Friday, 22 November 2013

Life Expectancy and the Stock Market

Cross-posted from Pieria

Suppose, dear reader, that you are about to purchase a company. You examine its cash flows and annual profits, and estimate that these are on average $10 million a year. How much would you be willing to offer for such a purchase? Standard asset pricing models usually incorporate dividend or earnings along with a discount factor and the forecasted growth of earnings. Yet these are rather heavy assumptions: we cannot really estimate either the discount factor or the growth in earnings in the future. Thus, in practice, what other firms usually do (after confirming that the purchase is beneficial for them) is offer a price which is close to the stated share price at the given time of the purchase. 

Now, returning to our example how much would you be willing to offer a firm which earns $10 million a year if you are in your 20's? Probably you would suggest something like $120-150 million. How about in your 60's? The answer will most likely be something much less than the previous one, wouldn't it? This is what is usually called the investment horizon: when I have a longer horizon I can be almost certain that I will cover my costs in the future, which may not be the case if I have a shorter horizon.

Think about people who have very long horizons. Who might they be? Most likely, those who are quite young at the moment and have a lot of planning for their old age to do. If average life expectancy is 79 years of age as I write these lines, a 30-year-old will be sure to cover the amount paid in our example above in 12-15 years and have the rest to enjoy his profits. Yet, is one 30-year-old the same as another? Of course not: people have different risk profiles, different strategies and different amounts of wealth. Yet, let me put it another way: was a 30-year-old in 1900 facing the same horizon as one in 2010?

The answer, as you may have guessed, is no. In 1900 the average person was expected to live for 47.3 years, so he was less willing to part with his money now for a gain in the future. In economic terms his rate of time preference was much higher for the present than for the future, i.e. his β was very close to zero. So the discount factor, which is related to the time preference (though not the same), would force the company's valuation to be lower than it is now. Certainty of longer life spans makes our time preference for the present lower, which means that we are more likely to postpone consumption now on the promise of more consumption in the future. This can be easily seen in the data:
The graph indicates the P/E earnings ratio for the S&P 500 index with outliers (defined as anything greater than the average plus or minus 2 standard deviations) removed, while the straight black line is a simple linear trend line. Although P/E ratios fluctuate over time, the overall trend is positive. For example, in the first decade of the 20th century the average P/E ratio was 13.8; in the first decade of the 21st century it averaged at 29.5. At the same time, the average life expectancy was 49.5 years compared to 77.5 in the 2000's. The trend in life expectancy in the US can be seen more clearly in the following graph:
The graph points out that even under rare events (such as WWI in 1915-1918) there is an upwards trend since life expectancy is not affected by business cycles, expectations or any other economic factors. Thus, even though there is some slight variation at times when there have been wars and/or other catastrophes, the overall trend is much stronger than the one for the P/E ratio. Still, it appears that the longer the expected life of a person, the lower his or her aversion to the future, even though the former has to increase by much more for the latter to do so.

A simple example would be the P/E ratios in a boom: before the 1990's, the highest multiple in the 20th century was approximately 24 in 1934. In 2009, after the 2007 sub-prime lending crisis it reached a high of 70.89. , At the time of writing it is trading at 19.5, a value exceeded just 18 times since 1900, 15 of which were in the last 20 years.

The point here is that the longer we live, the lower our appreciation of the present will become, and the greater our need to save for the future. As our horizon extends, our time preference for the present decreases, leading to lower discount rates and higher prices. Thus, as people will live longer in the future, equity values will appreciate (as already discussed here). As our investments and investment vehicles become more focused in the long-run, just as pension funds are doing at the moment, the upwards trend for equity will continue with or without assistance (by which I mean QE ).

As already mentioned, even with declining populations, equity prices will continue to rise, creating a short-term inflation effect; interestingly, this effect can also be passed on to property prices (and the associated bank loans). The short-term future will be even more interesting: population will increase until the mid-21st century and we can safely assume that life expectancy will increase for even longer, with equity prices following. The change in the latter will of course be much smaller than the change in the former but the direction will be the same. As with any other variable, the trend will be far from linear as prices will fluctuate; but the long-term course will continue to be positive as long as life expectancy continues to increase.

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