The question of stock allocation for an investment over a certain length of time is a key question that any investor is bound to ask.

## Optimizing the 5% risk

As the average gain increases with the equity allocation, if you want to gain as much as possible on average then the choice is clear: go all in. Except that investing purely in shares also means that you can lose a lot of money. The figure below uses the 5% risk instead, that is the loss of purchasing power that has statistically a 5% probability to happen over the investment period.

For each investment horizon I calculate the 5% risk for various equity allocations and keep only the one that minimizes this risk of losing purchasing power. So this is the best possible stock allocation if one tries to minimize the 5% risk. It gives the black dotted line in the figure. Then, for this allocation, I calculate the 5% risk (this is therefore the lowest 5% risk that can be achieved over that duration), giving the solid gray line.

## Three regimes

As could be expected, the optimal equity allocation increases with the duration of the investment. There are three periods in the figure:

• From about fifteen years on, the optimal allocation is purely in equities. As might be expected, in the long term, stocks reduce the risk of not achieving one's objective. (But of course this does not take into account other criteria, such as volatility, which may justify having some bonds.)
• An allocation with less than a quarter of shares is not optimal, even for investments over a few years. This is due to inflation making a pure bond investment liable to lose a lot of purchasing power (even though the risk of nominal loss is quite low). The exact percentage of shares depends on the criterion used, but it is clear that to minimize risks due to inflation, it is better to include stocks.
• In between (roughly between eight and fifteen years), the stock allocation grows rapidly and about linearly.

The increase of the optimal equity allocation with the investment period up to 100% of shares is not unexpected. However, the fact that the optimal allocation is stable between two and eight years surprizes me, and I am not really able to explain it.

The solid curve shows that the 5% risk worsens until about ten years and then improves. The reason for the lower short-term risk is simply that there is little time to lose money (the annualized 5% risk is higher on shorter terms: −8% p.a. over two years against only −2% over twelve years). The relative weakness of the 5% risk over a few years is thus rather artificial. (This is also why the curves start at two years: before that the risk is artificially low because the duration is very short.)

Note: The figure, based on the S&P 500 and US bonds for the period 1871–2014, is only intended as an indication of general trends in stocks and bonds.