Man Doth Not Invest by Earnings Yield Alone
Membership required
Membership is now required to use this feature. To learn more:
View Membership BenefitsAdvisor Perspectives welcomes guest contributions. The views presented here do not necessarily represent those of Advisor Perspectives.
The big question
The most popular indicator of the attractiveness of the stock market – Shiller’s CyclicallyAdjusted Price Earnings ratio (CAPE) — is currently at 39x in the US, higher than it’s been 98% of the time for the past 120 years. What’s a thinking investor to make of this? Should he stay clear of the US stock market, or stick to some preset strategic allocation to equities, or is there something else going on? In this note, we’ll argue that CAPE is far from irrelevant, but on its own, it doesn’t tell an investor how much stock exposure to have.
CAPE basics
When the CAPE ratio is high, the prospective return of the stock market is low. This finding makes logical and intuitive sense, and is borne out in historical data. We can say something more specific and powerful: 1/CAPE is a pretty good, though imperfect, predictor of the inflationadjusted return of the stock market.^{2} The measure of 1/CAPE is known as the CyclicallyAdjusted Earnings Yield (or just “Earnings Yield”), because it’s calculated as Earnings divided by Price. If you invest in the stock market when the Earnings Yield is 6%, your best expectation is that you’ll earn a longterm return (after inflation) of 6%. This is telling us that, contrary to popular belief, when Earnings Yield is low we shouldn’t expect to lose money from the Earnings Yield reverting to some average higher level, and vice versa. In other words, the predictive power of Earnings Yield over a long horizon is not improved by assuming that it is meanreverting (For a deeper dive, see our 2017 article “Market Multiple MeanReversion: Red Light or Red Herring?”). The chart below illustrates this, using a horizon of ten years:
Chart 1: Next 10Year Real Return vs. Earnings Yield at Start
US Equities, 1900 – 2021’
The first reaction of everyone who has seen this chart — your authors included — is: “Ooooeeee! Investor Hall of Fame, here I come!”
Alas, a backtest – as shown in the chart below – pours icecold water on these dreams: a simple dynamic approach based on Earnings Yield failed to deliver a higher Sharpe Ratio^{3} than a static allocation over the entire 120year period for which we have data, and has actually underperformed since 1943.^{4} This result is one reason you will find so few investment products that offer a dynamic asset allocation strategy based on Earnings Yield or similar metrics. See Asness et al. “Market Timing: Sin a Little” (2017) for a lively and detailed description of the wellspring of this cold water.
Chart 2: Static vs. Conventional Dynamic Asset Allocation:
US Stocks and TBills, 1900 – 2021
Worth another look?
This result is puzzling though, because it just seems like basic common sense that it should be better to have more exposure when the market is offering higher expected returns, and we’ve seen that Earnings Yield has some power as an indicator of when to expect those higher returns.
The rest of this note is devoted to exploring an alternative, more internally consistent approach to dynamic asset allocation using Earnings Yield as the driver, which has historically delivered the improved performance we’d expect.
When Occam’s razor shaves too close
The historical analysis of the use of Earnings Yield to dynamically allocate between US stocks and US Tbills presented in Chart 2 is done in Occam’s spirit of maximum simplicity. The rule sets the equity allocation to:
1. Be proportional to the Earnings Yield at each point in time,
2. Average 65% over the whole sample, the same as for the benchmark Static Strategy, and
3. Never be negative or in excess of 100% (i.e. no shorting and no leverage).^{5}
We’ll call this the “Conventional Dynamic Strategy.”
There are a number of problems with this approach, including:
1. The asset allocation decision in this strategy is comparing the attractiveness of equities to the attractiveness of Tbills. However, Earnings Yield is not a predictor of the relative attractiveness of stocks versus Tbills; it is only a predictor of the future real return of equities.^{6}2. Changes in riskiness of the stock market are ignored. It is intuitive that all else equal, an investor would want to have less allocated to equities when they are expected to be more volatile.
