One of the most prominent market debates is whether the US stock market is overvalued or possibly even in a bubble? In analyzing this question, I take a quantitative approach. That said, whether or not the US stock market is overvalued does not mean the market is going to go up or down. Financial asset prices are a function of supply and demand; are there more buyers or more sellers and what is the conviction of the buyers and sellers (meaning, do they have to buy/sell). And, numerous factors impact the number and ferocity of buyers and sellers: cash inflows/outflows (think 401K contributions and corporate share buybacks); portfolio re-balancing (think retiring baby boomers); relative valuations among different asset classes (an asset could be “expensive” but another asset could be even more expensive and thus the “expensive” asset looks cheap on a relative basis); and, of course, quantitative valuation metrics. In this report, I use the lens of classical financial valuation techniques, but please understand that while all assets should ultimately be valued based on the expected future stream of cash flows discounted back to the present, that does not automatically mean that assets will trade at those valuations.

### From the Charts, It's Clear the US Stock Market is Overvalued, Right?

In the charts below, I show the issue being raised. The S&P 500, which is a measure of the US stock market, is currently (as of August 3, 2018) valued at 16.8x 12 month forward expected earnings versus 14.4x over the past 10 years, thus a 16.7% premium. As a result, many investors and financial pundits state that the US stock market is overvalued.

Source: Factset Earnings Insight

Beyond the above ratio, there are charts provided by CMG Capital Management Group implying the US stock market is extremely overvalued.

Source: CMG Capital Management Group’s On My Radar August 3, 2018

Then, there is the Shiller PE chart again implying that US stocks are extremely overvalued.

Source: www.multpl.com website.

Finally, here is a chart from The Leuthold Group on price to sales showing the US stock market trading at Dotcom-era levels, implying the US stock market is in a bubble.

Source: The Leuthold Group

### But, What Does the Math Tell Us?

While the above charts all scream US stocks are overvalued, let’s instead do the underlying calculations to determine whether these charts tell the real story.

To start, a company is worth the net present value of its future expected cash flows (for the purposes of this analysis we will treat “earnings” and “cash flows” as the same, assuming capital expenditures and depreciation approximate each other). Thus, there are two variables. One, at what rate will current earnings grow. And, two, at what interest rate do you discount back those earnings. There is a formula to calculate the net present value using these inputs.

Net Present Value = (1 Year Forward Expected Cash Flow) divided by (Discount Rate minus Annual Cash Flow Growth Rate in Perpetuity)

The problem with someone saying the market is overvalued because it trades at a higher multiple today than historically is that the net present value (and resulting multiple of current earnings) should take into account interest rates and earnings growth rates at that point in time. To compare multiples today with multiples from five, ten or twenty years ago is comparing apples and oranges unless interest rates and earnings growth rates were the same at those same points in time. Looking at historical multiples relative to current multiples is therefore misleading.

Based on current earnings levels, future expected growth rates and future expected interest rates, what do the numbers tell us about the current market valuation? To start, the S&P 500 closed (August 3, 2018) at 2840.35 and the estimate for forward 12-month S&P 500 earnings is $169.24. Thus, the S&P 500 is trading at 16.8x 2018 earnings, which as I stated before is higher than the average of 14.4x over the past 10 years.

The next thing we need to consider is what should we assume for our earnings growth rate. Over the past 100 years, the S&P 500 has averaged 7% annual, nominal (i.e., not inflation adjusted) earnings growth. And, over the past 30 years, the S&P 500 has averaged 10% annual, nominal earnings growth. For our analysis, let’s assume earnings growth reverts to the long-term average of 7%.

Finally, we need to determine our discount rate. Without going into the Capital Asset Pricing Model, I use a 6.5% risk premium. The discount rate is the risk-free rate plus 6.5%. Based on these assumptions, the S&P 500’s current valuation of 2840.35 implies a 6.46% risk free interest rate. Remember from our formula before:

NPV = 1 Year Forward Cash Flow divided by (Discount Rate minus Cash Flow Growth Rate), so

2840.35 = 169.24 / ((6.5% + Risk Free Rate) – 7%). The risk-free rate implied by the current S&P 500 level is 6.46%. The following chart shows the various earnings growth rates and risk-free interest rates that result in the current S&P 500 valuation, assuming a 6.5% risk premium to calculate the discount rate.

The S&P 500 implies a US Treasury risk-free rate of 6.46% and 7% future annual earnings growth. If you believe that long-term earnings growth will decline to 5%, well below historical norms, then the implied risk-free rate is 4.46%. There is debate on whether it's most appropriate to use the 3-month, 10-year or 30-year US treasury as the risk-free rate. But, 4.46% is well above current levels for all three. And, if the long-term earnings growth rate were to decelerate to 5%, there likely would be little to no inflation and it would seem likely that the risk-free rate would be much lower than 4.46%.

