In investing there is the challenge of determining how much to invest in stocks and bonds. Stocks tend to have a higher average return but more volatility (price fluctuation and risk of loss), while bonds tend to have lower average returns and see lower price volatility. How much any investor allocates to each asset depends on their attitude towards risk. There are many formulas to quantify risk, but in general, losing half your wealth will decrease your happiness by more that the amount your happiness would increase if you were able to double your wealth. As humans, we feel the losses much more than we feel the gains.

But to be a better investor than the average retail investor does not take that much effort. As a matter of fact, it takes no effort at all once you start. A research project by Fidelity Investments found that the of the best performing accounts were either dead, or they forgot they had an account. The idea is that to do well, you need to trust your decisions and ride out the volatility in stock prices. In general, retail investors have some of the poorest returns compared to all asset classes.

In Peter Lynch’s book, Beating the Street, he recommended almost always being in stocks. There were only a few conditions where he recommended bonds. In general, the S&P 500 has outperformed most asset classes, so investing in an index fund over a long period of time seems like a good idea. But how long is long enough to be fully invested in stocks and to forget about the account?

Over the past 50 years, stocks have returned an average of 9.19% per year, and a volatility of about 12.37%. In terms of risk, this means there is about a 22.88% chance of losing money in any given year. On the other hand, over the past 50 years, the 10 year US government bond returned an average of 6.65% with a volatility of only 7.19%. This means there is 17.75% chance your bonds will be underwater from one year to the next. (NOTE: the calculation for bond mean and variance is more complex than with stocks. I didn’t do this and apologize to the bond experts reading).

A way to define risk aversion is want to maximize the portfolio return at a given percentile. This percentile can range from (0% to 50%]. A risk-neutral person, who only seeks the highest return will use a percentile of 50%. A very risk averse person would use a percentile of 1%. This means they want the highest return possible at the first percentile. They don’t care if they could make much more money the other 99% of the time, their focus is that 1% worst set of returns. To determine how long is long enough to set and forget, we want to find the shortest length of time where the S&P stock portfolio outperforms all the other portfolios at different risk percentiles.

For someone whose risk percentile is 1%, this timeline is 29 years. For someone whose risk percentile is increased to 10%, the timeline is only 9 years. The interpretation is that if you buy an S&P 500 index fund, forget about the account, and return 9 years later, there is a 90% chance it will have performed better than any other mix of stocks and bonds with a probability of 90%. It is also interesting to note that as the timeline shrinks, the allocation to bonds increases, as there is less time to make the bad years that stocks will inevitably have. What is interesting is that by the time the horizon decreases to five years, the model recommends investing almost completely in bonds.

In my next post I want to look at actual returns over time for stocks and bonds to determine if the theory matches up with the performance reality.