- We use a residual income model to compute an intrinsic value for the market. This model considers forecasts for future earnings and for long-term earnings growth to estimate the equity risk premium for the S&P 500.
- We combine the equity risk premium with the risk-free rate to produce an equity yield, and compare the equity yield to the yield on investment grade bonds to classify the market as undervalued, overvalued or fairly-valued.
- When the equity market is overvalued relative to investment grade bonds, it tends to see smaller returns and higher volatility. Currently, we consider the market to be undervalued.
Market Valuation, Equity Yields and the Residual Income Model
Many quantitative metrics have been put forth to evaluate the valuation level of the market, i.e. whether it is “cheap” or “expensive.” The forward price-to-earnings ratio is one example of such a metric. In this note, we introduce a unique and differentiated method for computing the level of market valuation.
Our method makes use of a residual income model to estimate the equity risk premium. The residual income model works like a dividend discount model or discounted cash flow model in that it computes the current value of an asset (in this case, the S&P 500) as the sum of a series of discounted flows. Instead of discounting future dividends or cash flows, however, the model discounts future residual income, where the “residual” reflects the return a company earns above and beyond its cost of capital. By supplying forecasts for future earnings and for long-term earnings growth, the model computes the equity risk premium that is currently priced by the market. A full description of the residual income model can be found in Appendix I.
What It Means: Stocks are valued in a variety of ways and one of the most common is price-to-equity (P/E) ratios. Stocks with higher P/E ratios are considered more expensive since the duration is longer, meaning a higher level of growth will be required to maintain the level of valuation. Our valuation model is similar, but uses residual income, or the amount of profits above the cost of capital, in place of earnings.
Fig. 1 below shows the historical equity risk premium as measured by the residual income model. The gray regions indicate recessions.
Fig. 1 – Equity Risk Premium from Residual Income Model
The equity risk premium represents the amount of return an equity investor requires over the risk-free rate. We can compute the “equity yield” as the sum of the equity risk premium and the risk-free rate. We can then compare this equity yield to the yield on traditional fixed income instruments to determine whether the equity market is attractively valued when compared to other asset classes. We compute the yield ratio as the equity yield divided by the yield on investment grade corporate bonds.
What It Means: The important thing to understand about the Equity Risk Premium measurement is that it allows the risk-adjusted return of stocks to be compared to debt. Since so many institutional buyers buy both stocks and bonds, the relative difference in valuation can imply whether capital will flow more towards stocks or bonds.
In Fig. 2, we show the history of the yield ratio as the blue line. The dashed black lines are the upper and lower quartile values for the yield ratio. When the blue line rises (falls), equities are cheap (expensive) compared to investment grade bonds.
Fig. 2 – Equity vs. Investment Grade Yield Ratio
Using the rolling upper/lower quartile value cutoffs (indicated by the dashed lines in Fig. 2), we can further segment the history of the yield ratio into 3 regimes:
- High (above upper quartile value) – indicates equities are undervalued
- Middle (between lower and upper quartile values) – indicates equities are fairly-valued
- Low (below lower quartile value) – indicates equities are overvalued
For example, during the 2008-2009 timeframe, as well as during 2015, the yield ratio was below the lower quartile value, indicating the market was overvalued. On the other hand, from 2010-2013, the yield ratio was generally above the upper quartile value, indicating that equities were cheap compared to investment grade bonds.
What It Means: The relative value of bonds versus equities is incredibly important in governing how institutional money flows. Many funds switch their distribution between equities and bonds based on the relative value between the two. Though there is a lot of commentary right now suggesting equities are overvalued, by the measure we use in figure 2, equities seem undervalued and less expensive than recent periods.
The Yield Ratio and Market Performance
We next consider the market performance conditioned on the level of the yield ratio. For each month, we determine which yield ratio regime we currently occupy (high/middle/low) and measure the market performance in the subsequent 3-month period. Fig. 3 shows the results of this study – the blue bars indicate return (plotted on the left-hand axis) and the orange bars indicate volatility (on the right-hand axis).
