What Is the Fair Value of the Stock Market?

By Bob Marshalla

October 7, 2003

In the past five years we’ve seen a stock market bubble of historic proportions, followed by a nasty three year bear market, and now by a robust comeback that has added 30% to the value of the S&P 500 since March 11[1]. So where are we now? Is the market over-valued or under-valued?  Or, as the efficient market purist[2] would say, is it just right all the time?

I’m not an efficient market purist, at least not anymore. To think the total equity in U.S. public companies was worth only half as much in July 2002 as in March 2000 strains credibility. It seems clear to me that periodic swings in investor sentiment and behavior causes the value of stocks to veer above and below their true values from time to time, with the late 90’s bubble being one of the most extreme examples of all time. But I believe equally strongly that the market knowledge and mechanisms exist to continually pull market mis-pricings back towards their true values.[3] As a result, it is valuable to have some idea of what the “true values” are.

But first, what do we mean by the “true”, or better to say “intrinsic”, value of the stock market?  To start with, it is the sum of the intrinsic values of all the companies in the market, or in the case of an index like the S&P 5000, the sum of the intrinsic values of all the companies comprising the index.

So what is the intrinsic value of a company? This question has a very simple and clear-cut answer in concept, but an extremely difficult answer in practice.  The intrinsic value of a company is simply the present value of its future stream of earnings.[4] If someone were to buy an entire company, this is the economic value they would be receiving.[5] That’s really all there is to it. But to actually determine this value in practice is very difficult because it is the present value of the future earnings of the company that one must use calculate. Historic values may help us set the framework for estimating the future values, but there is no way to get around the fact that intrinsic value is based on future outcomes, and these must be estimated or forecasted by the equity analyst.

In this article, I will attempt to do three things:

1. Describe the assumptions and forecasts we must make, and how they can be put together to estimate the fair value of the equities market.
2. Offer you my best estimate of the current fair value of the market.
3. Discuss how and when, if at all, such a forecast should affect our investment strategy.

(1) Key Assumptions

We will focus on estimating the fair value of the S&P 500, which represents over 80% of the market value of all U.S. equities, and is a common proxy for the large cap domestic equity asset class. We will take the approach of valuing the S&P 500 as if it were a single company; i.e., we will estimate the present value of the future earnings stream of the whole set of companies comprising the index. To do this, we have to estimate:

1. The current composite level of earnings for the S&P 500 companies
2. The future long run growth rate(s) of composite earnings
3. The proper discount rate to use in the present value calculation, which is the sum of:

a.       The future “riskless” rate of return, typically assumed to be the rate on long term Treasury bonds or TIPS, and

b.       The equity risk premium, which is the extra return above the riskless rate that investors expect to receive in return for taking on the risk of investing in equities.

I will spare you the math, but if we could estimate these values, then the fair value of the market would simply equal the current earnings level divided by the discount rate minus the earnings growth rate. In equation form we have:

                E     

FV    =            --------------                                                                               (1)

            (d – g)

where:

FV = fair value of the market (measured by the S&P 500 index)

E = current level of earnings of the S&P 500

d = discount rate used to compute the present value of future earnings[6]

g = future growth rate of earnings

As mentioned above, the discount rate is equal to the sum of the riskless rate of return plus the equity risk premium. To continue with our notation:

d = r + erp                                                                                                        (2)

where:

r = riskless interest rate

erp = equity risk premium

We can equally well focus on the real or nominal versions[7] of the discount rate and the earnings growth rate. Inflation presumably affects both terms about the same way[8], and since one is subtracted from the other in the denominator of equation (1), we will get the same answer for the denominator whether we use the nominal or real versions of each rate. Real rates tend to be more stable over time than nominal rates, so we will focus on the real versions of the rates.

Risk-Free Rate of Return - First let’s consider the risk-free rate of return. Currently, the nominal yield on 10 year Treasuries is 4.2%. Based on year-to-date inflation, this translates to a 2.5% real rate. The really long run average real rate of return for long term Treasuries between 1926 and 2002 has been only 2.3%. It is perhaps surprising that the current real risk-free rate is actually higher than its long run average. However, I do not think we should count on having lower rates in the future than we do now, so I have chosen to use the current real Treasury rate of 2.5% as my base case forecast for the risk-free rate of return.