3. For the equity allocation to average 65% over the period requires knowing what the Earnings Yield of the stock market was over the whole sample, which a nonclairvoyant investor who wanted to follow this strategy could not have known.
A more consistent asset allocation rule based on excess earnings yield
If we want to use Earnings Yield to decide how much to invest in the stock market, to be consistent we also need to evaluate alternatives to stocks in terms of their expected real return. It seems natural to turn to US Inflationindexed bonds (TIPS) as the relevant lowrisk alternative to stocks, since the yield on TIPS is a measure of their expected real return, and so provides a directly comparable measurement to the Earnings Yield of equities. Indeed, there are strong arguments that “the (inflation) indexed perpetuity is the riskless asset for a longterm investor, since it finances a constant consumption stream over time,” as suggested by Harvard professors Campbell and Viceira in “Who Should Buy LongTerm Bonds” (2001).^{7} For practical purposes, longterm TIPS are pretty close to the inflationindexed perpetuity they suggest.
It seems more natural to think about the attractiveness of stocks relative to inflationprotected bonds, rather than just by considering the level of Earnings Yield in isolation. For example, if the Earnings Yield of the stock market were 4% and the real yield on TIPS were also 4%, why would we want to own any equities?^{8 }Or for a historical illustration, consider that the Earnings Yield of the US stock market was about 2.7% at the end of 2000 and also at the end of 2021 – but the tenyear TIPS yield was 3.6% back in 2000 and 0.7% at the end of 2021. Would a rational investor choosing between equities and TIPS want to have the same exposure to equities at both points in time, just because the Earnings Yield was the same? We think most investors would agree that they should want to own more equities at the end of 2021 than 21 years earlier. And yet, the conventional analysis that uses the market’s Earnings Yield without reference to the real return offered by safe assets suggests owning the same amount of equities in both cases.
We propose three changes to the (disappointing) Conventional Dynamic Strategy presented in Chart 2, setting the allocation to equities at each point in time to be:
1. Proportional to the excess of the stock market’s Earnings Yield above the real yield of inflationprotected bonds (US TIPS). We’ll refer to this measure as “Excess Earnings Yield.”
2. Inversely proportional to the risk (measured as variance) of the stock market as might reasonably have been estimated by an investor at the point in time of the asset allocation decision.
3. At the level a UtilityMaximizing investor, with a typical and stable degree of Constant Relative RiskAversion (CRRA), would choose based on the estimates of Excess Expected Return and Risk set out in 1 and 2 above.^{9} By constructing the allocation decision from first principles in this way, we address the problem in the Conventional Strategy of needing to know the average level of Earnings Yield over the whole period.
We will call this the “Excess Earnings Yield Dynamic Strategy.”
Determining exposure to equities as a function of expected excess return, risk, and investor riskaversion to maximize Expected Utility under standard assumptions is known as the Merton Rule (see footnote 9). For this analysis, we’ll assume an investor with a degree of riskaversion we found typical in a survey we conducted in 2018. This level of riskaversion is such that an investor would choose to allocate 62.5% to equities if faced with an excess expected equity market return of 5% per annum, and equity riskiness of 20% per annum.^{10} The chart below shows the allocation to equities resulting from the Merton Rule, which we use in our historical analysis from the end of 1997 (the start of the TIPS market) to the end of 2021.^{11} In the first 3 1/2 years of the study, the desired allocation to equities was zero, because the Earnings Yield of the stock market was relatively low, TIPS yields were high, and therefore the Excess Earnings Yield was negative.
Chart 3: Allocation to US Equities Based on Merton Share vs. 10Year TIPS
1997 – 2021
The chart below shows the performance that these allocations would have generated, compared to a static allocation of 65% in stocks and 35% in bonds (TIPS being the type of bond). The Excess Earnings Yield Dynamic Strategy performed much better, delivering a return about 2% pa higher than the Static Strategy, with lower risk and a nearly 50% higher Sharpe Ratio.^{12} By contrast, over the same period starting in 1997, the Conventional Dynamic Strategy illustrated in Chart 2 generated a return about 1.5% pa lower than the comparable Static Strategy but with roughly the same Sharpe Ratio. Of course, this is a very short window, and we certainly are not suggesting that you should follow this approach or avoid the conventional approach solely based on this backtest.
