A very thoughtful post over at How to Invest Online looked at the opinions of various investment theory heavyweights on the question of whether owning an index of stocks becomes more or less risky the longer you hold them. I want to address the argument that because “the spread of possible ending dollar values get wider, not narrower, with time,” stocks keep getting more risky over time. At its core, this argument is playing a semantic game with the word “risk”.
To explain what I mean, imagine you have the chance to invest in the following hypothetical investment:
1or2 investment: Each month you toss a fair coin. If it comes up tails, you get a return of inflation+1%. If it comes up heads, the return is inflation+2%.
This looks like a fantastic investment. After one year, you’ll beat inflation by between 12.7% and 26.8%. Even the worst-case scenario gives a better return than most of us could possibly hope for. The 1or2 investment is risk-free in the every-day sense of the word “risk”.
If we use the technical definition of “risk” commonly used in finance, we need to look at volatility and standard deviations. Over one month, the standard deviation is about 0.5%. After a year, the standard deviation goes up to 1.7%. At a decade, it’s 5.5%, and after 50 years it’s 12%. The longer you hold the 1or2 investment, the riskier it gets, in a technical sense. It’s clear that the every-day meaning of “risk” is different from the technical meaning used in finance.
Now let’s look at a riskier hypothetical investment:
-2or3 investment: Each month you toss a fair coin. If it comes up tails, you get a return of inflation-2%. If it comes up heads, the return is inflation+3%.
Just as with the 1or2 investment, the -2or3 investment’s standard deviation keeps rising the longer you hold it. However, what if we focus on the probability that the portfolio will lose purchasing power over different holding periods? The following chart shows that the probability of losing purchasing power drops over time.
After 30 years, the probability that the -2or3 investment will lose out to inflation is less than 1 in 5000. So, if you’re trying to decide whether the -2or3 investment gets riskier the longer you hold it, which of the following facts seems more relevant?
1. The standard deviation keeps getting larger the longer you hold the -2or3 investment.
2. The -2or3 investment is expected to beat inflation by 5.8% per year, and the probability that it will lose to inflation over 30 years is less than 1 in 5000.
At this point Boston University professor Zvi Bodie would argue that with real stocks, the odds of losing money increases the longer you hold them. His justification is that option prices rise with the length of the term. However, the Black-Scholes pricing model does not even take into account the expected return of an investment. This means that the Black-Scholes price of using options to insure against losses with the 1or2 investment would rise with time as well, even though there is no risk of loss with this investment.
The bottom line is that if we’re going to talk about whether stocks are risky over the long run, we need to be precise about what we mean by “risky”. The way that most non-specialists would interpret this question, I think the correct answer is that beyond a certain holding period, owning stocks starts becoming less risky.