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Published December 1, 2007  |
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Wake me up when September ends
By
TEH HOOI LING
THE month of December has been a positive one for the stock market in 17 out of the past 22 years. That's 77 per cent out of the years since 1985. The average December return is 3.3 per cent and the median 2.4 per cent.
Seventy-seven per cent - that's very good odds. However, if we have more information, we can increase that probability even further. Out of the last 22 years, when stock prices increased in the month of November, then the following December had a 100 per cent record of being a positive month as well. There were 11 years when November saw a share price increase. And in every single one, share prices also climbed the following month - December. So if we only look at all the Decembers since 1985, then we would assume that we have a 77 per cent chance of making money in the stock market in the last month of the year. However, if we have the information that November was a good month, then we can update our probability computation by taking into account that new information. From past experience, it is a certainty that December is a profitable month if November is. In other words, the probability of December being a positive month, given that November is positive, is 100 per cent. That's not all - those Decembers also saw greater price appreciation. The average and median returns were 5.1 per cent and 4.2 per cent respectively. So for a bet which has 100 per cent certainty of being favourable, and with payout larger than normal to boot, the logical action is to bet big. This is what is referred to as conditional probability. The probability of some event, given some other event, is greatly increased over otherwise. I came across an interview where a successful fund manager noted the importance of conditional probability when making investment decisions. He said that market wisdom has always been to 'Sell in May and go away'. But he commented that if a certain previous month - I can't remember which, but it could be January - is positive, then chances of a May sell-down is significantly reduced. This gave me the idea to update the performance patterns for the 12 months of the year. Besides December, January is also a generally good month for stocks. It has been positive 73 per cent - or 16 - out of the last 22 years. The average and median returns are 2.4 per cent and 3.5 per cent respectively. However, if the December of the year before was a positive month, then the probability of January being an up month for stocks rises to 88 per cent. The average and median returns for those months were also higher, at 3.7 per cent and 4.6 per cent respectively. How about May? Contrary to popular belief, the month of May is not so bad for stocks. It made money 64 per cent of the time. Its probability increased slightly - to 69 per cent - if the previous January turned out to be an up month. Historically, the most treacherous month is in fact August. I'm sure many still remember the turbulence that we went through in August this year. Since 1985, 14 out of the last 23 Augusts were down months for stocks. That's a 60 per cent chance of a down market in August. Overall, the average and median return were -2.1 per cent and -1.3 per cent respectively. However, if July was a bad month for stocks, then one should think really hard about buying stocks in August. Chances of August turning out to be a bad month following a negative July is a high 88 per cent. And the declines in those Augusts averaged 4.5 per cent. The median was -3.9 per cent. While July, August and September tend to be months where the trend continued, October was the month when there was generally a reversal. If September turned out to be a bad month, then the chances of October reversing that fortune are a good 75 per cent. In the past 22 years, there were only three out of 12 times when a bad September has been followed by a bad October. In the remaining nine years, or 75 per cent of the time, the market rebounded in October. Now back to our question: What are the chances that this December will be a good month for stocks? Well, as mentioned, had last month (November) been a good month, then it is almost certain that December will be a good month as well. But the problem is in the month just past, the local market lost 7.5 per cent. That significantly reduces the chances of a positive December - to just 55 per cent. Still, that's more than an even chance of a positive return. And in those years when stock prices declined in November, December returns averaged 1.4 per cent. The median is 0.4 per cent. All things considered, and given the rather sharp fall in November this year, perhaps we might still see a Christmas cheer in the market. However, on the flip side, there is a 45 per cent chance of a cold and quiet Christmas. Back in 1985, a 7.3 per cent decline in November was followed by a 10 per cent plunge in December. Since we are on the subject of probability, let's try our hands at the following problem. Assume the following statements are facts: 1) The probability of a woman having breast cancer is 1 per cent. 2) If she has cancer, the probability that the radiologist will correctly diagnose it is 80 per cent. 3) If she has a benign lesion (no cancer), the probability that the radiologist will incorrectly diagnose it as cancer is 10 per cent. The question: What is the probability that a woman with a positive mammogram actually has breast cancer? Ninety-five of the 100 physicians presented with this problem (Eddy 1982) estimated the probability to be about 75 per cent. Does that sound about right? Not even close. The correct probability, as given by Bayes's rule (a theorem in probability), is 7.5 per cent. Try another. Question: What is the probability that a 20- to 30-year-old Singaporean male who does not engage in risky sexual behaviour is in fact infected with HIV if he gets a positive result on an Aids test? The background information is as follows: 1) The prevalence rate is 0.01 per cent. 2) The sensitivity of the test is 99.8 per cent. 3) The false positive rate for the test is 0.01 per cent. Clearly, this is a tremendously accurate test, identifying almost everyone who has the virus while hardly ever incorrectly identifying an HIV-negative man as positive. So if the test says a man has the virus, what is the probability that he really does? Or asked another way, what is the probability of an uninfected man being tested positive for HIV based on the above assumptions? The answer: 50 per cent! Here's how you work out the probability. Imagine 10,000 men in the low-risk group taking the test. One of them is infected (the prevalence rate is 0.01 per cent). He will almost certainly test positive (the sensitivity of the test is 99.8 per cent). Of the remaining 9,999 uninfected men taking the test, one will also test positive (the false positive rate for the test is 0.01 per cent). So if two men test positive; one actually has the virus, the other doesn't. Not such an easy problem to solve, is it? This just shows the concept of probability can be rather difficult to grasp. But someone who has the ability to understand it can greatly enhance their chances of making the right bets. The writer is a CFA charterholder. She can be reached at hooiling@sph.com.sg | |||||||||
