2000
You've probably read a statistic such as the following in the popular media:
"If you try timing the market and miss the single worst month - just one month! - over the past fifty years, your total rate of return will drop from [big number] to [astonishingly small number]."
Boy! You'd have to be a real idiot to try "timing the market." Right?
Wrong! There are many valid criticisms of market timing - or dynamic asset allocation - but this isn't one of them. As it turns out,
- missing the best months is not nearly as devastating to your total return as you might think (see below); for example, missing the top 1 month since 1945 would have lowered your total return by only 0.3% per year, to a still respectable 12.8% from 13.1% buy and hold;
- the odds of you having the sheer dumb luck to miss only the best months are about as great as your getting killed by an asteroid (see below); for example, the odds of missing the top month and only the top month over the past half century are 1 in 665 - the odds of missing 3 of the top months (and only those months) are almost 293 million to one! ;
- the benefit of missing the worst months is much greater than the cost of missing the best months; for example, had you been in cash during October, 1987 ("just one month!"), you would have been over $2.5 million richer by May, 2000, than someone who had invested $10,000 buy and hold since 1945;
- the best months are clustered very close historically to the worst months (over half of the 12 worst months occurred within 8 months or less of one of the 12 best months), meaning that an investor is much more likely to miss some of the worst as well as the best months if he is doing any sort of market timing;
- the effects of missing the best and the worst actually boost your total return (and mathematically are much more likely); for example, missing the 6 best AND the 6 worst months since 1945 would have led to a 0.5% average annual performance boost, translating into 2.5 million additional dollars on an initial $10,000 investment.
Once again, I challenge you to find out the story yourself by digging through the numbers. Using a spreadsheet's sort function and a few mathematical manipulations, it's easy to see how you would have done if you had missed the best months in the S&P500 from 1945 to May, 2000:
Effect of Missing the Top n Months in the S&P500 from January, 1945 through May, 2000, Dividends Included:
| If you missed the top: | $10,000 would have grown to: | Versus a fully invested Buy & Hold investor: | Your average annual rate of return would be: | Versus Buy & Hold: | For an average annual underperformance of: | But these are your odds of having the bad luck to miss only these best months… 1 in: | Probability of doing this: |
| 1 | 7,943,835 | 9,271,301 | 12.8% | 13.1% | -0.3% | 665 | 0.2% |
| 2 | 7,002,394 | 9,271,301 | 12.6% | 13.1% | -0.6% | 441,560 | 0.0% |
| 3 | 6,214,430 | 9,271,301 | 12.3% | 13.1% | -0.8% | 292,754,280 | 0.0% |
| 4 | 5,540,426 | 9,271,301 | 12.1% | 13.1% | -1.0% | 193,803,333,360 | 0.0% |
| 5 | 4,943,421 | 9,271,301 | 11.9% | 13.1% | -1.3% | 128,104,003,350,960 | 0.0% |
| 6 | 4,436,072 | 9,271,301 | 11.6% | 13.1% | -1.5% | 84,548,642,211,633,600 | 0.0% |
This table illustrates several things:
- True, even missing a single month, had that month just happened to be October, 1974, would have shaved 0.3% from your average annual return over the entire period (to make the case even stronger for the buy and hold advocates, I did not include the cash dividends you would have earned while uninvested), but you still would have earned a none-too-shabby 12.8% average annual return, turning an initial $10,000 investment in January, 1945, into almost $8 million.
- As you miss more of the best months, your rate of return drops relative to buy and hold, as would be expected: missing the best 6 months of the period would have translated to a full 150 basis points (1.5%) per year less average annual return than the buy and hold investor. Even so, this is no disaster, since you enjoyed an 11.6% average annual return, compounding your investment into $4,436,072.
- However, no financial planner touting these numbers ever tells you what the odds are of having the bad luck to be out of the market for the best months and only the best months over this study period. The odds of being out of the market for only the best month are the same as the odds of a drawing a single card from a deck containing 665 cards (since there were 665 months in the study period): 1/665 or 0.2%. If you are avoiding dynamic asset allocation out of fear of missing the best time period in the market, because of the low probability of this event (and only this event) occurring, I would not use this as an argument in favor of static asset allocation (buy and hold).
