Last week’s selloff has a lot of people asking, “How much is the stock market really worth?”. Here we attempt to answer this question and provide insight into the relationship between stock prices and interest rates.

# Stock Market Valuation

The value of a stock is ultimatly determined by just three factors; cash flows to shareholders, the growth rate of cash flows to shareholders, and the discount rate. Forecasting these three factors precisely is impossible, but solving for currecnt stock prices using assumptions about these values can be illuminating. For a cash generating asset like stocks the price should equal the present value of future cash flows. This approach will allow you, the reader, to see just what is implied by today’s prices so you can evaluate the obvious question more rationally.

### Cash to Shareholders

Dividends and stock buybacks both provide **cash flows to the Investor and amounted to $106.37 per share** at the end of 2017. Total annualized dividends of $436 Billion and total buybacks of $517.7 Billion equate to $47.41 and 56.29 dividends and buybacks per share. Dividing dividends per share by Friday’s S&P 500 close of 2619.55 gives a dividend yield of 1.818%. To double check our calculations we note that Yahoo Finance calculates the $SPY dividend yield at 1.7% while Robert Shiller’s website data puts the S&P 500 12-month dividend yield at 1.87% (below). Including buybacks provided a total cash to shareholder yield of 3.958%.

Figure: S&P 500 Dividend Yield. Note that dividend yields have been falling for much longer than the fall in interest rates. This is in part because of an increase in the popularity of buybacks.

Veteran investors will note that our inclusion of buybacks is a controversial decision. Buybacks are not as reliable as dividends. Buybacks have also been blamed for a lack of corporate investment despite Warren Buffett’s comments to the contrary. However, the fact-of-the-matter is that there is no theoretical difference between paying shareholders via dividends vs buybacks except that dividends immediatly trigger a taxable event. For example, suppose a $5,000 firm with 100 shares trading at $50 each decides to issue a dividend of $1 per share for a total of $100. Shareholders will be required to pay at least 15%. Suppose instead that the firm buys back $100 worth of the company. At $50 per share the firm buys back two shares resulting in each remaining share being worth $5,000 / 98 = $51.02. Now if all shareholders sold their gains they would recognize a total capital gain of $100 (same as with dividends), but if they hold these share the gains compound allowing shareholders to avoid a taxable event. This is one reason why firm’s have been doing more buybacks in recent decades.

### Growth Rate

Growth in cash to shareholders is arguably impossible to forecast accurately. For this reason, we use a long term average GDP of the United States since 2000 which comes out to **4% as our assumed growth rate**. This includes real growth and inflation so this assumption would be consistent with inflation of 2% and real economic growth of 2%.

A look at historical dividend and earnings growth since 2000 illustrates the difficulty in forecasting the growth rate (below). Dividend yield growth ranged from 17.5% in 2012 -17.7% in 2009 while earnings growth ranged from 400% in 2009 and -77.7% in 2008. Compounding a 4% growth rate to dividends in and earnings starting in January 2000 provides a final dividend and earnings at the end of 2017 that is 6.4% and 15.9% lower than actuals, suggesting that our assumed growth rate is conservative.

There are many reasons why this number may be wrong, but here are perhaps the top three.

- Growth in the US is not reflective of S&P 500 revenue, nearly half of which comes from foreign countries.
- Growth may not be sustainable given that firm’s are paying out 91.5% of their earnings (leaving only 8.5% for reinvestment).
- Growth in buybacks since 2000 may have been artificially inflated by generally falling cost of borrowing (i.e. lower interest rates).

Addressing each reason in turn:

Our growth rate assumption is considerably lower than the International Monetary Fund real GDP forecasts. The IMF forecasts real global growth to be 3.7% in 2018 and 3.9% in 2019. Their US forecast is 2.7% in 2018 and 2.5% in 2019. Current breakeven inflation for the 5yr and 10yr are 1.89% and 2.09% respectively so nominal growth in the US is forecasted to be about 4.6% over the next couple years. Note that this is in line with recent real GDP according to the BEA. Of course, if we have a recession then growth will fall and earnings will fall along with it. Using economic growth to proxy for earnings growth also assumes that corporate profits as a share of GDP will remain unchanged. Rising wages may actually reduce corporate profits as a share of GDP. Therefore, we are comfortable sticking with 4% because we want a growth rate that we can use in perpetuity (more on why later).

Sustainable growth requires investment. Currently, firm’s in the S&P 500 are paying out (dividends + buybacks) 91.5% of their operating earnings. This payout ratio actually exceeded 100% of after-tax earnings in 2016 although today it is closer to 100%.

Veteran investors will note that this is inconsistent with the concept of “Sustainable Growth Rate”. Recall the definition of SGR below. SGR makes three assumptions. It assumes that every dollar of profits not paid out in dividends is reinvested in the company, that those investments will generate a return on equity (ROE) in line with that of existing projects, and that firm’s without profits will ultimately stop growing. Its this last assumption that we take issue with.

