*General argument*: The US equities markets as a whole are probably overvalued by double-digit percentage points, which very likely bids down future returns well below historical levels. I am against a short of any US-based equities market despite the fact it seems reasonably overvalued, as there is no immediate catalyst.

**Overview**

About once a month I enjoy doing an exercise to estimate the intrinsic value of the S&P 500 (NYSEARCA:SPY) by incorporating various relevant factors that influence the price of the index. Having an idea of where the market should be trading is useful in determining how the index might be trading relative to historical norms and to obtain some understanding of how the current valuation might help back out forward returns expectation - and how this might relate in comparison to one's own expectations. Those who have 8% returns expectations are going to price the fair value of the market lower than those who require 6%.

For the discounted cash flow model used to value the S&P 500 index, I use the following inputs from the market:

- Current dividend yield
- Current earnings yield
- Expected cash payout ratio (the sum of dividends and net share buybacks as a percentage of earnings)
- Earnings growth rate
- 10-year US Treasury yield (used as a "risk-free rate")
- Equity risk premium (i.e., investors expected returns minus the 10-year Treasury)
- Terminal growth rate, set equal to the long-term real growth expectations of the US economy

As of February 3, the current dividend yield in the market comes to 1.99%. This figure is calculated by taking the average dividends dispersed on a trailing-twelve-months' ("TTM") basis and dividing the amount by the current value of the index. (The all-time low was 1.11% in August 2000 due to the extreme valuations (and relative newness of the companies) seen in the lead up to the dot-com crash. The all-time high was 13.84% in June 1932 during the Great Depression.)

The earnings yield of the S&P 500 currently sits at 3.88%, which represents a seven-year low. (The all-time low of 0.81% came in May 2009 (financial crisis) and the all-time high of 18.82% came during World War I in December 1917.)

*(Source: multpl.com)*

This value is obtained using the same TTM approach, and will be the figure used in the discounted cash flow model. This figure is same as it was last month.

The cash payout ratio is an input that can be estimated from historical norms. Companies cannot sustainably pay out more than their earnings in dividends and net share buybacks. In the recent earnings downturn that lasted through 2015 and the first three quarters of 2016, many companies compensated by paying out more than 100% of their earnings to keep investors on board and prop up share prices. This has contributed to some of the lift in the market. This nonetheless requires forgoing business reinvestment, dipping into a retained earnings surplus (if available), and/or issuing higher quantities of debt to support the increase in buybacks or dividends.

Payout ratios have tended to hover around 75% on average, with rates in the high-80%'s (and sometimes higher) seen during recessions, markets shocks, or periods of lower earnings. Over the past thirty years, we've seen five different periods at which payout ratios in the market were above this threshold: 1989 (Japan debt crunch), 1998 (Russian crisis), 2001 (dot-com bubble), late-2007 to mid-2009 (financial crisis), and most recently with an elongated earnings recession (seven quarters measured year-over-year; five quarters measured quarter-over-quarter), which incentivized management teams to repurchase shares to wait out the earnings drought.

With private non-residential fixed investment lagging in the US, above-trend cash payout ratios are likely to remain in place. As business investment picks up again, the ratio will likely normalize back in the mid-to-high 70%'s. Non-residential fixed investment recently emerged from a three-quarter recession, increasing 0.3% year-over-year in Q4 2016.

(*Source: U.S. Bureau of Economic Analysis; modeled by the Federal Reserve Bank of St. Louis*)

In the DCF model used for this exercise, I've set the cash payout ratio to 80%, a rate that is sustainable yet still reflective of the current elevated trend.

Earnings growth is a volatile thing and can fluctuate heavily year to year. As mentioned, it was previously on a negative slope for several consecutive quarters, but appears to be recovering, up in Q4 2016 and Q1 2017. The recent spring up in the market also provides the expectation of an earnings recovery and future higher earnings on the back of expansionary fiscal initiatives.

(*Source: macrotrends.net*)

Since Q1 1990, year-over-year earnings growth has approximated 8% at the median. Forward-looking growth rates take into account a 1.8% long-term growth rate, as estimated by the Fed and a rate that I believe is quite accurate. Even if we were to assume that earnings growth comes to 10% in year-over-year terms during 2017 (i.e., above trend growth) and converges to the long-run growth rate of the economy over a period of 10 years, this would place the compounded average at 6.20%. If we use a period of 20 years to converge to 1.8% growth, this value would change only slightly to 6.06%.

(*Source: author*)

I've used 6.2% as the earnings growth estimation, but a valuation range can be sensitized to this input. The model isn't particularly touchy to this input, as it's a numerator term and will change the output linearly rather than exponentially as in the case of a change to the denominator term.

The 10-year Treasury rate was 2.47% after last Friday's market close, holding roughly steady throughout the month of January. A higher 10-year Treasury, or "risk-free rate," will work to lower the valuation given the way in which it raises the discount rate used to value the cash flows. And on the basis of relative attractiveness, higher Treasury yields - which coincide with higher fixed-income yields generally - will reduce the appeal of equities from a risk-to-reward perspective.

The equity risk premium is one additional option as a sensitivity parameter, as it helps to back out the current returns expectations in the market. The equity risk premium of the S&P 500 has historically trended around an average of 4.1% when defined as the annual average sum of the S&P 500's earnings yield and dividend yield minus the year-end 10-year Treasury bond yield.

