12/11/2008
By Carlos Guillen, Research Analyst

More Articles by Carlos Guillen

A Slow, Painful Recovery

Apple Takes Everyone by Surprise

Equities Get Axed

Is the Market Fairly Valuing the S&P 500?

By Carlos Guillen

As we all know, the S&P 500 is a market-value weighted index of 500 companies that are selected to represent the entire universe of traded companies in The United States. The essence of market weighing is that each company has a stronger effect on the index calculation depending on how large its market capitalization (share price multiplied by shares outstanding) is. This differs from price-weighted indexes, such as the Dow Jones Industrial Average (DOW), which are strongly driven by stocks that have larger prices, independent of how large the stock's market capital is. As it turns out, both types of indexes are very effective in providing a diagnosis of the general state of the entire market. In fact, when we run a correlation of the S&P 500 and the DOW, from 1980 to the present, we find a correlation coefficient to 99.2% (This was calculated by our analyst David Silver). We also ran a correlation between the S&P 500 and the NASDAQ for the same time period and found a correlation coefficient of 95.9%. Therefore, we can conclude that both indices are fair measures of the market in general.

As a result of the current financial crisis, the S&P 500 (and all indexes) has suffered a precipitous drop. In fact, this index peaked at $1,562 back in October 10, 2007, and now it stands at $899 (as of December 10). This drop represents a contraction of 42.4%. From a year-ago perspective, the S&P 500 has fallen by 40.7%, and its current level is comparable to that achieved back in March 2003. The big question now is whether the current level represents a fair value, but how is one to know what the fair value actually is?

One approach used to determine the intrinsic value of the S&P 500 uses the Dividend Discount Model. In this method, dividends are projected out perpetually and then discounted back to the present, resulting in the present value of these projected cash flows.

In our valuation of the S&P 500, we broke up our projected cash flows in two stages. The first stage of cash flows is projected dividends for the next five years. The second stage of cash flows is projected dividends for the sixth year till eternity (similar to perpetuity). We used two stages because we expect growth rates to be different in the first stage than in the second stage. In order to summarize this concept, we provide the following equations which describes the Dividend Discount Model we used.

Here D₀₉ to D₁₃ represent the projected dividends for year 2009 to 2013. D_Term represents the projected dividend for the terminal year, which in this case is 2014. D_Term will then grow at the rate g_{e_Term} forever. r_E09 to r_E13 are the discount rates (rates that put future values in terms of present value) used for the next five years (2009 to 2013) and r_{E_Term} is the discount rate used in the terminal year. The present value (PV) of the two stages is simply the sum of the two results.

The expressions just described illustrate the essence of the valuation process we used. In the table below, we show the actual values that were used in the process.

The "dividends" represent all dividends in the S&P summed together. We must also point out that we expanded the definition of dividends to include buybacks. After all, share buybacks are also cash flows to equity investors and should also count as part of the value of the index. To determine the initial "Divedend+Buybacks" of $43.88 per share, we used the five-year average dividend yield of 4.88% (including buybacks) and multiplied it by the current index closing price of about $899. The remaining cash flows are determined by growing the initial $43.88 by the corresponding growth rate g_e. This growth rate is determined by using the S&P 500 expected earnings per share for 2009 ($49.15) and the actual earnings per share for 2008 ($49.04), which implies a growth rate of 0.22%. By 2013 this value is up to 7.08%, which represents expected dividend growth over the next five years from the present value. The annual growth rate we used for the terminal year of 3.0% is selected based on our expectation that in the long term, earnings growth should revert to the historical average GDP growth.

For the Risk Premium (the market return minus the risk free rate), we used the 40-year average risk premium of 4.46% (data from Kenneth R. French at Dartmouth University). For the risk free rates r_f, we used the appropriate bond rates from the Treasury website. The sum of the risk free rate and Risk Premium gives us the discount rates r_E that we need to find the present values of the cash flows as the equations above show.

Finally, we simply add up all the PV values and arrive at an intrinsic value of $1,091. This value represents a premium of 21.3% over the $899 closing prince on December 10, 2008. Therefore, according to our analysis the S&P 500 is intrinsically undervalued. As such, we believe that for long-term minded investor this is an incredible time to start cherry picking quality companies that are just to cheap to resist.

Carlos Guillen
Wall Street Strategies