Fig. 3 – Market Subsequent Return and Volatility Conditioned on Yield Ratio
The chart indicates that the market performs best when it is undervalued compared to investment grade bonds, as the S&P 500 subsequently gains 5.2%, on average, in this scenario. When the yield ratio indicates the market is fairly-valued, the S&P typically gains 4.0% in the following 3 months. When the yield ratio indicates that the market is overvalued, however, the market only returns 0.8%, with much higher volatility.
From Fig. 2, we see that recently, the market re-entered the undervalued state. The last time the yield ratio considered the market to be overvalued was November 2018. In the following 3 months, the market rallied, but by less than 1%. As of December 17, the yield ratio is 2.08, which places us in an undervalued regime.
What It Means: Equity markets perform best when they are undervalued, which might seem obvious. However, even when equities are fairly valued, they have a three-month return averaging 4%. Volatility actually is historically lowest when equities are fairly valued. This is all based on historical analysis and of course, doesn’t take into account headline risks like the Omicron variant.
Appendix I – Residual Income Model
We estimate the equity risk premium using a residual income model. The residual income approach has been used in the past to estimate valuation. At the company level, the residual income model computes a valuation based on current book value and a sum of discounted residual income. The residual income component is derived from the return the company expects to generate in excess of its cost of capital.
We apply this methodology to the S&P 500 – a theoretical value for the S&P 500 is generated from the current book value for each S&P 500 constituent, along with a series of discounted residual income figures. We assume the sum of these theoretical values across all S&P 500 constituents should match the total market capitalization of the index. We use a two-stage approach to estimate the value for each firm:
V = estimated theoretical value for firm
NIt = net income at time t
r = cost of capital
Bt-1 = book value at time t-1
ROEt = return on equity at time t
Stage 1 (years 1-5)
We use the following approach to calculate net income for each year. For years 1 & 2, we use the mean of consensus forward earnings estimates.
NI1 = mean of consensus forward net income estimates for months 1-12
NI2 = mean of consensus forward net income estimates for months 13-24
For years 3-5, we apply an estimate for long-term growth rate to arrive at net income in year 5. We then use linear interpolation to estimate the net income values for years 3 & 4:
LTG = estimate for long-term earnings growth (we use an estimate of 6.5%, see below)
Stage 2 (years 6 and forward)
We assume the return on equity (ROE) converges toward the cost of capital following an exponential decay process with a half-life of 10 years (i.e. 10 years into stage 2). As such, we can express the excess of ROE over r in year t as:
Where ROE5 is the ROE in year 5 (i.e. last year of stage 1).
We assume a firm life of 100 years, so the original equation becomes:
The book value in year t-1 (i.e. Bt-1) is computed as:
Bt-2 = book value in year t-2
NIt-1 = net income in year t-1
payout = average dividend payout ratio over the past 10 years
With the net income in year t-1 (NIt-1) during stage 2 being computed as:
The equity cost of capital (r) can be broken into two parts:
rf = risk-free rate
rp = equity risk premium
Using the yield on the 10-year Treasury note as the risk-free rate, we can back into the equity risk premium.
Estimate of long-term earnings growth rate (LTG)
To estimate the long-term growth rate for earnings, we analyze the historical growth rate of earnings for the S&P 500. As we are looking to proxy for the long-term growth rate in earnings, we consider the annualized growth rate in realized earnings, looking at overlapping 5-year periods. Fig. 4 below shows the annualized 5-year earnings growth rate for the S&P 500, back to 1980.
Fig. 4 – S&P 500 Realized Earnings Growth Rate
The dashed black line in Fig. 4 shows the average realized earnings growth since 1980, which runs at 6.5%. Looking over different horizons, the average growth rate in earnings is 6.8% since 1990 and 6.3% since 2000. Taking this information into account, we use an estimate for the long-term growth rate of earnings of 6.5%.