- But it gets worse: the odds of picking the two very best months to be fully in cash are 1 in 441,560 (1/665 * 1/664). The odds of picking the three very worst months (and only those three) are 1 in 292 million. The odds of picking the four very worst months are 1 in 193 billion, and the odds of picking the five very worst months to miss are 1 in 128 trillion! How any financial pundit can try to frighten you away from market timing because of an event that has a 128 trillion to one odds of NOT happening is intellectually lazy and dishonest.
- By the way, if you use the best and worst days (I use months, since it is more realistic to assume that a market timer would be moving in and out for a period of months, not individual days), the odds are even more against your missing the best days:
- The odds against your missing the single best day of the study period is 1 in approximately 13,854 (I am assuming 250 trading days a year).
- The odds against your missing the two best days of the study period are 191 million to 1.
- The odds against your missing the three best days of the study period are 2.6 billion to 1.
Bottom line: although the effect of missing the best months (and only the best months) on your total return would not be that devastating, the odds of it happening are so astronomically low that you should not realistically consider this possibility.
The Other Side of the Coin: The Effect of Missing the WORST Months
It is unfair and unbalanced to consider the effect of missing the best months without considering what would happen if you were to experience the other statistically unlikely extreme: being fully in cash for the WORST months of the study period. In other words, if the COST of market timing is the risk of being out of the market during the BEST months, does it not make sense to consider the BENEFIT of market timing, namely being out of the market during the WORST months? Although the odds of this happening are no greater than the odds of being fully out of the market only during the best months, if you are realistically considering one for purposes of illustration, you should also consider the other. (Later, we will consider the effect of missing BOTH the best and the worst months, which statistically is much more likely than you might suppose since these months are clustered together.)
With all the caveats about astronomically low probabilities mentioned above, let's just suspend disbelief and see what would happen if we were lucky enough to be out of the market when it melted down:
Effect of Missing the WORST n Months in the S&P500 from January, 1945 through May, 2000, Dividends Included:
| If you missed the BOTTOM: | $10,000 would have grown to: | Versus a fully invested Buy & Hold investor: | Your average annual rate of return would be: | Versus Buy & Hold: | For an average annual performance advantage of: |
| 1 | 11,806,282 | 9,271,301 | 13.6% | 13.1% | 0.5% |
| 2 | 13,802,897 | 9,271,301 | 13.9% | 13.1% | 0.8% |
| 3 | 16,116,157 | 9,271,301 | 14.3% | 13.1% | 1.1% |
| 4 | 18,202,393 | 9,271,301 | 14.5% | 13.1% | 1.4% |
| 5 | 20,473,421 | 9,271,301 | 14.8% | 13.1% | 1.6% |
| 6 | 22,666,811 | 9,271,301 | 15.0% | 13.1% | 1.8% |
This table says it all. If you had the good fortune to miss the worst month of the study period (October, 1987), this single month would have added over $2,600,000 to your final portfolio value! This works out to a positive 0.5% average per year boost to performance. Compare this to the $1,300,000 "loss" of not being fully invested during the single best month, and it's clear that the payoff from missing the worst month is about twice the cost of missing the best. The other combinations, increasingly unlikely, show a similar pattern: missing the 6 worst months and being fully invested during the entire balance of the study period would have added over $13 million to your final tally.
The moral of the story is clear: the impact of missing down periods is much greater on your total wealth accumulation than is the risk of being out of the market for similar periods. Avoiding even one devastating loss will have a much greater positive impact on your lifetime portfolio performance than fully participating in every market rise. Avoiding risk not only decreases volatility, it can substantially enhances total return.
A More Realistic Scenario: The Effect of Missing BOTH the BEST and the WORST Months
If you are skeptical at this point about the benefits of market timing, consider what would happen if you were a mediocre market timer. You develop a system that gets you out of the market during the worst months, but it also would keep you out of the market during the best months. In other words, you get the best and worst of both worlds. How would you have done?
As it turns out, much better than if you had simply bought and held.
