Because of the magnitude, persistence, pervasiveness and robustness of their related premiums, several factors have dominated the academic literature. Among them are market beta, size, value, momentum and profitability. However, despite their persistence, each factor has undergone even fairly long periods during which it produced negative returns.

Said another way, while investors can raise expected returns by increasing their exposure to the market, size, value and profitability premiums, over any given time period—no matter how long—the realized premiums can be negative. And that fact is what’s tempted many to find a way to “time the premiums”—to tactically allocate by shifting from stocks to bonds, small-caps to large-caps, value to growth and so on.

Asset class (or factor) rotation is a strategy that many active managers employ in an effort to enhance performance. As a strategy, it certainly has appeal, assuming you can identify (in advance) the best-performing asset class (factor). It would seem that a logical way to do this would be to rely on relative valuations.

When an asset class looks cheap relative to its historical relationships, rotate into it. For example, when the spread between the book-to-market (or price-to-earnings) ratios of value and growth stocks is wider than the historical average, then investors should load up on value stocks. On the other hand, when the ratio is relatively low, they should abandon value stocks and move to growth stocks.

This would seem to make sense, as the historical data shows that when the spread in book-to-market (BtM) ratios between value stocks and growth stocks is high, the subsequent value premium tends to be larger. The reverse is also true. Based on that information, if next year’s value premium is expected to be high, it would seem logical to own value stocks. If it were expected to be negative, then growth stocks would seem to become the logical choice.

But is it really that simple to earn abnormal returns? Does a statistical relationship always translate into a viable portfolio strategy?

**A DFA Study**

Wei Dai of the research team at Dimensional Fund Advisors (DFA) sought the answer to those questions in her March 2016 paper, “Premium Timing with Valuation Ratios.” Dai studied the performance of the market, size and value premiums over the period July 1926 through June 2015, as well as the performance of the profitability premium for the period July 1963 through June 2015.

Looking for trading rules that outperformed the long-only benchmarks by at least 25 basis points per year and where that outperformance was reliably different from zero, Dai examined timing strategies that trade back-and-forth between the long and the short sides of the premiums in an attempt to generate abnormal returns. The strategies rebalanced annually on June 30.

Dai considered *nonparametric* trading rules (a test that no assumptions regarding the specific form of the relationship between the spread and the premium, other than the direction of the relationship) that invest in the long side of a premium and then move into the short side when the valuation spread of interest is small. For example, when the book-to-market spread between value and growth is small, it suggests the subsequent value premium may be low, so the trading rule invests in the growth side.

To implement such a strategy, it is necessary to define a “small” valuation spread. Small spreads are defined as those below the 10th, 20th or 50th%ile (breakpoint) of the historical distribution. Dai also considered various strategies for when to switch back, including when the spread crosses a breakpoint, and until it crosses the 50th%ile.

She also examined data that covered all past data up to the trading day, as well as data that covered only the most recent 20-year periods. For each pair of premiums and valuation spreads, Dai ran a variety of trading rules defined by breakpoint, switchback and window. In all, he tested 200 trading rules.

**Results**

Following is a summary of her findings:

- There were only five rules that showed reliably positive excess returns in excess of 0.25%.
- The attempt to time the market premium was the least successful, as none of the rules yielded higher returns than the simple strategy of remaining in the stock market all the time.

Dai also tested 480 *parametric* trading rules (rules that employ a regression approach to forecast future premiums). Since a premium is constructed by subtracting the return on the short side from the return on the long side, they reflect the relative performance of each side. Thus, the trading rule invests in the side of a premium that is predicted to do better (or the one that is more likely to do so). She found that only about 2% of simulations produced a reliably positive excess return greater than 0.25.

Given the large number of simulations, we should expect some chance of what is called a “false discovery.” For example, under a simplified multiple-testing framework in which trials are independent, about 5% of trials will appear statistically significant even if all the signals are pure noise.