No one really *likes* risk. We all can deal with it, but that doesn’t mean we want to. Yes, there are people who live to jump out of airplanes and walk on tight ropes with no net, but I’m talking about *financial* risk.

Unfortunately, at least in investing, risk and return are tightly intertwined. If you want to do better than just sticking your money in the bank, you have to accept some level of risk. But what if there was a better way? What if we could create trading strategies that would allow us to get better returns with less risk?

As you can imagine, there’s no shortage of folks looking for ways to do this (see large swaths of the financial services industry and financial media). And a lot of people like to look at different valuation metrics as the answers.

So we wanted to see if there is a way to reliably predict what the risk premiums will do in the future using these valuation metrics. If that’s possible, we should be able to capture premiums when they look high and avoid them when they look low. This would pretty much be the holy grail of finance.

The only problem is, there’s no evidence that you can actually do this.

Dimensional Fund Advisors did a study that tried to identify ways of predicting future risk premiums based on two of the most common valuation metrics: Price to Earnings (P/E) and Book to Market (B/M). Specifically, they were looking for trading rules that would let them trade in and out of the equity risk factors and yield a better return than a simple buy and hold portfolio.

They used two different approaches to look at this question: regression analysis and trading rule tests. While there are some very interesting results, neither method shows much that could be used with any practical application.

**Regression Testing**

Regression analysis is the bread and butter of academic finance. It’s really good at teasing out how things relate and the strength of the relationships. So this seems like a good place to start, and there are some very interesting results.

We are trying to specifically test if spreads in these valuation metrics allow us to make predictions about the size of the risk premium in the next year. In other words, we want to see if the difference in the ratio between stocks with high B/M ratios and stocks with low B/M ratios can tell us anything about what the risk premiums will look like next year.

Over the very long term (1926-2014) B/M spreads seem to have pretty strong predictive power for all three risk factors—the Market Premium, Size Premium, and Value Premium (profitability data isn’t available until the 1960s). All three regression slopes show a statistically significant positive relationship with solid explanatory power.

But this actually seems pretty period specific. If we break the period in half, we get very different results. Over the first half of the period we still see the same sort of strong relationship, but it starts to fall apart in the second half of the period (1963-2014). Only the size and profitability premiums show statistically significant slopes, and those have only moderate explanatory power (adjusted R^{2} of 0.09 and 0.06 respectively).

What’s even more interesting is that the strength of these relationships in the first part of the period is largely driven by a single year (1932). If we remove that single observation, these relationships come back to Earth.

If we exclude 1932, the only premium in the whole time period with a statistically significant relationship to B/M spreads was the market premium, and that had very low explanatory power (adj R^{2} was only 0.04).

If we look at the period 1926-1962 (excluding 1932), the relationship between the B/M spread and the market premium is no longer significant, but there is a statistically significant relationship with the size premium. But again, there is relatively low explanatory power there.

Looking at the P/E spreads, we don’t have quite as interesting of results, but there does seem to be a relationship between the P/E spread and the size premium. However, just like the B/M spreads, the explanatory power is limited.

In total, the regression results are interesting, but the time specific nature—especially the effect of a single data point—indicates we should be cautious in interpreting them. We can’t confidently say that the spreads of either the B/M or P/E ratios can reliably predict the size of the risk premiums in the future. Though we can say there is some stuff worth testing here.

**Trading Rule Testing**

Regressions are a great starting point, and they can point us in the right direction, but for any of this to be useful, you need to be able to trade on these relationships. To test this, Dimensional created a large number of trading rules (680 trading strategies) that covered a pretty wide gamut:

- Different definitions of the P/E ratio to account for the volatility of company earnings as well as negative company earnings (the B/M ratio is pretty cut and dried)
- Parametric and nonparametric trading rules
- Differing breakpoints and switch points (the points that the strategy exits and returns to the long side of the premium)
- Differing time periods used to identify the breakpoints and switch points

Running the tests, sixteen of these rules showed a statistically significant monthly premium of at least 0.02% per month, or 0.24% per year. In other words, they were reliably better than a simple buy and hold strategy.

This is great! We should figure out the best one and start using it, right?

Well, no.

These results don’t take into account either trading costs or taxes, both of which would eat up 0.02% per month pretty quickly. Also, none of these sixteen rules had a statistically significant premium across all four risk premiums. We would need to compromise our exposure to at least one of the risk premiums to attempt to outperform on the other.

But the biggest thing to consider is something called a “false discovery rate.” For this analysis (for *most* statistical analyses, actually), we used 5% as our test of significance. This basically means we wanted to make sure that there was less than a 5% chance that the results were random noise.

So just by chance, we expect 5% of our tests to show significant results even if there is no actual relationship. We wound up with a hit rate of only 2.35%—well below our expected false discovery rate. In other words, even though they individually looked statistically significant, there is still a real chance that this is just noise.

Overall, the results of both the regression and trading rule analysis don’t provide much support for the idea that you can time the premiums by looking at valuation metrics. There simply is no magic trading strategy that will help you beat a boring “buy and hold” strategy.

If you step back and think about the logic, it shouldn’t come as a surprise that valuation metrics won’t help you time the premiums. These valuation metrics are everywhere. They are all publicly available, which means they’re already baked into the prices.

The spread of these ratios is baked in, as well. If a high spread meant that one of the premiums—say, the value premium—was going to do better next year, then as soon as that spread started to widen everyone would run out and buy value stocks, which would eliminate the potential premium.

It’s impossible to predict what the market is going to do next. Everything is based off of the next piece of information, and until we can predict the future, we can’t know what that is going to be.

For us, this means a long term approach that harvests market returns is still the way to go.

For more on the power of long term, disciplined, buy and hold investing, take a look at our ebook “Investing through the Decades.”