Purely Academic

The Cost of a Perfect Market Timing Strategy

What if we could construct a strategy with a correlation close to 1 with a perfect market timing strategy? Can we estimate what its returns would have been? Can we use these estimates to understand what the market would have “charged” for a perfect market timing strategy?

To answer these questions, first let’s define what a perfect market timing strategy needs to know and what it is. A perfect market timing strategy needs to know, with certainty, the future returns of the assets that are eligible for investment. Armed with this information, the perfect market timing strategy always chooses the highest returning asset to invest in. For example, imagine a strategy that can invest in US stocks [for simplicity, the S&P 500 Total Return (TR) Index] and One-Month US Treasury Bills. It rebalances once per month and on that day knows with certainty the return of US stocks and US Treasury bills over the following month. This perfect market timing strategy would then invest all in equities or all in the One-Month US Treasury Bill, depending on which one will have the higher return over the following month. The challenge here is obvious. How can we know with certainty what the future returns on any asset class will be? Without that knowledge, there is no way to create a perfect market timing strategy. Or is there?

Long-Term Predictability & Short-Term Asset Allocation

Stock market commentators frequently say that day-to-day fluctuations in share prices may be hard to predict, but long-term returns are more predictable. The implication seems to be that investors should reflect these long-term return predictions in their current asset allocations. While the degree of predictability of long-horizon returns is an interesting subject for debate and analysis, this article approaches the practical implications of predictability from a different angle. Suppose long-term returns really are predictable. How should that impact my allocation today? For example, assume that 10-year returns are highly predictable. An investor who revises her asset allocation once every 10 years would find that information very useful. Is that predictability just as useful for investors who adjust their allocations more frequently—e.g., annually? When the return predictability horizon and the allocation frequency are not aligned, the benefits of predictability may be limited.

This study provides evidence on that question by setting up an experiment in which the degree of long-term return predictability is known. The benefit of this predictability is then measured for investors who adjust their asset allocations once per year based on the prediction. The results indicate that when there is a large difference between the allocation frequency and the horizon of return predictability, even relatively strong predictability may not benefit investors much.

I simulate 5,000 investment lifetimes, each 40 years long, by bootstrapping annual returns from the historical sample of US equity and Treasury bill returns.1 Each of my 5,000 hypothetical investors has a model for forecasting the average 10-year equity premium (i.e., the return difference between stocks and T-bills). I determine how good the forecasting model is by setting the R² of the model to a pre-specified level. The R² indicates how much of the behavior of the average premium is captured by the model. For example, an R² of 1.0 indicates that the model explains all the variation in the 10-year average equity premium, while an R² of 0.0 indicates that the model explains none of it. The Appendix describes how the desired R² is imposed on the bootstrapped samples of the equity premium. The 5,000 investors observe their forecasts of the average equity premium over the next 10 years at the beginning of the year and use that forecast to decide whether to invest in stocks for the year. If the forecast is positive, the portfolio is 100% stocks. If the forecast is negative, the portfolio is 100% Treasury bills. Investors adjust their allocations every year based on their forecast, even though their models can only forecast the average premium for the next 10 years.

Investors need a benchmark to determine if their forecast-based allocation has been successful. The benchmark used in this study is the simple strategy of remaining invested in the stock market. If the long-horizon predictability is beneficial, the forecast-based allocation strategy should produce higher ending wealth for a high proportion of the 5,000 investor lifetimes. If the pre-specified R² of the forecasting model is high, investors have a lot of information about the average equity premium over the next 10 years. The unanswered question is: How much information does this long-horizon predictability provide for the equity premium in the very next year? For investors who change their allocations every year, that is the important question.