Chart 4: Excess Earnings Yield, Dynamic vs. Static Allocation
US Equities and 10Year TIPS
19972021, Logarithmic Scale
It would be nice to see this analysis taken back further – unfortunately, the US Treasury has only been issuing TIPS since 1997. However, we do think it’s possible to construct a decent hypothetical history of longterm US real interest rates going all the way back to 1900, which we present in the chart below.^{13}
Chart 5: TenYear Real Yield Series
Actual & Hypothetical
Using this hypothetical history of US real rates, we get the chart below, which shows the performance results back to 1900. Bottom line: the Excess Earnings Yield Dynamic Strategy did a lot better than a Static Strategy. Not only did the Excess Earnings Yield Dynamic Strategy do much better in terms of absolute return and quality of return than the 65/35 Static Strategy, but perhaps even more remarkable, it outperformed being 100% in US equities over the entire period, which generated a lower total return of 10.0% with 40% more risk.
Chart 6: Excess Earnings Yield, Dynamic vs. Static Allocation US Equities and 10Year TIPS 19002021, Logarithmic Scale
One more thing to consider is that it’s hard to say how an investor would have decided on a 65/35 stock/bond asset allocation to begin with, without use of some sort of framework, such as the Merton Rule, that put a price on risk. If an investor in 1900 were thinking about how much to invest in equities based on some other objective – such as maximizing Expected Wealth – he would have tried to invest the most that he could in equities with maximum leverage. Following such an approach, the investor would have likely gone bust in the 19291933 stock market meltdown of over 85%, and possibly in the several other greaterthan50% market declines experienced over this period.
In the Appendix, we provide details of all our assumptions and sources of data, and find that the BaseCase historical result just outlined is robust to changes in many of the assumptions. We also show the significant improvement delivered historically from including TimeSeries Momentum as an additional indicator of the expected risk and/or the expected return of equities.
Improvement in Sharpe ratio is a twofer (squared!)
Since 1900, the Excess Earnings Yield Dynamic Strategy has generated a Sharpe Ratio about 25% higher than that of the Static Strategy. Just how big a deal is a onequarter increase in the Sharpe Ratio on one’s investment portfolio?^{14} A very big deal indeed! A onequarter increase, whether it comes from a higher expected excess return or lower risk, delivers a compound benefit to an investor in that it:
1. Provides a onequarter higher return per unit of risk, and,
2. It also increases the optimal allocation to equities by onequarter, generating an additional onequarter improvement.
So, a onequarter increase in Sharpe Ratio generates roughly double that improvement (a 56% improvement, to be exact!) in the RiskAdjusted Return of the investor’s portfolio.^{15} An improvement of this magnitude in expected RiskAdjusted Return, compounded over the longterm horizons over which individuals typically save and invest for retirement, can make truly lifechanging enhancements to investor outcomes.
Can everyone be a dynamic asset allocator?
An Excess Earnings Yield Dynamic Strategy is not an approach that all investors can pursue at the same time. Economists would say that such a strategy is not macroconsistent. This is a pretty stringent test of an investment approach. Even a static asset allocation strategy that aims to keep a fixed fraction of wealth in equities would fall foul of this test. In fact, the only strategy that all investors can pursue at the same time is buyandhold at global marketcap weights. Whenever an investor is considering pursuing a strategy that not everyone can follow, he needs to have a good look in the mirror and ask why he is different from the average investor.^{16} An Excess Earnings Yield Dynamic Strategy is probably a good fit for longterm investors who expect their riskaversion to remain steady through time, and who are willing and able to estimate expected real returns and risk offered by their investments.