Equity Risk Premium - Estimating the equity risk premium is a major issue of financial economics. There are many different ways to approach the problem, and dozens of papers and books have been written about the subject. The long run average premium for large cap US stocks since 1926 has been about 5% over and above the return on government bonds. (Large cap stocks have generated compound annual returns of about 10%, while long-term government bonds have returned about 5%.)  While estimates vary, most everyone who has studied the subject seriously believes the forward-looking equity risk premium will be somewhat lower than its long run average. Estimates are generally in the range of 2% to 4% lower. For this analysis, I have adopted the optimistic end of that range, which translates to a future equity risk premium of about 3.0%. If inflation averages 2.5%, then combined with my 2.5% real risk free rate assumption, this implies large cap U.S. stocks should generate long run nominal returns of about 8.0% per year[9].

Earnings Growth Rate - The next key assumption is the real rate of growth of corporate earnings. The very long run average growth rate of earnings on large cap US public companies has been about 2% real, which also about matches its value for the past twenty years. Thus, it seems prudent to estimate the future earnings growth rate to continue to average about 2% real. Of course this is much lower than stock analysts normally forecast. But the actual historical numbers are based on reported earnings, not the more forgiving operating earnings. Operating earnings excludes all sorts of “one time” charges such as for restructuring and mergers and such. But for the group of all companies, such charges are hardly “one time” expenses. They occur every single year, and cannot be ignored. Also, analysts have always been notoriously over-optimistic, even in forecasting operating earnings.

Starting Level of Earnings - The remaining variable we must estimate is the current level of earnings for the S&P 500. This may seem at first like a straightforward number to estimate, but it too is beset by numerous options and caveats. Should we use historic earnings or forecasted earnings? Reported or operating earnings? One year’s earnings, or an average of several years?  What about the distortions caused by stock option accounting? It is beyond the scope of this paper to discuss all of these issues. Suffice to say I have decided to use a “normalized” notion of earnings, as computed by Litman-Gregory, a well-respected company that is in the business of providing research and analysis for financial advisors. Their notion of normalized earnings is an average of the last four years reported earnings, plus next year’s forecasted earnings. By extending the average to cover five years, it smoothes out the variations due to the business cycle. By using reported earnings rather than operating earnings, it accounts for the elusive “one time” charges and some of the distortions due to stock option accounting. And by basing the estimate mostly on past earnings, it avoids being overly influenced by the over-optimism of analysts. L-G’s latest estimate of normalized earnings for the S&P 500 is $38.82. By way of comparison, the Zacks-reported consensus analysts’ forecasted earnings for the next 12 months as of October 6 is $56.68, which is significantly higher.

(2) Fair Value of the Market

We now have all of the assumptions needed to estimate the fair value of the S&P 500, which we re-summarize below:

·         Real risk-free rate = 2.5%

·         Equity risk premium = 3.0%

·         Real discount rate (the sum of the above) = 5.5%

·         Real long tern earnings growth rate = 2.0%

·         Starting level of S&P 500 earnings = $38.82

Plugging these values into equation (1) above is all we need to do to come up with our estimate of the fair value of the S&P 500. The answer is 1109. By comparison, the market closed at 1039 as of this writing (October 7), which is just about 6% lower. So my conclusion is that within the bounds of accuracy of my model (which are quite broad, as we will see below) the market is currently in a fair value range.  

As one point of reference, we can compare my estimate of fair value to that of Litman Gregory. Litman Gregory uses a model that is similar in approach to mine. Although I used their estimate of the starting level of S&P earnings, I did not use their valuation model or their other assumptions. Nevertheless, their current estimate of the fair value for the S&P 500 is 1034, which is within 6% of my estimate, and is coincidentally almost exactly where the market is right now.

