My previous post described how the S&P 500 Index performance is overwhelmingly predictable. In fact, there is a 96% chance that it will deliver a 6.76% annual return over the long term. But what about that remaining pesky 4% of wild fluctuations that keep the worried investor up at night? Let's take a look at one of these events in the price data of the S&P 500 Index. This chart shows the log transformation of the S&P 500 Index price by week over the past 95 years.
The red line is the best fit trend line. We can see that the price sometimes falls over the trend line and sometimes under. Sometimes the price changes are gradual and sometimes they are severe. Take a look at the plunge and recovery at the start of the chart highlighted by the orange box below, this is the Crash of 1929 and the start of the Great Depression.
The S&P hit a high of around $31 in the fall of 1929 and fell to around $4.50 in 1932. At its high of $31, the red trend line implies the fair value was just $6.50 (take the exponential of the LN value to convert back to price). In 1929, the S&P was severely overpriced compared to the trend line. In fact, it has never been as overpriced since that time. It bounced back through 1937 to about $18 and then fell below the trend line again. It then followed a gradual trend upward until it recovered its 1929 high in 1954. You may have heard that it took 25 years to recover from the 1929 crash.
What chain of events caused the crash is a subject for historians. To a mathematician, knowing that the data follows the red trend line at a 96% fit over 95 years is enough to presume that the red trend line represents fair value. Whatever underlying forces drive this valuation will also force periods of overvaluation and undervaluation to self-correct. The self-corrections manifest themselves in different ways throughout the history of the market.
From a certain point of view, one could say that the 1929 crash was "caused" by the overvaluation itself. The more severe the overvaluation the more severe the correction must be to return to the trend line. The "recovery" ending in 1954 was simply the fair market value increasing over time. We can see that the 1954 value was right on trend (upper right corner of the orange box on the chart). Since 1929 there have been numerous ongoing corrections, both large and small, upwards and downwards as the S&P price follows a random walk around the trend line. When markets correct downwards, investors may fear that there is no end to the daily losses and that they could lose all of their money. This drives some to "cut their losses" and sell when the price is low. Knowing that the market will ultimately return to the trend line in this analysis should ease some of these fears. I will look at the details of other significant correction events in future posts.
Komentar