By Riz Jao
THE year 2016 turned out to be a roller-coaster ride for the Philippine stock market. After a disappointing start by dropping 2.13 percent at the end of January, the index managed to regain its footing and entered an uptrend in the first half that culminated with increasing by 14.09 percent year-to-date (YTD) at the end of June. By July 21, it came within a breath of its all-time high of 8,127.48 (posted in April 10, 2015) closing at 8,102.30 (up 18.57 percent YTD) before losing a bit of ground, but ultimately retesting that 8,100 level the week after closing at 8,100.48 on July 27. Since then, however, the Philippine Stock Exchange index (PSEi) has entered a downtrend virtually giving back all the gains of 2016 closing the year at 6,840.64 (up just 0.11 percent).
All this activity has brought about the resurgence of such advice, like “buy the dips and sell the rallies”. While this is good advice, the stock market has a few properties that make this advice the financial equivalent of “eat more fruits and vegetables” (i.e., we understand it but we lose it when cakes and ice cream come our way).
Figure 1.1 plots the daily PSEi returns by how likely they have occurred in the last 21 years from 1995 to 2016 and contrasts this with a set of hypothetical normally distributed returns.
We can see that the daily stock returns are positively skewed—the data has a skewness of 0.47—this has two key implications for investing. First, there is slightly more observations to the left of the mean of 0.03 percent than to the right, in fact, 51.51 percent of all days saw the PSEi either drop or stay flat. Second, the right tail of the distribution is longer than the left tail, this means there are slightly more positive extreme values (0.09 percent) than there are negative extreme values (0.07 percent). Thus, we shouldn’t lose sleep if the PSEi closes flat or negative for the day, it usually does so, and we should avoid obsessing over the next big crash, as they are extremely rare and our time would be much better spent doing what we love instead.
Returning to Figure 1.1, we can also see that stock returns are not normally distributed, rather, the data is leptokurtic. Just like our earlier observation, this has two important implications for investing in the stock market. First, the central peak is higher than what we would expect from a normal distribution, put another way, “average” outcomes are very common indeed, e.g., almost 40 percent of days experienced a return of approximately 0.66 percent and a whopping 81.17 percent of days saw returns between -0.34 percent and 1.65 percent. So the next time the market moves 1.50 percent in a day, don’t be surprised, that’s common. Second, the tails are fatter, i.e., extreme events occur much more often than what a normal probability distribution would predict. For example, the largest one-day gain occurred back in January 22, 2001, which saw the PSEi advance 17.56 percent, assuming normally distributed returns implies that the probability of this occurring is 8.55E-34 (yes, you read that right). Similarly, the largest one-day loss that occurred back in October 27, 2008, which saw the PSEi suffer a stomach churning drop of 12.27 percent, well, the odds of that happening is just 3.04E-18 (again, yup, you’re reading that right). And these aren’t just one off freak events, 1.52 percent of total trading saw returns either less than -4.15 percent, or greater than 4.20 percent, whereas under a normal distribution, we would have expected just 0.27 percent of days to experience such extreme price changes.
An important corollary of this is that the frequency of these extreme events exerts a disproportionate influence on returns. For example, average daily returns from 1995 to 2016 annualizes to a 9.94-percent rate. However, if we are unlucky enough to have missed the 50 best days (which represents just 0.88 percent of days) the annualized return drops to -8.82 percent. Of course, it’s a two-way street, if we’re lucky enough to avoid the 50 worst days our return jumps to 36.30 percent. Simply put, while there are vast rewards for those who can time the time the market successfully, we should be aware of the fact that the odds of such an endeavor are certainly not with us.
To conclude, over the last 21 years, Philippine stock-market returns have exhibited a slight positive skew and high kurtosis, this implies that trying to time markets is an especially difficult task, as we risk missing out on the large, but infrequent, gains where so much of the PSEi’s historical returns have come from. This, coupled with the fact that transaction costs quickly pile up with frequent short-term trading, means that we are much better off simply staying the course rather than reacting spasmodically over every blip.
****
Riz L. Jao is a lecturer of economics and a research associate for Eagle Watch at the Ateneo de Manila University.