(3) Implications for Investment Strategy

How, if at all, should such estimates of fair market value affect our investment strategy? First of all, I do not believe that this or any other valuation model should be used as a short term forecasting tool. Even if it showed the market to be way under- or over-valued, there is no guarantee that the market would not become even more under- or over-valued over the next year or so. Its value is in assessing the stock market’s return potential over the longer term.

Second, we should realize this is a fairly imprecise tool. The assumptions needed to drive it are uncertain, and even fairly modest changes in these assumptions can lead to large changes in its results.  For example, if we change the equity risk premium up or down by a half percentage point, the fair value of the market ranges from 970 all the way up to 1294. So we should consider our fair market value estimate as a plus or minus 15% kind of estimate, and not as a precise measure of value.

But even given those limitations, it can serve a very useful role by informing us if the market is way over-valued, way under-valued, or in a reasonable range of fair value, as appears to be the case now. We typically develop our investment strategies based on the idea of fairly valued markets, so if our analyses confirm these assumptions, then no changes in strategy are called for. If our valuation tools indicated that the market was more than 25% or so over- or under-valued, then we would have cause for concern, and might be incited to take actions such as the following:

1. Try to confirm our conclusions by examining other valuation methodologies and checking with other respected analysts.
2. If these examinations confirmed our conclusions, then we would first investigate whether there were other asset classes with similar risk-return characteristics as U.S. large cap stocks in which we could redirect some of our asset allocation to or from. This could include international stocks, small cap stocks, real estate, commodities, high yield bonds or even hedge fund strategies.
3. If such alternative asset classes failed to show significantly different valuation characteristics, only then would we consider the more aggressive step of shifting assets to or from stocks into or out of safer assets like fixed income. And even then, before taking such actions, we would also need to consider the individual client’s risk tolerance, liquidity needs, tax implications and transactions costs prior to taking any such actions.

In this article we reached the conclusion that the S&P 500 is in a fair value range. Perhaps the most important implication for the reader is that we can relax a bit, not having to worry either that we are headed for another bubble implosion, or that we are “missing the boat” if we don’t put every last dollar into the market now.

It should be noted that the valuation measure developed here applies only to large cap U.S. stocks.  We also regularly use other methods to evaluate the relative and absolute valuations of other asset classes, such as small cap stocks, international stocks, real estate, and high yield and investment grade bonds. A year to two years ago, all of these asset classes except investment grade bonds had valuations suggesting they were better buys than domestic large cap stocks, and we have been over-weighting them in our portfolios as a result. And, in fact, in recent quarters all of them (excluding investment grade bonds) have indeed outperformed large cap U.S. stocks, to the point that their valuations are no longer so attractive on a relative basis as before. Still, they generally do remain marginally more attractive than domestic large cap stocks, and except for high yield bonds (whose asset allocation target we have decreased), we have not yet lowered their target allocations.

Before closing, we note an interesting implication of our market valuation model. The more optimistic we may be about the equity risk premium, the more pessimistic we must be about the current fair value of the market, and vice versa. This is a simple implication of equations (1) and (2). Increasing the equity risk premium increases the discount rate used to compute the present value of future earnings. As shown in equation (1), a higher discount rate means a lower fair value for a given stream of earnings, and vice versa.

The equity risk premium tells us how much more we can expect to earn from stocks than from safe investments starting from a fair value plateau. But the higher that return premium is, the lower must be our assessment of the fair value plateau. Conversely, if we expect a lower long run rate of return from stocks, then the discount rate will be lower, and the fair value of the market will be higher.

We should think about our future returns from stocks as having two components. One is the change needed (if any) to get from the current market value to the fair market value. The second is the long run rate of return we can expect when starting from the fair market value. This is what the equity risk premium attempts to estimate.

This is a “good news – bad news” story that is seldom made explicit when we read about various prognosticators forecasts of the market. So the next time you hear someone say how much lower rate investors should expect to earn from stocks in the long run future, remember that the good news that goes with this is that such an environment is consistent with a higher current fair value level for stocks. Conversely, if someone says the current level of the market is way too high, know that this is consistent with higher long run rates of returns from stocks, once the market returns to its fair value level.