The Accidental Investor Blog


Pascal's Wager and a Diversified Portfolio

Written by Kevin McGrew on .

Several years ago we discussed Blaise Pascal's wager in our Quarterly Commentary.  Pascal was a seventeenth century French philosopher, mathematician and physicist.  He had a theory that all people bet that God either exists or does not exist and live their lives accordingly.  If God does exist, and assuming the infinite gain (heaven) or loss (hades) associated with either one believing or not believing, a rational individual would choose to believe in God, or at least live as though God does exist and not treat other people with disdain.  If you are wrong in pursuing this path and God does not exist, then you have given up only a few things in life that you may have otherwise enjoyed.  I suppose this last point has a fair degree of variability to it, depending upon your personal preferences.

The point of our discussing Pascal's wager in that commentary was not to begin a religious or philosophical discussion about the existence of God, but to point out that bull markets do not last forever.  There are certainly periods in which it feels like the market can keep climbing, such as 1982 through 1999, but have you ever looked at a chart of the S&P 500 from 1998 through 2012?  It is like running on a treadmill – lots of movement but you end up getting nowhere. Our intent with this analogy was to show why we invest in a globally diversified portfolio and not just in a single stock index.

Russell Investments has compiled data to show a comparison among an all-stock portfolio and allocations that are 80/20, 60/40, 40/60 and 20/80 stock/bond percentages from 1974-2013.  Over that period of time, if we had wagered that a 100% stock portfolio was the path to infinite joy, we would have enjoyed annual returns of 11.46% with a standard deviation of 16.99%.  However, periods like 1998-2012 surely would have tested our resolve of being faithful to such a strategy.  In contrast, the 40/60 portfolio would have returned 9.6% annually, with a standard deviation of 8.76%.  For those of you so inclined to do the math, the Sharpe ratio on the 40/60 is higher.

What do we learn from this exercise?  Certainly, for the long-term investor who is bereft of emotions (remember Pascal assumed a rational person in his wager, which may have violated the entire premise) or has possibly been in a comatose state for years, a 100% stock portfolio is perfect.   However, for the rest of the investing public, who may adhere to a specific investment philosophy for only the better part of a month, a more diversified portfolio with less volatility is more appropriate.  Roger Gibson's book, Asset Allocation:  Balancing Financial Risk, is an excellent resource for explaining the benefits of a diversified portfolio.

While an all-stock portfolio might work for some people, if we examine Pascal's wager about the existence of God, it is probably more rational to believe that equity markets do not always go up, but do indeed sometimes fall precipitously and that you should design your portfolio accordingly.   If, on the other hand, equity markets do always go up, at least you have participated in that to a certain extent with a diversified portfolio.