Sustainable growth rate = (1 – Payout ratio) (Return on equity)

As we argue here, firm’s without earnings can grow. The reason is that firm’s today are able to fund growth through expenses that reduce earnings (ex. Amazon). Firm value is increasingly derived from intangible assets, also called knowledge assets or intellectual capital. Intangible assets include key personnel, computerized information (such as software and databases), innovative property (such as scientific and nonscientific R&D, copyrights, designs, trademarks), and economic competencies (including brand equity, firm-specific human capital, networks joining people and institutions, organisational know-how that increases enterprise efficiency, and aspects of advertising and marketing). Firm’s can expense much of its “investment” in intangible assets in the the form of wages. The result is growth that far exceeds what the traditional SGR calculation would suggest.

The final reason we address recognizes that our growth rate was derived from a period of generally falling interest rates. We are concerned that perhaps today’s new environment of flat (or perhaps rising?) interest rates will make it harder for firm’s to maintain growth rates. The most obvious reason for this would be if firm’s were continually taking advantage of falling rates to increase borrowing and buy back stock. Suppose firm’s stop doing this resulting in a dramatic and permanent drop in buybacks. That would result in a gross overestimate of the growth rate in cash flow to shareholders, because a majority of it comes from buybacks.

If the rise in buybacks since the 1990s was driven by falling rates we should see really high leverage ratios today relative to the 1990s. However, leverage ratios today do not appear particularly high. Debt to earnings is about 10% today compared to around 9% in the 1990s, but total debt to assets is under 4 compared to well over 4 in the 1990s. Interest coverage is very high reflecting manageable debt service.

### Discount Rate

The discount rate is the sum of two components; government bond yield (i.e. “risk-free” rate) and the equity risk premium (ERP). We will use the current 10 year tresury rate of 2.83% as our risk free rate in order to reflect the risk for a long term investor. We assume an ERP of 5.23% which is the geometric average return of the S&P 500 over the 10 year treasury rate from 1928-2015. Our ERP is roughly consistent with current expectations, but readers should note that there is a considerable amount of uncertainty involved in estimating an appropriate ERP. Many including Professor Aswath Damodaran @AswathDamodaran cite 6% as the long term average. Combining the 10 year treasury rate with our ERP gives us our **discount rate of 8.06%**.

We recognize that these are all big assumptions, but big assumptions are necessary in order to evaluate something as large and complex as the S&P 500. Again, the point here is to see if reasonable assumptions can be used to justify current prices. We don’t need to be exactly, right, we just want to avoid being completely wrong.

### Gordon Growth Model

We apply the Gordon Growth model we get the present value of S&P 500. This model assumes that cash flow to shareholders will grow at a constant rate forever (a perpetuity). Here are our 3 inputs:

- Cash to Shareholders = E = $106.37
- Growth Rate = G = 4%
- Discount Rate = R = 8.06%

Gordon Growth Valuation Model = E x (1 + G) / (R – G)

= 106.37 x 1.04 / .0806 – .04

= 110.625 / .0406

**Our valuation = 2,724.75**

This is 4% above Friday’s close of 2,619.55. Importantly, we didn’t play with these assumptions until we got close to Friday’s close. But before you get excited lets take a look at our benchmarking exercise and sensitivity analysis. What we find is that valuations today are high and very sensitive to our assumptions.

# Benchmarking Valuation to Prior Years

We benchmark this valuation by comparing the implied ERP and CAPE with prior years. What we find is that our valuation is higher prior years by both measures. However, we think that this is to be expected given the (still) generally lower interest rate environment and willingness of investors to accept higher stock valuations in order to increase returns.

We chose to make this calculation for every third year starting in 2003. Here are four takeaways from this benchmarking:

- 2003 was an expensive year according to implied ERP of only 2.56% (outlier), but turned out to be a good time to invest.
- The buyback component of cash to shareholders has varied considerably. This is one reason some ignore buybacks as we pointed out earlier.
- 2006 through 2015 had an implied ERP of above 6% (cheap).
- CAPE and ERP suggests valuations are considerably higher today than in recent years.

So do high valuations mean we should be fearful and sell our stock? We don’t think so, and the reason may surprise you.

Over the past 100 years stocks have outperformed treasury bonds by an average of 6%. This 6% is the average historical ERP. Now if you could go back in time with this knowledge and place your best what would you do? For most people with a long time horizon they would buy stock!

There are many reasons why stocks grossly outperformed bonds. To start, investing in stocks during the 1920s was a lot like trading cryptocurrencies in 2017. No one but the CEOs (developers) really knew what they were buying. All they had was a nice story written by the CEO without any accounting or accountability. Old school investors considered investing in stocks to be more like gambling than true investing (which they did via bonds). Investors bought single stocks because it was expensive to transact and theories like CAPM didn’t exist and the importance of diversification were not well understood. In short, the risks and performance of stocks were highly uncertain and the costs of investing were high. Fast forward to today and pretty much everyone with capital knows it’s important to diversify stocks and can do it via Vanguard’s $VOO for a whopping 0.04% per year.