Effect of Missing the WORST n Months AND the TOP n Months in the S&P500 from January, 1945 through May, 2000, Dividends Included:
| If you missed the BOTTOM AND the TOP: | $10,000 would have grown to: | Versus a fully invested Buy & Hold investor: | Your average annual rate of return would be: | Versus Buy & Hold: | For an average annual performance advantage of: |
| 1 | 10,115,857 | 9,271,301 | 13.3% | 13.1% | 0.2% |
| 2 | 10,425,001 | 9,271,301 | 13.4% | 13.1% | 0.2% |
| 3 | 10,802,446 | 9,271,301 | 13.4% | 13.1% | 0.3% |
| 4 | 10,877,547 | 9,271,301 | 13.5% | 13.1% | 0.3% |
| 5 | 10,916,347 | 9,271,301 | 13.5% | 13.1% | 0.3% |
| 6 | 10,845,470 | 9,271,301 | 13.5% | 13.1% | 0.3% |
| 7 | 10,712,216 | 9,271,301 | 13.4% | 13.1% | 0.3% |
| 8 | 10,572,499 | 9,271,301 | 13.4% | 13.1% | 0.3% |
| 9 | 10,470,277 | 9,271,301 | 13.4% | 13.1% | 0.2% |
| 10 | 10,373,846 | 9,271,301 | 13.4% | 13.1% | 0.2% |
| 15 | 10,048,054 | 9,271,301 | 13.3% | 13.1% | 0.2% |
| 20 | 9,576,342 | 9,271,301 | 13.2% | 13.1% | 0.1% |
| 25 | 8,888,602 | 9,271,301 | 13.0% | 13.1% | -0.1% |
What this illustrates is that even if your market-timing system was so bad that it managed to miss the top 20 months of the last half century, but also managed to keep you out of the worst 20 months, for example, you would still have beaten buy and hold. Only when you get to 25 best-and-worst months combinations and above does your performance slip (but remember that cash dividends are excluded here for the substantial periods (50 months total in this case) in which you are out of the market. If you include these dividends (assuming you get 1/12th of the 90 day Treasury bill yield for every month in cash), your relative return goes way up:
Effect of Missing the WORST n Months AND the TOP n Months in the S&P500 from January, 1945 through May, 2000, Dividends Included AND CASH DIVIDENDS Included On Uninvested Cash (90 Day Treasury Bill Rate):
| If you missed the BOTTOM AND the TOP: | $10,000 would have grown to: | Versus a fully invested Buy & Hold investor: | Your average annual rate of return would be: | Versus Buy & Hold: | For an average annual performance advantage of: |
| 1 | 10,258,220 | 9,271,301 | 13.3% | 13.1% | 0.2% |
| 2 | 10,685,629 | 9,271,301 | 13.4% | 13.1% | 0.3% |
| 3 | 11,155,302 | 9,271,301 | 13.5% | 13.1% | 0.4% |
| 4 | 11,366,454 | 9,271,301 | 13.6% | 13.1% | 0.4% |
| 5 | 11,582,986 | 9,271,301 | 13.6% | 13.1% | 0.5% |
| 6 | 11,723,398 | 9,271,301 | 13.6% | 13.1% | 0.5% |
| 7 | 11,739,603 | 9,271,301 | 13.6% | 13.1% | 0.5% |
| 8 | 11,768,264 | 9,271,301 | 13.6% | 13.1% | 0.5% |
| 9 | 11,848,523 | 9,271,301 | 13.6% | 13.1% | 0.5% |
| 10 | 11,849,197 | 9,271,301 | 13.6% | 13.1% | 0.5% |
| 15 | 12,146,901 | 9,271,301 | 13.7% | 13.1% | 0.6% |
| 20 | 12,096,755 | 9,271,301 | 13.7% | 13.1% | 0.5% |
| 25 | 11,720,253 | 9,271,301 | 13.6% | 13.1% | 0.5% |
| 30 | 11,573,565 | 9,271,301 | 13.6% | 13.1% | 0.5% |
| 50 | 10,640,115 | 9,271,301 | 13.4% | 13.1% | 0.3% |
As you can see here, once you take into account the return on cash which would be even higher if you parked it in a money market fund, you can miss up to the 50 best and worst months and still have an advantage over buy and hold (even though you are out of the market for almost 10% of the time).
