Applying the Gordon Growth Model to the S&P 500

The Gordon Growth Model is a very old and very useful stock valuation model. It's based on the insight that the value of stock today is the present value of all future dividends the stock holder will receive. If one can argue the dividends will grow at a constant rate, then we can use the simple Gordon model:

where P is the value of the stock today, D is the dividend in one year (normally), r is the required return on the stock, and g is the expected growth rate of the dividend. Now, using the simple model takes a lot of care, and shouldn't be applied to every stock. But, it does make sense, as an initial approach, to apply this model to the S&P 500 so we can try to get a sense of the fair value of the S&P 500. 

Now, according to Prof. Shiller's data, the dividend you would receive if you held one share of the S&P 500 index (yes, it's not possible but this is a theoretical exercise), is 34.4. Note the current index level (which can be interpreted as the price of one share of the index) is 1776. 

I built a little table to see how reasonable the current level of the index is, given the dividend. The range of the required return (r) that I use is 5-8%, and the growth rate (g) range is 0-4%. The range of index values I generate is 430 (required return of 8%, growth rate of 0%) and 3444 (required return of 5%, and growth rate of 4%). In only three situations can I generate a value above the current index value: required return of 5% and growth of 3.5% or 4%, and required return of 5.5% and growth of 4%. 

It is important to note that a reasonable range of required return for the S&P 500 is 6-8%. The historical (back to 1871) average growth rate of dividends is 3.5%. For those values, the range of index values I find is 765 - 1377. Note that, using the current dividend yield (34.4/1776) and growth rate, we can calculate the current total return as around 5.5%. That seems abnormally low to me.

According to my little exercise, the S&P 500 is currently above most reasonable values I can generate. I think that growth of 3.5% is rather high to expect right now. Most estimates I see are between 2-3%. That means the S&P 500 is going to drop down. I don't know when, so rather than shorting the index, put options are a better choice. 

Certainly we can "tech up" the situation, which will be my next exercise. Notably, we can include risk aversion measures, because if risk aversion is down, then it is conceivable that required return is lower than normal. That could justify higher stock valuations.