#### Assessing the Attractiveness of Stocks Versus Bonds | July 22, 2023

Have you ever heard analysts express concern about how expensive stocks are relative to bonds? In this report, we will explain the reasoning behind this view. We will introduce a fundamental valuation signal, “implied earnings growth,” to assess the relative value of stocks versus bonds. Through our analysis, you will gain insight into why many investors are cautious and underweight equities – and why they are wrong.

## Constructing the Signal One Step at a Time

The justification for comparing returns from stocks and bonds is clear: both asset classes compete for your savings, so you should price them relatively. To compare, we must express both assets in return space. In the case of bonds, that would be the nominal yield, while in the case of stocks, the earnings yield, which is the inverse of the price-earnings ratio (P/E).

Ideally, you would want to use the Forward P/E (which uses estimated earnings over the next 12 months) but as this data is less readily available for everyone, we will be using the Trailing P/E (which uses earnings over the past 12 months). Note, however, that Forward P/E is 13% lower than Trailing P/E, and trending lower given the improved earnings outlook. This is particularly so for tech stocks such as Nvidia, as discussed in our report The Big Picture. Therefore, using Trailing P/E makes stocks look much more expensive than what the market perceives them to be.

We start with the Fed Stock Valuation Model, in which the 10-year nominal treasury yield should be equal to a fairly priced earnings yield (E/P). You can see below that both series move together and seem correlated, which is exactly what you would expect, given that they compete for the same savings.

Figure 1: Bond yield vs. earnings yield

A shortcoming of the FED Model is that it does not provide an apples-to-apples comparison, as stocks are riskier assets than US treasuries. To overcome this, we use the equity risk premium (ERP), which compensates investors for the additional risk they take on when investing in stocks compared to bonds. One can solve for the ERP, given that the nominal yield and E/P ratio are known, which is what most analysts do. However, we are going to consider it as another input: we will use 5% for the ERP, a commonplace assumption derived from the historical excess return of stocks over bonds.

The Earnings yield (E/P) can be broken down into two components: dividend yield and price appreciation. Since not all earnings are paid out to investors as dividends, the retained portion is reinvested in the company, increasing its value and leading to price appreciation.

As you may know, dividends are notoriously sticky (fun fact: Lehman paid dividends until it died). Additionally, since price equals earnings multiplied by P/E, if we assume the P/E multiple is constant, price appreciation comes entirely from earnings growth. Therefore, by rearranging the equation, we get:

In other words, this model provides the implied nominal earnings growth given nominal yield, dividend yield, and ERP as inputs. We can further subtract inflation expectations (derived either from surveys or market prices) to arrive at the implied real earnings growth.

Robert Shiller provides most of the information needed to calculate this on this website. The exception is inflation expectations, which can be found on FRED.

## The Situation Today

Using the model from the previous section, we can construct the time series for Nominal and Real Implied Earnings Growth. The latest figure of real implied earnings growth is 5.22%, and is calculated using an earnings yield of 3.9% (25.4 P/E) and a payout ratio of 38.9%. As the chart below shows (see Figure 2), implied earnings growth has not been this high since the Great Financial Crisis (GFC).

Figure 2: Implied earnings growth

One way to interpret this is that the advent of Generative Artificial Intelligence and other technological advances may merit the return to growth rates like those seen before the GFC. If one believes so, as we at Asgard do, equities could be fairly priced relative to bonds (or even cheap).

On the contrary, if one believes in a thesis of stagflation or economic activity slowing down significantly, this signal suggests equities are expensive relative to bonds. Of course, that assertion assumes bonds are fairly priced. As covered in our prior report, The Fabric of Interest Rates, we expect a bullish steepening in US rates and long bonds to rally (i.e., to go up in price).

To bridge these figures with our expectations, we take two additional steps. First, we replace the Trailing P/E we used earlier with the Forward P/E (18.9x), which results in an earnings yield of 5.3%. This is significantly higher than the backward-looking earnings yield of 3.9% (see Figure 1) and reduces the real implied earnings growth from 5.22% to 4.69%.

In the second step, we adjust the input for the 10-year nominal treasury yield to reflect a Rates Normalization scenario. Instead of using the current yield, we use a forecast for what the yield is expected to be in six months, based on a Reuters poll of 75 bond strategists. This forecasted yield of 3.5% is more in line with historical trends and our expectations. As a result, the real implied earnings growth is further reduced to 4.38%.

Below we present these revised figures (in light blue) along with historical annualized growth rates (in orange). Forward-looking real implied earnings growth is lower than real implied earnings growth pre-GFC, lower than actual earnings growth since the GFC, and slightly lower than actual earnings growth during the last decade. Therefore, one can conclude that market expectations for earnings growth are not unreasonably high.

Figure 3: Revised real earnings growth vs. historical rates

## Conclusion

We have built an implied earnings growth model to gauge the pricing of stocks relative to bonds. Even though stocks may look expensive to those who believe the economy may be about to enter stagflation or hit a severe recession, we have shown how, contrary to popular belief, stocks can also be seen as fairly valued. This is a significant finding, as many analysts and portfolio managers currently use variations of this model to conclude equities are very expensive and remain heavily underweight.

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