What About the Effects of Transaction Costs (Commissions and Slippage) and Taxes?
Opponents of market timing cite transaction costs and taxes as additional barriers to beating buy and hold. The reasoning is that if you switch out of the market one month, then back in the next, you must pay transaction costs each way, plus pay capital gains taxes as soon as you exit the market.
Although I did not calculate the effects of transaction costs on this strategy, with today's deep discount brokers and a wide array of no load mutual funds to switch into and out of, one's transaction costs become negligible, especially as the size of a portfolio increases. As far as taxes are concerned, you must pay taxes on your capital gains eventually, so it is an unfair comparison to assume that the buy and hold investor will never pay taxes.
Valid tax criticisms of market timing are that:
- a young investor in a higher tax bracket now might be better off deferring taking a capital gain until retirement, when her tax bracket may be lower;
- frequent switching in and out of the market may lead to short term capital gains which are currently (2000) taxed at a higher rate than long-term capital gains.
- Deferring a tax payment until later allows more money to compound over time than paying the capital gains tax at various points along the way.
As they say, consult you financial and tax advisor before making any decisions regarding taxes, but you can do most of your trading in a tax-deferred account such as a 401(k) or an IRA. But history seems to show that a severe market decline will be far more taxing to your wealth than will the IRS.
Let's say that you own a stock, XYZ, currently trading at $100. You've bought it 3 months ago at $80 and are wondering whether to lock in your profit now by selling, paying short term capital gains, or hold for 9 months to get the lower capital rate. How much must the stock fall to wipe out any tax benefit from the longer holding period?
As it turns out, if the stock falls by only $2 (2%) ($1.51 if you include the after-tax money earned in a 4.5% money market fund) over the next 9 months, the advantages of the lower tax rate are wiped out. (Click here for the calculations.) You are vastly increasing your risk for a small difference in after tax profit. This does not mean that you should not hold the asset for other reasons; it only means that it would be foolish to hold the asset only for tax reasons. The market will most likely be far more taxing that the IRS! (Click here for a detailed discussion of taxes and trading.)
What Were the Best and Worst Months In the Stock Market?
If you isolated the best months by total return, then identify the worst months, something becomes evident very quickly: the best months are much closer to the worst months than you would expect by chance.
This has implications for trading, since it means that it is highly unlikely that someone attempting to time the market would only manage to miss the best months without also managing to miss some of the worst. I created a table listing the 12 best months, then calculated the nearest of any of the 12 worst months. For example, the best month by total return, October, 1974, came immediately after the 4th worst month, September, 1974. The second best month by total return, January, 1987, came just 9 months before the stock market crash of October, 1987, and so on. In fact, the median distance of the 12 best months from the nearest of the 12 worst months was 12.5 months. If the 24 months (12 best and 12 worst) were randomly distributed, you would have expected 1 of the best months to have been 27.7 months away from one of the worst months on average. The fact that half of the 12 best months were 12 months or less away from one of the worst months - and 4 of the 12 best occurred within 4 months of one of the worst months - tells you that the clustering is about 3 times what you would expect by chance.
* but note the proximity of these two months to each other (2 months apart); also note that 3 of the 4 top months by total return are clustered within one 15-month-span (from October, 1974, to January, 1976).
The same is true, even more so, of the bottom 12 months:
*This outlier is no doubt a result of the fact that this sample began in January, 1945, so excluded the intrawar volatility; it is highly likely that a strong up month occurred during the war which would have been significantly less than 194 months distant from September, 1946.
Remarkably, 5 of the 12 worst months occurred within 6 months or less of one of the 12 best months. 3 occurred within 2 months or less!
So what does this mean from a practical perspective?
- That if you have the misfortune to miss out on one of the best months, assuming you have a system that is not flipping back and forth from bullish to bearish every month, you are highly likely to also miss out on one of the 12 worst months. And as was illustrated above, missing the best AND worst months leads to higher average returns than being fully invested during the entire study period.
- That if you remain fully invested at a market peak, then find after a severe decline that you really don't have the stomach for that much exposure to stocks, you are likely to sell at the bottom and miss out on a subsequent rally. In fact, this is how most investors behave regardless of what they tell themselves they will do.
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