There was an interesting discussion earlier this week over at Canadian Financial DIY about how much people should invest in stocks. This post pointed to an article by Zvi Bodie and Paul Hogan that discussed the cost of insuring a portfolio against loss among other things.
You may remember Bodie as a co-author of the book “Worry-Free Investing” (see my review of this book starting here). He is a big proponent of investing in inflation-protected bonds rather than stocks. His reasoning is basically that stocks are too risky, even though they are expected to give higher returns.
In their article, Bodie and Hogan make the following claim about insuring a portfolio: “proof positive of how stocks are risky even in the long run is that if you try to insure a portfolio against a shortfall, you will find that the premium rises as the time horizon lengthens.”
Let’s look at an example to explain what they mean. Suppose that you are about to invest $10,000 in a stock index, but are very worried about losing some of your money. You would like to pick a date in the future and buy insurance that tops up your stocks to $10,000 on that date if the stocks are worth less than $10,000. If they are worth more than $10,000, you get to keep the excess and the insurance pays nothing.
How much should this insurance cost? This depends on how far into the future you choose for the insurance top-up date. Bodie and Hogan claim that as you push this date further into the future, insurance costs rise.
Does this really make sense? I agree that insurance for a month will cost less than insurance for a year, but what about comparing 5 years and 30 years? It seems to me that there is much less risk of losing money over 30 years than over 5 years. This would make the 5-year insurance more expensive and would contradict Bodie and Hogan.
I decided to do some figuring to test my hunch. I had to make some assumptions about stock returns. Suppose that the expected compound stock return is 7% per year with a 30% standard deviation (both of these figures are worse than historical US data).
Here are the results of what the insurance should cost for different lengths of time before the insurance top-up date:
As we can see from this chart, the insurance cost rises to a maximum after about 5 years, but then starts to drop. By this measure, after the first 5 years, owning stocks starts to become less risky. This casts doubt on Bodie’s arguments against owning stocks.