Conclusion
We believe it’s never a good idea to adopt an investment strategy based primarily on historical simulations. However, when you believe a strategy makes sense a priori, it is worthwhile to challenge and update the strength of that belief with a look at the empirical evidence. Before looking at the historical record, we firmly believed it made intuitive sense to dynamically change one’s allocation to equities based on their expected return relative to the appropriate safe asset, and the empirical record reinforced that belief. It is time to correct the record regarding the efficacy of Dynamic Asset Allocation using the market’s Earnings Yield as a key input. And it is also time to differentiate this disciplined approach grounded in theory from the many seatofthepants dynamic approaches that go under the pejorative heading of “Market Timing.” The magnitude of improvement in welfare that is available to investors who are willing and wellsuited to vary their exposure to equities as their expected excess real return and risk change over time is too big to be left on the table.
Appendix
Data and sources
S&P 500 Stock Index Prices (1870 – 2021 monthly) 
Standard and Poors, Online Data: Robert Shiller 
S&P 500 Earnings and Dividends 

US TBill Rates 

US TenYear Treasury Yield 

UK TenYear InflationLinked Bond Yield (19851997) 
King and Low (2014) 
US TenYear TIPS Yield (1997 – 2021) 

US CPI Inflation (1880 – 2021) 

Implied Inflation Forecasts (1955 – 1970) 
KozickiTinsley (2006), Ilmanen (2011) 
Surveybased Inflation Forecasts (May 1970 – November 1984) 
Philadelphia Fed, Cleveland Fed, Blue Chip Economic Indicators, Livingston Survey 
Construction of US TenYear TIPS Yields and Total Return Series from 1900 to 2021
From 1997 to 2021, we use TenYear TIPS yields directly. From 1985 to 1997, we use TenYear UK InflationLinked Bond yields. From 1900 to 1984, we use the US nominal TenYear bond yield minus an estimate for the ten years of US inflation, and we subtract a further 0.5% from the resultant real yield as a representation of a riskpremium that investors are likely to have demanded to bear inflation risk. The prospective inflation forecast we use from 1900 to 1984 is the average of survey data from 1970 to 1984, implied inflation forecasts from KozickiTinsley (2006) from 1955 to 1970, a weighted average of realized 20year, 10year, 5year and 1year inflation with weights of 40%, 30%, 20% and 10% respectively from 1933 to 1955, and the weighted average of realized inflation itself averaged with 0 from 1900 to 1933 to represent some bounding of expectations at 0 inflation during the period the US was on the gold standard. Our approach to constructing this series owes a debt to Antti Ilmanen (2011).
Construction of Equity Market Volatility Forecast 1900 – 2021
We calculate a series of rolling 10year equity volatility and rolling 2year equity volatility from monthly closing prices of the S&P500. We then take a weighted average of the lifetodate average of the rolling 10year volatility and the most recent 2year volatility. We put 75% and 25% weight on the 10year and 2year volatility measures, both expressed as variances, and then take the square root of that weighted average to arrive at the spot estimate of equity volatility that an investor might reasonably have used in deciding how much equity exposure to take using the Merton Rule. The chart below shows the volatility estimate we used in the historical simulation.
Chart 7: Equity Market Volatility Estimate Used in Historical Simulation
Shiller CyclicallyAdjusted Earnings Yield and Excess Earnings Yield Histories
Chart 8: Shiller CyclicallyAdjusted Earnings Yield
US, Dec. 1899 – Dec. 2021
Just a Good Draw?
We cannot say whether or not the past 120 years were just a favorable period of time for dynamic asset allocation. However, we can answer the question of how much better we would have expected dynamic asset allocation to perform given the range of expected excess returns equities offered at different times. To do this, we ran a simulation in which half the time, the excess expected return of equities was 1% and the other half of the time it was 9%, which roughly matched the spread of expected excess returns experienced in the past 120 years.^{17} We found that dynamically scaling the exposure to equities over many simulated histories delivered a roughly 30% average improvement in the Sharpe Ratio versus a static strategy. Against this backdrop, the historical experience of the past 120 years appears to be just a little bit worse than we’d have expected. The simulation also suggests that over a shorter horizon of 40 years, the dynamic asset allocation has an 85% probability of generating a higher return and a 65% chance of resulting in a higher Sharpe Ratio than a static weight strategy.
