This is a guest post by Mathieu Bouville, PhD
What on Earth is the CAPE?
The price-earnings ratio (P/E) is a common tool for valuing a stock or a group of stock (such as an index). A difficulty is that there are multiple choices for the earnings. One generally uses forecasts, but these are basically guesses. One can instead prefer earnings for the past year. In any case, either of these two earnings may be negative in a recession, making the P/E ratio negative as well. And if earnings drop temporarily due to the state of the economy and the stock price drops to the same extent, the P/E ratio does not change; yet it is a good time to buy because earnings will recover along with the economy. So the P/E ratio is not a very reliable guide to time the market.
A third choice is to use a longer-term historical number, for instance the average earnings over the past ten years. The idea is that such a number gives a reasonable idea of what the earnings will be over an economic cycle. The so-called cyclically-adjusted P/E (CAPE) is simply a P/E ratio calculated using such an average over an economic cycle for earnings.
The historical average of the S&P 500 CAPE was 16.4 (and the median was 15.8). When the CAPE is quite above this value, stocks are deemed expensive, and cheap when the CAPE is low. The CAPE was at or above 30 for three months in 1929, and we all know what followed. It was even above 40 in 1999 and 2000!
The predictive power of the CAPE
Figure 1 shows the annualized real return over the next 20 years as a function of the current CAPE. When the CAPE was below 10, the return of the S&P 500 has never been below 5% p.a. over the next 20 years (i.e. one at least multiplied one’s purchasing power by 2.7). And it has never been above 3% when the CAPE was above 23. (This does not mean that this will never happen, just that it is quite unlikely.) With the 1999–2000 CAPE of more than 40, it is hard to see how one could dream of making money in the long run.
The S&P 500 CAPE is currently around 20. We can thus expect a real return over the next twenty years of somewhere between 0 and 7.5%. This implies that it is unlikely that the return will match the historical average of 6.5% p.a. Note that other markets (for instance in Europe) can currently have lower values of the CAPE.
The blue line in Fig. 2 shows the annualized real return over 20 years for the S&P 500 (known up to August 1991). The orange line corresponds to the CAPE (the scale is inverted, so the curve going up means that the CAPE decreases). The CAPE is reasonably well correlated with the real return over the next twenty years.
The main failure is seen in 1912: the CAPE did not stand a chance of predicting what would happen twenty years later in 1932. Likewise the CAPE was overly optimistic between 1955 and 1965, but what it missed was the high inflation of the seventies. The return over the coming twenty years depends on how expensive the market currently is and on what may happen in the next two decades, but obviously the CAPE can know nothing of the latter.
If the CAPE has some predictive power, it can be used to improve the efficiency of one’s asset allocation. One can for instance increase one’s equity allocation when the CAPE goes down, since future returns should improve. The CAPE going down means that the price is going down, so instead of just rebalancing one would increase the target allocation. For a stock–bond allocation of 50–50, if the stock market loses 20% one is now at 40–50. Rebalancing means selling 5 units of bonds and buying stocks to get to 45–45. But since the CAPE is now lower one could instead wish to aim for something like 50–40, i.e. over-rebalancing.
Strategy based on the CAPE
Historically, the CAPE was between 11.6 and 19.7 half the time. We will consider this range as normal: anything lower (bottom quartile) is cheap, and anything higher (top quartile) is expensive. At or below 11.6 we will hold 100% of stocks, but only bonds if the CAPE skyrockets to 19.7 or above. The stock allocation will vary linearly between 11.6 and 19.7, as shown in Fig. 3. If CAPE = 16 then one holds 46% in stocks for instance. I will use the S&P 500 for the stock allocation and 10-year U.S. treasuries for bonds (mostly because data are easily accessible at http://www.econ.yale.edu/~shiller/data/ie_data.xls).
The stock allocation cannot depend on the CAPE in this simple way: if the CAPE goes from 10 to 25 and back down to 10, you would sell at 20 and then buy back at 20. This way, you may reduce volatility somewhat but you would make no extra money. It would be better to sell at 22 and buy back at 18.
Instead of the current CAPE value, we use the average over the past two years. This creates a delay in buying and selling: you do not sell as soon as stocks get expensive, i.e. you do not exit the market far too early (when prices are still increasing). Likewise you do not buy as soon as prices are low (but still going down). This adds an implicit element of momentum: a CAPE of 20 when markets go up is treated differently from a CAPE of 20 when markets go down. The blue line in Fig. 4 shows that the result is indeed good. (Another advantage is that it changes more smoothly, so one does not have to buy lots of stocks now to sell them back in a month, as shown by the bottom plot in Fig. 4.)