Now, let’s review the implied multiple of various risk-free interest rate and earnings growth rate scenarios, the resulting implied level of the S&P 500, and the implied percentage change from current levels of the S&P 500.

Reviewing the above charts, let’s walk through the results assuming the 10-year US treasury represents the risk-free interest rate. The 10-Year is currently 2.94%. To be conservative, let’s assume it increases to 5.25% (which is above the upper band of the normalized average over the past 150 years). If we further assume 7% annual earnings growth in perpetuity, the correct multiple on 12-month forward S&P 500 earnings is 21.1x, a 25.4% increase from current levels. But, what if annual earnings growth is 6% instead of 7%, then the implied multiple is 17.4x, still 3.6% upside from current levels. If you assume the 10-Year US treasury is 3.75% and long term annual earnings growth is 7%, the correct multiple on 12-month forward S&P 500 earnings is 30.8x, a 83.3% increase from current levels. Bring the earnings growth rate down to 6%, and the multiple is still 23.5x, a 40.2% increase in the S&P 500 from current levels.

The conclusion I derive from this analysis is that the S&P 500 is not expensive and one could easily argue is quite inexpensive. Just because the market has increased substantially since the financial crisis does not automatically mean the market is expensive. What is more likely is that the S&P 500 was simply over sold during the financial crisis and way, way too cheap. The current bull market is just catching up to the true S&P 500 valuation.

Many market pundits do not believe that interest rates will stay low. They believe that the 10-Year US treasury is going back to 5% or 6% since that is a “normal” rate. This, then, is the key debate. If you believe that interest rates will stay low and earnings will be no less than the historical average of 7%, then the stock market is extremely cheap. If you believe the 10-Year US treasury is going back to 6% and that long term annual earnings growth will decline to 5% to 6% (below the 100-year average of 7% and 30-Year average of 10%), then the S&P 500 is 20.6% to 8.3% overvalued, respectively.

As it relates to price to sales multiples and price to book multiples, the problem is they do not take into account profitability margins and return on assets. As more companies derive cash flows from intangible assets such as intellectual property as opposed to physical assets, every dollar of sales will generate more free cash flow from less capital expenditures and resulting physical assets. As a result, price to book and price to sales are simply not as relevant as they were in the 1960s and 1970s when cash flows were derived primarily from plant and equipment. The value in many companies is not capitalized on the balance sheet because it did not derive from capital expenditures, making price to book a less relevant metric. And, higher operating margins renders looking at price to sales in a vacuum meaningless.

Finally, there is one more thing I want to address. In addition to earnings and cash flow multiples, a statistic attributed to Warren Buffett argues that the stock market is overvalued based on the ratio of the value of US stocks to US GDP.

Source: www.advisorperspectives.com

Based on the above chart, some argue that US stocks are at record valuations. I believe this chart is extremely misleading because it compares US stock market valuation to US GDP. In reality, S&P 500 companies (which comprise most of the US stock market capitalization) derive 30% to 50% of sales outside of the US. So, if you want to consider this ratio, you need to compare US stock market capitalization to global GDP, not US GDP.

### Conclusion

I do not believe the US stock market is overvalued. To the contrary I believe on a valuation basis it is cheap and offers significant upside. But as I stated in the beginning, that does not mean that US equities can’t sell off for reasons other than valuation. The factors that could most likely move equity markets are:

- Central bank policies and the impact on capital flows and interest rates
- China’s economic growth and the risks inherent in the Chinese government’s goal of deleveraging
- The magnitude of US corporate share buybacks and dividends and resulting impact on demand for stocks
- The rise of populism/nationalism and the impact on free trade
- Global debt levels and the impact on future credit growth (which impacts GDP growth)
- The level of the US dollar and the impact on S&P 500 earnings and emerging market debt

It is very difficult to quantify these as it pertains to equity prices. But, the market does not like uncertainty, and these factors could definitely create uncertainty. If these do not become issues, then the market can focus on earnings. And, based on earnings, US stocks are cheap.

**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.

**Additional disclosure: **Disclaimer: Opinions expressed herein by the author are not an investment recommendation and are not meant to be relied upon in investment decisions. The author is not acting in an investment advisor capacity. This is not an investment research report. The authors opinions expressed herein address only select aspects of potential investments in securities of the companies mentioned and cannot be a substitute for comprehensive investment analysis. Any analysis presented herein is illustrative in nature, limited in scope, based on an incomplete set of information, and has limitations to its accuracy. The authors recommend that potential and existing investors conduct thorough investment research of their own, including detailed review of the companies SEC filings, and consult a qualified investment advisor. The information upon which this material is based was obtained from sources believed to be reliable, but has not been independently verified. Therefore, the authors cannot guarantee its accuracy. Any opinions or estimates constitute the authors best judgment as of the date of publication, and are subject to change without notice.