As a result, investors are willing to invest in stocks even when the ERP is below the historical average. Beating treasury bonds by 6% is a steal. Beating by 5% is probably still really good. This reality is a key reason why the CAPE is clearly no longer mean reverting. The long run ERP is falling because investors are realizing that historical stock valuations were too low after accounting for diversification and lower costs.

So what’s the right ERP? No one knows. Stocks are still way more volatile than 10yr Treasury Bonds so its reasonable to expect a healthy ERP to compensate investors. That said, the only way for everyone to get more exposure to stocks, and for this seemingly inefficient arbitrage to disappear, is for stock valuations to rise. Only then can realized stock returns drop to something more reasonable relative to government bonds. We would not be surprised if ERP fell to 4% by 2028. A generally rising ERP over the next 10 years is critical to our bullish stance on stocks. Its a contrarian view, but that’s kinda the point.

So how sensitive is our valuation to our assumptions? The answer is *very* sensitive.

# Sensitivity Analysis

Results are very sensitive to all our assumptions, but for this post we are going to focus on sensitivity to the discount factor and its components.

Lets start by examining a move up in the 10yr Treasury to 3% (or an increase of 17 basis points). First, we solve for the implied ERP of 5.412% using Friday’s S&P 500 close of 2,620. Initially, we take the 10yr Treasury rate from Friday close of 2.83% for a total discount rate of 8.242%,

- S&P 500 = 2,620
- Cash to Shareholders = E = $106.37
- Growth Rate = G = 4%
- Discount Rate = R = 8.242%

Gordon Growth Valuation Model = E x (1 + G) / (R – G)

2,120 = 106.37 x (1 + 4%) / (8.242% – 4%)

Now increasing the 10yr Treasury rate to 3% (17bps). Assuming no other change in input variables.

- Cash to Shareholders = E = $106.37
- Growth Rate = G = 4%
- Discount Rate = R = 8.412%

Gordon Growth Valuation Model = 106.27 x (1 + 4%) / (8.412% – 4%)

= 106.37 x 1.04 / .08412 – .04

= 110.625 / .04412

= 2,507.37

This result illustrates how sensitive the stock market has become to changes in the risk free rate. A 17bps move up in the 10yr Treasury rate would decrease the S&P 500 by 4.5%, or about 0.26% per basis point. So yes, the stock market should fall in response to rising rates. However, as Josh Brown @reformedbroker pointed out in a post earlier today, financial markets are a *“complex, adaptive, biological system”*. The 10yr Treasury rate is arguably the most important price in financial markets. When it moves it is the result of countless factors including inflation expectations and strength in the economy. For example, when the 10yr Treasury moves higher it may coincide with a rise in expected future nominal earnings growth. This may mitigate the impact of rate rises on S&P 500 valuations.

Given the sensitivity of the S&P 500 to changes in both the 10yr Treasury rate and ERP we examine a range of possibilities. Below we illustrate a data table of S&P 500 valuations that are consistent with a range of discount rate components given our other assumptions; specifically a nominal growth rate of 4% and cash to shareholders of $106.85% (slightly more than year end 2017 to account for a 4% annualized growth rate).

The ranges we chose are judgmental but not completely arbitrary. The 10yr Treasury rate was about 2.4% in December before it started its rapid move higher to the current 2.83%. Some are calling for the 10yr Treasury to rise as high as 3.5%. Professor Aswath Damodaran, an expert on ERP, often cites 6% as being a very long term historical average ERP for the US. However, as explained earlier, we believe this historical average is an upper bound.

Note the range of possible S&P 500 valuations…this is why its so hard to make reliable forecasts.

# Conclusion

- By applying some defensible assumptions to a Gordon Growth Model we arrive at a S&P 500 valuation of 2,724.75 or 4% above Friday’s close of 2,619.55.
- A 1bp move up in the 10yr Treasury rate coincides with a 0.26% decrease in stock prices. However, this assumes that economic growth and other inputs remain constant, a strong assumption.
- S&P 500 is more expensive today, in terms of both implied ERP and CAPE, than most periods since 2003.
- We believe that higher stock valuations will continue as investors are willing to accept market volatility in exchange for higher longer run returns (i.e. ERP is likely to fall in the long run).
- S&P 500 valuations are very sensitive to interest rates and ERP. This makes forecasting stock prices extremely challenging and subjective.

Ultimatly, there will be a bear market for stocks, but it is more likely to coincide with a recession than some general concensus that prices are “too high”.

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Feel free to share your own thoughts on stock market valuations. There is no better compliment you can give us than your thoughtful criticism. You can reach us at intuitecon@gmail.com, or follow us on Twitter @intuitecon

Sincerely,

IntuitEcon Team

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Disclaimer: These are our personal views. This article is not, and should not be regarded as investment advice or as a recommendation regarding any particular security or course of action. Our hope is that these observations will merely help you to more critically examine your own beliefs about finance and stimulate dialogue.

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