Robustness of Simulation Results to Different Assumptions
There are many other popular metrics used in dynamic asset allocation strategies, such as Tobin’s Q, Equity Market Value to GDP and Aggregate Investor Allocation to Equities (AIAE), to name a few. We prefer Earnings Yield because it directly gives an estimate for the longterm real return of the equity market, whereas all the other metrics need to be regressed against their historical averages in order to provide a return estimate. A surveybased forecast of future earnings may be better than using the past ten years of inflationadjusted earnings as done in the CyclicallyAdjusted Earnings Yield, but we do not have that survey data going back very far and so could not run the historical simulation on that basis. Another metric, CyclicallyAdjusted Dividend yield plus dividend growth, closely relates to Earnings Yield and might be effectively used in conjunction with it, but this metric suffers from requiring an estimate of growth and being more sensitive to changes over time in corporate earnings payout policies.
We consider Time Series Momentum an indicator of prospective risk (it can also be thought of as a return indicator with much the same practical effect), which can be effectively used in combination with Earnings Yield to significantly improve riskadjusted returns. We give results for the joint application of Excess Earnings Yield and Momentum in the table below, and also in the chart below.
We explored a range of different assumptions applied to the historical simulation. Below we describe each change in assumptions and the resultant Sharpe Ratio for the dynamic and static strategies over the entire period and the period since the introduction of inflationprotected bonds in 1985 in the UK.
Chart 9: Excess Earnings Yield, Dynamic vs. Static Allocation
Using Momentum as Risk Proxy
US Equities and 10Year TIPS
1900 – 2021, Logarithmic Scale
Decade by Decade Results
The Excess Earnings Yield Dynamic Strategy experienced a lower Sharpe ratio in 3 of the 12 decades examined.
Higher Turnover
A dynamic strategy is likely to experience higher turnover than a static strategy, and hence will incur higher transactions costs and possibly a higher tax cost as well. In our simulation with monthly rebalancing, the average turnover of the dynamic strategy was 29% per annum, versus 10% for the static weight strategy. Both of these turnover figures could be reduced by rebalancing less frequently and less fully to targets. Implementing a dynamic strategy is more complex and takes more of an investor’s attention, although on the other hand, a rulesbased dynamic approach may be easier for an investor to stick with as it can scratch the investor’s itch to feel responsive in the face of a changing world.
If Expected Equity Returns Are Inversely Related to Changes in Market Level
By construction, when the market drops over a short period of time, the CyclicallyAdjusted Earnings Yield will go up, because CyclicallyAdjusted Earnings is based on the past ten years of earnings, which hardly changes from day to day. If an investor believes that the Expected Return of the stock market goes up when the market falls, then he should want a higher allocation to equities than suggested by the basic Merton Rule. This extra amount of equities was called “hedging demand” by Merton (1971), because it represents a hedge against the investment opportunity set faced by the investor. When the market goes down, the investor’s portfolio value goes down, but the increase in attractiveness of his investment opportunities offsets some of that loss in value, and so he can afford to own more equities. Pushing in the opposite direction of this hedging demand is the tendency for the market to be more volatile when it falls, which the market for options exhibits through the volatility “skew.” We view these phenomena as important, but not changing the basic conclusion that dynamic asset allocation driven by estimated expected return and risk is a sensible approach to investing.
As per the assumptions in the Merton Rule described above, riskadjusted return is calculated by subtracting from the expected or realized excess return of a portfolio the cost of risk defined as:
Where ƒ is the fraction of the portfolio allocated to the risky asset, and and are as described in the Merton Rule above.
Victor Haghani is founder & CIO and James White is CEO of Elm Partners Management, LLC, a Philadelphiabased asset manager.
Further Reading and References:
 Asness, C., Moskowitz, T., and Pedersen, L. (2013). “Value and Momentum Everywhere.” Journal of Finance 68 (3): 929–985.
