Some investment managers and individual investors attempt to improve their performance by timing the market and adjusting their portfolio according to predictions about the market or specific sectors. Examples of market timing include switching among sectors, switching among different countries’ securities, switching between stocks and bonds, or switching between stocks and risk-free treasury bills. The effect of correctly timing the market would be to increase the portfolio beta in up markets and decrease it in down markets. For the purpose of this discussion, an up market is one in which the market return exceeds the risk-free rate, and a down market is one in which the market return is less than the risk-free rate.

**Proponents of market timing** may argue that the market timer does not have to be correct 100% of the time in order to benefit from timing. Some even may argue that for market timing to be worthwhile, the timer simply must be right more often than wrong.

**Opponents to market timing** may argue that the financial markets are fairly efficient, and therefore there is little to be gained from attempting to time them. Furthermore, there are transaction costs and tax implications associated with buying and selling stocks, both of which create an inherent disadvantage for the market timer. Finally, opponents of market timing may argue that no market timer can be correct 100% of the time, and the lost opportunity caused by missing a bull market or the significant losses of getting caught in a bear market require much more than 50% of a market timer’s predictions to be correct in order to benefit from the strategy.

One can test this argument by creating a model to determine how accurate the market timer’s predictive ability must be in order to benefit

from the strategy. William Sharpe provided such a framework for evaluating the potential of market timing in his 1975 publication *“Likely Gains from Market Timing”*. The potential gains from market timing can be modeled by considering an investor who switches between 100% equity and 100% cash equivalents invested at the risk-free rate. The goal is to determine what the probability of correctly predicting up or down markets must be in order to make timing worthwhile. Define:

π_{up} = probability of an up market

π_{down} = probability of a down market

p_{correct} = probability of correctly predicting an up or down market

where an up market is defined as the situation in which stock returns exceed the risk-free rate in the period under consideration. Historically,

π_{up} = 67% and π_{down} = 33%

One then can draw a tree that leads to four outcomes:

- Up market, predicted up. [ probability = π
_{up}p_{correct}] - Up market, predicted down. [ probability = π
_{up}(1 – p_{correct}) ] - Down market, predicted up. [ probability = π
_{down}(1 – p_{correct}) ] - Down market, predicted down. [ probability = π
_{down}p_{correct}]

Using historical market data from 1934 to 1972 and analyzing returns assuming various levels of predictive ability, the result is that in order to perform better than simply remaining fully invested in stocks, one must be able to predict the market with at least 83% accuracy, a predictive ability that would be extremely difficult for even the best market timer to sustain.

However, this comparison has not considered risk – staying fully invested at all times results in more portfolio variance. The market timer is not invested in stocks 100% of the time, and therefore experiences less variability in portfolio return. To make a fair comparison, one must adjust for the differences in risk. If one compares the market timer’s return to that of a portfolio of stocks and cash weighted to have the same standard deviation as the market timer’s portfolio, the result is that **the market timer must be correct 74% of the time** in order to perform better than the passive portfolio of the same risk. So even after adjusting for risk, a significant predictive ability still is required.

One can evaluate the success or failure of a portfolio manager’s market timing strategy by performing the following regression:

R_{pt} – R_{Ft} = a + b(R_{mt} – R_{Ft}) + c(R_{mt} – R_{Ft})^{2} + e_{pt}

where R_{p} is the portfolio return, R_{F} is the risk-free rate, R_{m} is the market return. If the value of c is greater than zero, than some ability to time the market has been demonstrated. An alternative method is to perform the following regression:

R_{pt} – R_{Ft} = a + b(R_{mt} – R_{Ft}) + c[(R_{mt} – R_{Ft})D_{t}] + u_{pt}

In this regression, D_{t} = 1 if R_{mt} > R_{Ft}, 0 otherwise. If the value of c is greater than zero, than some ability to time the market has been demonstrated. Using this equation, b is the beta in down markets, b+c is the beta in up markets, and c is the difference in the up market and down market betas.