Dynamic asset allocation and the Equity Risk Premium

Asset Allocation

The past is not always prologue

The holy grail in investing is a magic formula that will tell you what to do and when to do it. Legend has it that Arthurian knights over 1000 years ago were searching for it. The quest continues.

Current quests revolve around some model that will tell us the riskiness of stocks and when to lighten up on equities and when to increase your allocation.


In 1999 the first edition of Robert Shiller’s book Irrational Exuberance was published. It was the height of the dot com bubble. With reference to the CAPE ratio, he wrote: “Long-term investors would be well advised, individually, to lower their exposure to the stock market when it is high, as it has been recently, and get into the market when it is low.” For readers not familiar with CAPE, take a look at this post first and, to dig deeper, these others.

Professor Shiller’s basic claim for CAPE was expressed this way: “The relation between price-earnings ratios and subsequent returns appears to be moderately strong…” and that, “We believe, however, the relation should be regarded as statistically significant.” (Shiller, Irrational Exuberance, 2005 Second Edition) p.187. All this means is that a high CAPE suggests lower expected returns. He presented no evidence that it could be used as a market timing tool. Specifically, he presented no evidence that one should lower one’s exposure to the stock market when CAPE was high. i.e., use it as a tactical or dynamic asset allocation metric.

Upside down CAPE and Excess CAPE Yield

CAPE knows nothing about interest rates. This is a major shortcoming of CAPE when it comes to assessing the riskiness of stocks.

On Nov 30, 2020, ROBERT J. SHILLER, LAURENCE BLACK, and FAROUK JIVRAJ published a paper titled Making Sense of Sky-High Stock Prices. They tell us: “…the level of interest rates is an increasingly important element to consider when valuing equities. To capture these effects and compare investments in stocks versus bonds, we developed the [Excess CAPE Yield] ECY, which considers both equity valuation and interest-rate levels. To calculate the ECY, we simply invert the CAPE ratio to get a yield and then subtract the ten-year real interest rate.” (Emphasis added)

They explain: “This measure is somewhat like the equity market premium [Equity Risk Premium] and is a useful way to consider the interplay of long-term valuations and interest rates. A higher measure indicates that equities are more attractive. The ECY in the US, for example, is 4%, [at that time] derived from a CAPE yield of 3% and then subtracting a ten-year real interest rate of -1.0% (adjusted using the preceding ten years’ average inflation rate of 2%).” (Emphasis added)

The authors’ state: “…a key takeaway of the ECY indicator is that it confirms the relative attractiveness of equities [at that time], particularly given a potentially protracted period of low interest rates.” (Emphasis added)  See article here.

The tantalizing proposition is that if at a particular time equities are more attractive compared to bonds, then one should increase equity weighting in one’s portfolio. And, if equities become significantly less attractive, one should lighten up. If ECY can be used as a dynamic asset allocation tool, one would have found the Holy Grail.

How much to invest in the stock market?

Just published is The Missing Billionaires, a book by Victor Haghani and James White. Chapter 5 is titled “How much to invest in the stock market?” The authors are principals of Elm Wealth described as a multi-billion-dollar wealth management practice. Previously they spent years as quantitative researchers and arbitrage traders.

They have developed a formula that they use in a dynamic asset allocation strategy. That is, they vary the fraction of their portfolio invested in equities on a dynamic basis according to the formula. They offer some evidence that, following their formula, an investor might generate compounded total returns in the order of 1.5% per annum above a fixed equity/bond asset allocation strategy. This is a kind of alpha and beating the market using a formula.

The Haghani and White formula has two key inputs and is based on maximizing expected utility. This is different than optimizing an expected return and results in a model that in many ways is comparable to the Kelly Criterion. Read here for more on the Kelly Criterion. Read the book to understand expected utility and their formula.

The first key input in the formula is the CAPE yield (1/CAPE – which we saw above in the 2020 Shiller article). They rename it and call it the “Earnings Yield” (not to be confused with the S&P 500 earnings yield) in their work. They tell us that “…the predictive power of earnings yield over a long horizon is not improved by assuming that it is mean-reverting.” (Haghani and White, The Missing Billionaires, 2023) p.51. That is, if I understand them correctly, when CAPE has a value over 30 one does not have to assume it will mean-revert to its long-term average of 16 for it to have predictive power.

The authors tell us that the issue of how much to invest in the stock market revolves around an evaluation of alternatives to stocks in terms of their expected long-term real returns. The asset they chose for this evaluation is ten-year U.S. Treasury inflation-protected securities (TIPS). These are the relevant low-risk alternative.

Readers will immediately appreciate that this is essentially the same as Shiller’s Excess CAPE Yield (ECY).

Haghani and White’s book tells us that their formula would have suggested no U.S. equity allocation at all from the end of 1997 until the middle of 2001. This is shown graphically in their Exhibit 5.2. They explain: “throughout this period, U.S. equity expected returns were below the real yield available from 10-year TIPS. By contrast, the highest allocation to equities was called for in the second half of 2012 when the earnings yield [1/CAPE] was around 4.7%, 10-year TIPS were yielding -0.7%, and we estimated stock market volatility at just over 16% per annum.” (Haghani and White, 2023) p.53 For the second half of 2012 the chart shows a 100% allocation to equities. The strategy calls for monthly rebalancing based on the formula.