 Asness, C., Ilmanen, A., and Maloney, T. (2017). “Market Timing: Sin a Little.” Journal of Investment Management 15 (3): 2340.
 Campbell, J. and Shiller, R. (1988). “Stock Prices, Earnings and Expected Dividends.” Journal of Finance 43 (3): 661676.
 Campbell, J. and Viceira, L. (2001). “Who Should Buy LongTerm Bonds?” American Economic Review 91 (1): 99127.
 Cochrane, J. (2022). “Portfolios for LongTerm Investors.” Review of Finance 26 (1): 142.
 Cochrane, J. (2011). “Presidential address: Discount rates.” Journal of Finance 66 (4): 1047–1108.
 Haghani, V. and White, J. (2018). “Measuring the Fabric of Felicity.” Elm Wealth. https://elmwealth.com/measuringthefabricoffelicity/
 Haghani, V. and White, J. (2017). “What if High Stock Values Revert to Normal Levels?” Bloomberg. https://www.bloomberg.com/opinion/articles/20171002/whatifhighstockvaluesreverttonormallevels
 Haghani, V. and White, J. (2017). “What Our Market Return Forecasts Really Mean: Equity Convexity and Investment Sizing.” Elm Wealth. https://elmwealth.com/whatourmarketreturnforecastsreallymeanequityconvexityandinvestmentsizing/
 Haghani, V. and White, J. (2017). “Market Multiple MeanReversion: Red Light or Red Herring?” Elm Wealth. https://elmwealth.com/marketmultiplemeanreversionredlightredherring/
 Haghani, V. and White, J. (2020). “Taking Stock.” Elm Wealth. https://elmwealth.com/takingstock/
 Ilmanen, A. (2011) Expected Returns. London: Wiley.
 Keimling, N. (2016). “Predicting Stock Market Returns Using the Shiller CAPE — An Improvement Towards Traditional Value Indicators?” SSRN Electronic Journal. https://dx.doi.org/10.2139/ssrn.2736423
 King, M. and Low, D. (2014) “Measuring the `World’ Real Interest Rate.” NBER Working Paper Series 19887. https://www.nber.org/papers/w19887
 Kozicki, S. and Tinsley, P. (2006). “SurveyBased Estimates of the Term Structure of Expected U.S. Inflation.” Bank of Canada Working Paper No. 200646. https://dx.doi.org/10.2139/ssrn.953959
 Merton, R. (1969). “Lifetime Portfolio Selection under Uncertainty: The ContinuousTime Case.” Review of Economics and Statistics 51 (3): 247257.
 Merton, R. (1971). “Optimum Consumption and Portfolio Rules in a ContinuousTime Model.” Journal of Economic Theory 3 (4): 373413.
 Merton, R. (1973). “An Intertemporal Capital Asset Pricing Model.” Econometrica 41 (5): 867887.
 Micaletti, R. (2021) “Market Timing Using Aggregate Equity Allocation Signals.” Alpha Architect. https://alphaarchitect.com/2021/04/29/markettimingusingaggregateequityallocationsignals/
 Rintamaki, P. (2021) “Total Wealth Portfolio Compositioin and Stock Market Returns.” SSRN Electronic Journal. papers.ssrn.com/sol3/papers.cfm?abstract_id=3924180
 Samuelson, P. (1994). “The longterm case for equities.” Journal of Portfolio Management 21 (1): 1524.
 Jivraj, F. and Shiller, R. (2018). “The Many Colours of CAPE.” Yale ICF Working Paper No. 201822. http://dx.doi.org/10.2139/ssrn.3258404
1. ^{1}This is not an offer or solicitation to invest, nor should this be construed in any way as tax advice. Past returns are not indicative of future performance.
