Life only follows one path, but we can’t predict which path we will follow into the future. The fact that investments have risk means that we don’t know for sure what returns we will get. What we can do with some analysis is to list possible outcomes and estimate the chances of each outcome.

The company Financial Engines uses a technique called Monte Carlo simulation to generate possible outcomes as part of personalized investment advice to its clients. (Disclosure: I have no connection to Financial Engines or its products.) Monte Carlo methods are well-known in the sciences, and it’s not surprising that they are useful in economics as well.

Christopher L. Jones, who works for Financial Engines, includes examples of their simulations in his book

The Intelligent Portfolio. I found the long-term simulations of stocks and bonds particularly interesting.

The way the simulations work is that you start with some portfolio of investments, and the software generates thousands of possible futures for this portfolio based on the expected returns, risk level, and correlations of the various investments. Then the software finds the 5th and 95th percentile of outcomes and calls these the downside and upside. This gives us an idea of the range of possible outcomes.

Jones did this for two different portfolios:

Bonds: 100% invested in long-term US government bonds

Stocks: 100% invested in large-capitalization US stocks

All results are given as real returns, meaning that inflation has been taken into account. The dollar amounts in future years are adjusted so that they will have the same buying power as today’s dollars.

Here are the ranges for the two portfolios after investing $10,000 for 20 years:

Bonds: $8260 to $29,700

Stocks: $8070 to $100,000

Given these results, I can’t see why anyone would hold bonds for 20 years; the downsides are almost identical, and stocks have a huge advantage in upside. For shorter periods I can see why one might shy away from the volatility of stocks, but Jones’ results make it difficult to justify holding bonds for the long term.

Jones goes on to say that “in those scenarios where the equity portfolio underperforms the fixed-income assets, the degree of underperformance can be dramatic.” For some reason he doesn’t say that when stocks outperform bonds, the difference can be far more dramatic.