The main driver of their asset allocation is what they call the Excess Earnings Yield and what Robert Shiller calls the Excess CAPE Yield. Shiller also says that it is “somewhat like the equity market premium” which is the Equity Risk Premium. We will look a bit deeper into the Equity Risk Premium later.

My initial reaction

My main concerns about using Excess Earnings Yield as an indicator of expected returns of equities can be expressed this way:

Firstly, based on a careful look at the Equity Risk Premium which we will do near the end of this post, I am convinced that the expected returns generated by the Excess Earnings Yield will be noisy and thus will be unreliable.

Secondly, the percent to allocate to equities each month is based on an expected utility model that only a sophisticated finance math expert can run. This violates my KISS rule (Keep it Simple Stupid). If I can’t work it out on a scratch pad, it’s too complicated.

Thirdly, the authors support the system with extensive back testing. There is no evidence given of it having been used and used successfully in a real portfolio at any time. It is conceivable that the back testing success over the last 40 years is a function of a massive secular decline in inflation and interest rates between 1980 and 2022 or some other function of the structure of the economy and world of business.

Finally, the model is particularly dependent on the stationarity of the data inputs. In particular, one of the key inputs is the earnings yield. In the last 40 years companies have shifted from making most of their long-term capital investment in tangible assets to making the bulk of their capital investments in intangible assets of lasting value. Under the accounting rules, much of this investment is expensed rather than capitalized. As a result, reported earnings have been artificially depressed. For more on this see my post The emergence of a new model of capitalism

Equity Risk Premium

Now we come to the heart of this post. What can we learn from the Equity Risk Premium? Can it be used to support some form of dynamic asset allocation. Or, is it limited to its role in developing a discount rate for the valuation of equities. See my post on discount rates and the valuation of equities here.

Aswath Damodaran, is a Professor of Finance at the Stern School of Business at New York University, where he teaches corporate finance and equity valuation.

He wrote recently: “If you have been reading my posts, you know that I have an obsession with equity risk premiums, which I believe lie at the center of almost every substantive debate in markets and investing.” See here.

Here’s how Damodaran defines Equity Risk Premium in the above linked post:

“Investors are risk averse, at least in the aggregate, and while that risk aversion can wax and wane, they need at least the expectation of a higher return to be induced to invest in riskier investments. In short, the expected return on a risky investment can be constructed as the sum of the returns you can expect on a guaranteed investment, i.e., a risk-free rate, and a risk premium, which will scale up as risk increases.

Expected Return = Risk free Rate + Risk Premium”

Damodaran adds: “Since the equity risk premium is a price for risk, set by demand and supply, it stands to reason that it is driven not only by economic fundamentals, but also by market mood.”

He comments that: “…one symptom of a market bubble is an equity risk premium that becomes so low that it is disconnected from fundamentals, setting up for an inevitable collision with reality and a market correction.” This observation gets my attention.

How does one come up with the Equity Risk Premium?

We can’t measure the Equity Risk Premium directly. That’s because equity investors are not explicit in fixing an expected return when they buy stocks. What we are looking for is a number set by the market for the price of risk. There are a number of approaches to estimating the Equity Risk Premium.

Damodaran looks at four approaches: Historical Risk Premium; Historical Returns-Based Forecasts; The Fed Model: Earnings Yield and ERP; and, Implied ERP

His favorite approach is the Implied ERP. He starts with the same general model for value that the earnings yield approach does but makes three adjustments: He adds buybacks to dividends in recognition of the fact that U.S. companies have shifted from returning cash in the form of dividends to stock buybacks; He makes an allowance for near-term estimated growth in earnings; and, he adjusts the cash return percentage over time, as a function of growth and return on equity.

He has prepared a table to see whether the different approaches work well in practice in predicting future returns on stocks. He says he has tried “…to capture that in a correlation matrix, where I look at the correlation of each ERP measure with returns in the next year, in the next 5 years and in the next 10 years.”

His conclusion is that: “None of the approaches yield correlations that are statistically significant, for stock returns in the next year, but the implied ERP and historical ERP are strongly correlated with returns over longer time periods, with a key difference; the former moves with stock returns in the next ten years, while the latter moves inversely.”

He adds: “While that correlation lies at the heart of why I use implied ERP in my valuations as my estimate of the price of risk in equity markets, I am averse to using it as a basis for market timing, for the same reasons that I cautioned you on using the EP ratio regression: the predictions are noisy and there is no clear pathway to converting them into investment actions.(Emphasis added)

Damodaran does a scatter plot. He reports: “You can see, from the scatter plot, that implied ERPs move with stock returns over the subsequent decades, but that movement is accompanied by significant noise, and that noise translates into a wide range around the predicted returns for stocks. If you are a market timer, you are probably disappointed, but this type of noise and prediction errors is what you should expect to see with almost any fundamental, including EP ratios.”


I’ll let Aswath Damodaran have the last word. He comments in the post: “The past is not always prologue, and market and economic structures can shift, undercutting a key basis for using historical data to make predictions.” Bottom line: I’ll steer clear of formulae, systems and dynamic asset allocation techniques with a ten-foot pole. I’m still satisfied that the only timing investors should be engaged in is what Ben Graham called timing “by way of price”, when we buy an individual high-quality stock at a price substantially less than fair value so as to obtain a margin of safety.


You can reach me by email at rodney@investingmotherlode.com

I’m also on Twitter @rodneylksmith


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