Stock prices continue to climb. The obvious question is whether these prices can be justified by fundamentals. Here is a simple approach to evaluating the reasonability of stock prices. We find no evidence of a “bubble” and argue that valuations are too uncertain to affect short term price dynamics.

The value of a stock is ultimatly determined by just three factors; cash flows, interest rates, and growth. 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.

To start, lets focus on the S&P 500 using current cash flows, current treasury rates, historical equity risk premium, and global economic growth.

Dividends and stock buybacks represent cash flows to the Investor. Both amount to $112 per share (payout yield of 4.37%). However, this total is more than earnings which amount to only $101. It is unsustainable for corporates to pay out more to shareholders than they earn, so we will use earning of $101 instead for our long run forecast.

Current interest rates include both the risk free rate and the equity risk premium (ERP). We will use the current 10 year tresury rate of 2.38% 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 there readers should note that there is a considerable amount of uncertainty involved in estimating an appropriate ERP. Combining the 10 year treasury rate with our ERP gives us our discount rate of 7.61%.

Earnings growth for the S&P 500 ultimatly has to come from economic growth. The international Monetary Fund estimates global growth to be 3.6% in 2018. We use this as a proxy for earnings growth because the S&P 500 consists primarily of global companies that already receive nearly half of their revenue from outside the United States. We feel that expected global growth in 2018 is the best simple proxy for S&P 500 growth because it assumes global growth, and the S&P 500 share of that growth will remain constant.

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.

Applying the Gordon Growth model we get the present value of S&P 500 earnings where:

- Current Earnings = E = $101
- Earnings Growth = G = 3.6%
- Discount Rate = R = 7.61%

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

= 101 x 1.036 / .0761 – .036

= 104.636 / .0401

= 2,609.38

This is close to Friday’s close of 2,575. Importantly, we didn’t play with these assumptions until we got close to Friday’s close. But how sensitive is our valuation to our assumptions? The answer is *very* sensitive.

Lets take growth as an example. Our 3.6% is actually quite a bit lower than the 5.5% geometric average earnings growth since 1980, and way lower than the 16% earnings growth over the past four quarters. Analysts expect growth over 10% in 2018. That range is massive and including a grwoth rate over our discount rate will actually lead to non-sensical valuations via the Gordon Growth Model.

It turns out that historical averages and near term expectations are poor proxies for future long term growth. Many forces since 1980 have allowed S&P 500 earnings to grow at an unsustainable rate relative to economic growth such as corporate tax cuts, global supply chains and related use of foreign labor, expansions into emerging markets, and falling interest rates which make it ever cheaper to borrow. This has led to rising corporate profit margins. At the same time, slowing productivity and aging populations, and perhaps other factors have led to a general fall in global economic growth since WWII.

But lets go ahead and trying using the average historical earnings growth rate of 5.5% anyway, just to see what happens.

- Current Earnings = E = $101
- Earnings Growth = G = 5.5%
- Discount Rate = R = 7.61%

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

= 101 x 1.055 / .0761 – .055

= 106.56 / .0211

= 5,050.24

Clearly, this is nonsense as it would entail a far valuation of the S&P 500 of nearly double Friday’s close.

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The purpose of this piece is to illustrate two points:

- Calling a “Bubble” is actually nearly impossible because of reasons we explain here. The key takeaway is that one can only reliably call a bubble if there is no reasonable scenario that can justify current prices. We took current earnings as given, assumed historical average equity risk premiums, assumed constant global growth, and constant share of S&P 500 earnings. This may seem unlikely to some, but it is certainly not unreasonable.
- Valuations can fluctuate by huge margins because underlying assumptions like growth and interest rates are nearly impossible to forecast with accuracy. Because of this, valuations are unlikely to play a big role in determining near term price movements. No one knows what the “correct” price is so they keep pilling their money into stocks because TINA.

Ultimatly, there will be some big correction in the stock market, but it is more likely to coincide with a recession than some general concensus that prices are “too high”.

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Note: The true stock market guru @jesse_livermore pointed out that our use of earnings in the Gordon Growth Model is atypical and potentially inappropriate. Specifically,

“The problem with using earnings is that some of those earnings are being used to fund the growth, and therefore do not represent an actual cash flow to the investor. Instead of directly getting the reinvested portion of the earnings, the investor is getting that portion via the growth.

“If the equation is written using the full earnings rather than the dividend (i.e., the portion of the earnings paid out), a type of double counting takes place. It’s as if the investor were getting directly paid the (reinvested) portion of the earnings, and *also* getting the benefit of the growth that reinvestment causes. But that’s not what actually happens. The investor only gets the growth–the reinvested portion of the earnings is used to purchase that growth.”

We agree with this view. Here are four points to consider:

1) We feel a need to recognize stock buybacks in addition to dividends because buybacks have played an increasingly important role in cash flows to investors.

2) Growth should eventually be constrained when dividends plus buybacks exceed earnings. Including only dividends in the numerator would fix this issue, but fail to recognize that buybacks are not being invested to support growth.

3) The Gordon Growth Model ignores the value of cash on balance sheet. Firms are only able to pay out more than they are earning because of cash on hand (or additional borrowing). One could try to capture this by simply adding total cash on balance sheet to the valuation. We opted to ignore the cash and simply accept a 100% earning payout over the current 111% earnings payout, but we admit this is not very scientific.

4) The use of earnings or dividends + buybacks at this point in the cycle probably leads to an overvaluation, all else equal. What we really want is a through the cycle measure of cash flows to the Investor. What we have today is probably closer to peak cycle. The problem here is that we don’t really know when the next recession will hit or how hard it will be. A “cyclically adjusted” cash flow seems worth consideration.

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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.