^{2}A variety of corporategrowth models can produce the result that real equity returns will be centered around the earnings yield. One basic condition under which real returns will equal the earnings yield would be if company earnings can grow with inflation with all earnings paid out currently to shareholders. While these models are all caricatures of the real world in a variety of ways, they nonetheless provide a solid starting point for thinking about expected stock market returns and making sense of longterm historical data. For a more uptodate evaluation of CAPE as a predictor of real equity returns, particularly assessed in nonUS equity markets, see Keimling (2016). They conclude: “Existing research indicates that the cyclically adjusted Shiller CAPE has predicted longterm returns in the S&P500 since 1881 fairly reliably for periods of more than 10 years. Furthermore, the results of this paper indicate that this was also the case for 16 other international equity markets in the period from 1979 to 2015.”
^{3}A measure of riskadjusted return.
^{4}Unless otherwise stated, all historical analyses presented in this note are exclusive of trading costs and taxes.
^{5}The simplest asset allocation rule that meets these three requirements is: , where k* is the allocation to equities, EY is the Earnings Yield of the stock market at the time of the asset allocation decision, and will be the allocation to Tbills, and assuming at all times.
^{6}Comparing Earnings Yield to the yield on Tbills also would not be consistent, as Earnings Yield is a real return estimate while the yield on Tbills is a nominal return estimate. Using Earnings Yield minus the Tbill rate as the asset allocation driver results in the same conclusion conveyed by Chart 2. A Dynamic Asset allocation rule based solely on the Earnings Yield of the stock market would make sense if the expected real return of Tbills was constant through time, but we know this is not the case.
^{7}As Stanford economist John Cochrane further elaborates in “Portfolios for LongTerm Investors” (2021), “Their (Campbell and Viceira’s) proposition is obvious if you look at the payoffs. An (inflation) indexed perpetuity gives a perfectly steady stream of real income, which can finance a steady riskfree stream of consumption. It is the riskfree payoff stream.”
^{8}This statement ignores taxes, which generally favors holding equities for taxable US investors. There are other reasons an investor may want to own some equities under these circumstances, such as to avoid putting 100% faith in the Earnings Yield metric, as a form of hedging demand as described in Merton (1971) or as a partial hedge of an affluent investor’s consumption basket.
^{9}The formula we use is known as the Merton Rule and is: Where is the optimal fraction of the portfolio to allocate to equities, is the Excess Earnings Yield, represents the level of riskaversion of the investor in CRRA Utility and π is the expected volatility of equities. was set to 2 in the historical simulation, a round number representing an investor slightly more risk tolerant than the average of those surveyed by Haghani and White (2018).
^{10}Using the Merton Rule with we get: .
^{11}We assume that the Earnings Yield is an indicator of the real Arithmetic return of equities, although there is a good argument that Earnings Yield is predicting the real Geometric return. See Haghani and White, “What Our Market Return Forecasts Really Mean: Equity Convexity and Investment Sizing,” (2017). We constrain the allocation to equities to be between 0% and 100%, i.e. no shorting, no leverage. Relaxing the noshorting and noleverage constraints does not change the results materially.
^{12}In calculating the Sharpe Ratio, we are adding to the Geometric realized return to convert to an Arithmetic return to use in the numerator of the ratio.
^{13}Of particular note is the decade following WWII, during which we estimate tenyear TIPS would have traded at an average yield of 1.5%. During this period, the tenyear nominal Treasury bond yield averaged 2.5% and inflation ran at about 5%, touching 20% in the years directly following the end of the war.
^{14}A longterm investor may choose to measure risk in terms of the longterm real annuity value of his wealth – for example, using a perpetual inflationprotected bond as his numeraire. See Appendix for Sharpe Ratio of the Excess Earnings Yield Dynamic Strategy with returns measured relative to 10year TIPS, which also shows a roughly onequarter improvement versus a static strategy.
^{15}The improvement is (5/4)^{^2} – 1 = 9/16 = 56%.
^{16}See John Cochrane’s “Portfolios for LongTerm Investors” (2021), pp 1920 for a deeper discussion of the “Average Investor” theorem and the “LookintheMirror” test.
^{17}Assumptions: = 2, = 20%, annual rebalancing.
Membership required
Membership is now required to use this feature. To learn more:
View Membership Benefits