Estimate Fair value of S&P 500 Index?

Question

Hi,

I was looking to calculate the fair value of S&P 500 index using the Gordon Growth Model. Could somebody please explain it to me. How can I do that?

Answer 1

The Gordon Growth model is one of the more conservative valuation models. It is also, in my humble opinion, one of the least accurate due to its simplicity.

The Gordon Growth model builds off the annuity valuation model [Price = coupon/(r-g)]. Instead of an annuity payment, it's the dividend. Instead of "r" rate of return, it's the required rate of return on the market. In this case, "g" is how much dividends are expected to compound each year into perpetuity.

We know what the "coupon" is. According to my handy-dandy E-trade account, AMEX says that the S&P 500 has a 1.71% yield at the current 1386.72 closing price. That equals a historical dividend of 23.713 compared to the Index "unit".

The required rate of return is a bit tricky. In finance classes, the oft-abused statistic is an expected 11% return on the market - of which 7% is capital appreciation and 4% is from dividends. For grins, let's use the 7% as our "r" in terms of expected return.

Earnings growth has been growing at double digit for the past 18 quarters in a row - an all time record. We cannot assume super-growth in perpetuity. Historically, earnings growth has averaged around 5-6%, with pronounced dips and rebounds during cycles. Let's assume 5%.

Using the perpetuity model, this equals a fair value of 1186 [23.71/(7%-5%)].

To show you how inaccurate this is, let's change the denominator by a measly 50 basis points. We'll change the growth rate from 5% to 5.5%. The fair value pops to 1580.86, a third higher. If we go a full percentage point, we off by 100%.

Pretty huge margin of error for one percentage point!

Answer 2

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