The equity allocation dropped to zero from early 1929 to the end of 1931 to jump to 100% in 1932 (staying there for several years). This feature is what makes the CAPE strategy superior to static stock–bond portfolios: you dump stocks as they get overpriced and buy them back at bargain prices. You thereby dodge the bursting bubbles exhibited by the black line in Fig. 4.
Consequently, the CAPE-informed strategy can return about as much as stocks, but with lower volatility (14% against 19%), and with much smaller drawdowns (drops from peak to trough), as shown by Table I.
Table I: The nominal drawdowns for the S&P 500, a 70–30 portfolio and the CAPE-based strategies for several time periods.
The equity allocation is zero again from 1994 to 2008 (yes, a decade and a half). Over this period, a stock investment behaved like a roller-coaster. The CAPE-based strategy, on the other hand, grew very steadily, as shown by Fig. 5. Between 1995 and today it did about as well as stocks, but its worse drawdown was around 10% over the period (instead of a dive of more than 40% followed by another of 50% a few years later), as shown by Table I.
The blue circle in Fig. 5 shows the return of the CAPE-based strategy as a function of its volatility. It compares very favorably with static stock–bond portfolios (solid line).
Varying the strategy
The dashed line in Fig. 6 corresponds to increasing by half the outperformance compared to a 10–90 portfolio (the allocation with the lowest volatility): 1.5 × (portfolio return − 10–90 return) + 10–90 return. It so happens that by changing the thresholds in Fig. 3, one can obtain CAPE-based strategies that follow this line pretty well (an efficient frontier for these strategies). I have no idea why. In any case, this shows that the outperformance is greater for greater stock allocations (and the difference is of course even larger when compounded over decades).
One may tweak the strategy a bit further and get the orange line in Fig. 6: an average 62% allocation to stocks, a return of nearly 7.9% p.a. for a volatility of 14.3%. This second strategy is shown as an orange diamond in Fig. 5.
The outperformance during the thirties is huge. After that the strategy tracked stocks, only with fewer bumps in the road (right part of Fig. 6) — just what one wants to use the CAPE for. And after 1990, it went up smoothly while the stock roller-coaster was making everyone vomit without returning much more than this strategy.
Table II shows that the biggest drawdowns ever for the two CAPE-inspired strategies (28–29%) were smaller than the sixth biggest one for stocks (34%). The second CAPE-inspired strategy outperforms the first one essentially in the early twentieth century, the thirties and the sixties; its strength is an ability to keep in stocks more at the right time, rather than a greater likelihood of avoiding losses (drawdowns are very similar).
|CAPE strategy 1||28%||24%||23%||19%||19%||17%|
|CAPE strategy 2||29%||28%||26%||23%||20%||13%|
Table II: The worst nominal drawdowns from Table I for the S&P 500, a 70–30 portfolio and the CAPE-based strategies.
Over ten years, there is about a 5% probability of losing purchasing power using a CAPE-based strategy, whereas with stocks there is a 5% probability of losing about 22% in real terms. It takes 15 years for stocks to have a 95% chance of making money in real terms.
Historically, the worst result over twenty years was a gain of 24% in real terms with the CAPE-based strategy, against a loss of 22% with stocks. Since the strategy reduces the risk of a major loss compared to an investment in stocks it can be used more safely for shorter time horizons. Note, however, that the focus of this post was strategies returning about as much as stocks, not strategies designed for the short term.
A few comments
Everything presented here is based solely on dynamic changes to the stock–bond allocation. There is no short position. There is no stock-picking. There is no leverage. There are no asset classes other than stocks and bonds. The strategies use only data that are publically available (e.g. at http://www.econ.yale.edu/~shiller/data/ie_data.xls).
A drawback of these strategies is that they may require to stay out of the stock market for over a decade. And I am not sure whether one would have the nerve to try to beat stocks by shunning equity for so long. Note that it was assumed that bonds would be bought in such instances, but you may decide to look elsewhere when stocks are expensive (e.g. real estate).
It seems that a weakness of these strategies is that they buy bonds when stocks are deemed expensive, regardless of the intrinsic appeal of bonds. I tried taking bond yields into account (using a kind of equity premium), but results are similar. The most plausible reason is that when the stock market is set for a crash, what matters is simply selling stocks.
A common claim regarding any strategy is that if it were so easy to outperform, everybody would do it. But one must remember that mutual funds care about returns only indirectly. Why will they not stay out of the market for half a dozen years when there is a bubble? Because by the time they are proven right (having a higher return than competitors with lower volatility), the fund has been closed down because all “investors” fled. The main risk for fund managers is outflows, the rest matters only inasmuch as it can lead to outflows.
This guest post was written by Mathieu Bouville, PhD
I appreciate the detailed analysis that Dr. Bouville has brought to the table; thanks for the great guest post! Dear reader, what are your thoughts on the cyclically-adjusted P/E (CAPE) and how it relates to asset balancing and investing in equities?