**General Methodology**

This valuation exercise is done on the basis of cash flows. Therefore, to find the projected cash flow for each year we need to multiply the expected earnings yield by the current value of the S&P 500 index, then multiply by the expected payout ratio.

This is completed for each year of the projection period, with five years projected in total. These cash flows are discounted back to the present by dividing by a discount rate equal to the sum of the equity risk premium and the 10-year Treasury yield to the power of whatever year in the future we're projecting.

After the five-year projection, a terminal value is taken as the expected cash flow in what is essentially a sixth year (the expected earnings in the fifth year of the projection period multiplied by the long-term growth rate of the economy). This is then divided by a discount rate calculated as: 10-year Treasury yield (2.47%) + equity risk premium (4.1%, historically) - the expected perpetual growth rate of the economy (1.8%)

With this discount rate, the terminal value can then be discounted back to the present. This value can then be added to the present value of the other cash flow to derive an intrinsic value for the index.

The 10-year Treasury yield is currently higher than the expected real long-run growth rate of the economy, which is normally the case. This means the discount rate used with respect to the terminal value will be higher than the equity risk premium. In terms of real-world behavioral implications, this reflects that investors will expect higher returns on stocks when bond yields increase without an accompanying increase in growth expectations.

**Results**

Based on these assumptions, if we adjust the earnings growth assumption by +/- 150 bps on each side of 6.2%, we would obtain a valuation range of **1740-1980**, or anywhere from about **14%-24% overvalued**.

If we edge some of our assumptions higher, such as the boosting the long-run growth rate back up to 2.0% (from 1.8%), the cash payout ratio up to 85% (from 80%), discount at an equity risk premium of 4.0% (down from 4.1%), that would give the index a value of 2090 rounded, for about a 9% overvaluation.

If we uniformly return to our aforementioned assumptions (1.8% long-run growth, 80% payout, 4.1% ERP), earnings growth would need to approximate **9.7% for the next five years** to value the S&P 500 at its current level near 2300. Considering the median has held around 8% in real terms since 1990 and economic growth has become progressively harder to come by due to a variety of factors (e.g., slowing innovation, aging demographics), this performance is unlikely.

**Investors Returns Expectations**

If we were to sensitize the current value of the index to the equity risk premium, it comes in at **3.44%**.

(*Source: author*)

The 3.44% figure is 49 bps lower than the figure calculated from late September and 34 bps lower than the pre-election figure. That stocks are continuing to hold their value despite the steepest gains in Treasury yields since November 2009 suggests a highly optimistic stance toward the reflationary measures that have been proposed by the Trump administration.

In terms of historical returns, from February 5, 1971 (the first day the S&P 500, Dow Jones (NYSEARCA:DIA), and NASDAQ (NASDAQ:QQQ) traded simultaneously), the S&P has yielded 7.13% annualized; the Dow Jones has yielded 7.02%, and the NASDAQ 9.18%. These figures are adjusted for inflation and dividend reinvestment. At a 10-year yield of 2.47% currently, this suggests about **5.9% in nominal returns** moving ahead. Hence stocks have been bid up to the point where they offer around 4% in forward real terms.

**Conclusion**

Given where the US is currently in its economic development, with aging demographics and a progressive slowing of technological innovation, it's unlikely for US equities to continue to return 7%+ per year in real terms as they've averaged over the past 46 years. The equities market still remains very crowded toward the long side. An asset class that returns a projected 4% in forward real returns with the degree of volatility inherent in equities represents fairly poor risk-to-reward fundamentals.

Looking at the market from a historical lens would suggest that the market is a decent bit overvalued. Engineering from central banks through ultra-low interest rates and trillions of dollars worth of quantitative easing has increased bond prices, bid down their yields, and consequently bid up the prices of risky assets, such as stocks and real estate where investors are forced to go when fixed-income yields become as bad they are.

I believe the S&P 500 is still likely a good 14%-24% overvalued and should be trading somewhere around **1860** as a median figure. If the market were to continue to maintain a ~90% payout ratio, grow toward the upper end of the earnings range used above (around 8% year-over-year), equity risk premium of 4.1%, this would push the value to around 2230, or just under the current value. However, I do believe both the payout ratio is unsustainable and the future earnings growth is overestimated.

The valuation is of course justifiable at more normal assumptions if we bring returns expectations down. But for the volatility that equities bring as an asset class, I don't believe prospective 4% forward real returns (at the market's current point) is worth it in terms of passively indexing the S&P 500 as a whole.

And I should always stress this is not an argument to short the index, as economic shocks are generally required to reprice a market. Ultra-accommodative monetary policies throughout the world in Japan, EU, and the US (rates are still roughly negative-1% in real terms) can also justify higher valuations for longer periods of time. I remain net-long the US equities market as a whole, but am "underweight" in terms of representation in the portfolio as a whole.

**Disclosure:** I/we have no positions in any stocks mentioned, and no plans to initiate any positions within the next 72 hours.

I wrote this article myself, and it expresses my own opinions. I am not receiving compensation for it (other than from Seeking Alpha). I have no business relationship with any company whose stock is mentioned in this article.