Predicting the Future Returns of the S&P 500

March 20, 2007

While reading James O’Shaughnessy’s Predicting the Markets of Tomorrow (full review to come later), I came across an interesting section with three different models used to forecast the Standard & Poor’s 500 Index. I have my doubts as to how accurate these models are, but they are still interesting to look at.

Market Implied Real Expected Rate of Return

Earnings Yield + Dividend Yield = Expected ROR - Inflation = Real Expected ROR

An example O’Shaughnessy uses in his book:

5.97% + 1.81% = 7.78% - 3.00% = 4.78%

Remember that the earnings yield is the inverse of the P/E ratio. So, according to this equation, the expected REAL rate of return for the S&P 500 Index at the time that O’Shaughnessy wrote his book, was 4.78%.

Capital Asset Pricing Model

Risk-Free Rate* + (Beta × Equity Risk Premium) = Real Expected ROR

Again, using the numbers in the book, the equation looks like this:

1.70%* + (1 × 5.40%) = 7.10%

*This is the inflation-adjusted risk-free rate. The equity risk premium is the difference between the return one should earn on stocks and the return earned on safe investments like bonds. For more on the Capital Asset Pricing Model (CAPM), see this page.

Equity Cost of Capital (Dividend Discount Model)

Current Dividend Yield + Expected Dividend Growth = Expected ROR - Inflation = Real Expected ROR

And now, the equation with numbers from the book:

1.81% + 7.00% = 8.81% - 3.00% = 5.81%

O’Shaughnessy used Value Line‘s estimate for Expected Dividend Growth.

Finally, O’Shaughnessy simply takes the average of these three numbers (5.90%) to get his real expected ROR.

There you have it. Keep in mind that these are REAL rate of return numbers, which means that inflation has been taken into account. Also, no one knows for certain what the market is going to do. The purpose of these numbers is to give a person something to go off of when making their plan. The actual results will vary.

6 responses to Predicting the Future Returns of the S&P 500

  1. The thing about forecasting is being able to justify your numbers. You can still be wrong, but if you can make a case for why you’re wrong you might salvage your job. Each of the three models has room for personal judgement, so there’s no answer that is always right.

    I’m curious as to what justification he uses to average the three models against each other though.

  2. “I’m curious as to what justification he uses to average the three models against each other though.”

    He doesn’t say. All he says is that he averages the three estimates. I think this is his way of admitting that all three formulas are legitimate and taking an average of the three is a way of finding a consensus.

  3. tinyhands,

    At least with the first method, you can use objective numbers based on past performance. Obviously, you have to determine which past period(s) are comparable enough to be used. That’s where the personal judgement comes in. I agree that an unweighted average of the three methods looks to me like so much hand-waving.

Trackbacks and Pingbacks:

  1. Money Articles for the Week of March 24, 2007 » Silicon Valley Blog About Money - March 24, 2007

    […] All Financial Matters has Predicting the Future Returns of the S & P 500. Here’s a post for you math nuts out there as it’s packed with interesting formulas. Plus, check out JLP’s new furniture. He’s busy doing some house projects these days. […]

  2. - March 24, 2007

    Weekly Roundup – 03/23/07

    Here’s a quick look at some of the articles that caught my eye over the past week…

    Jim writes about the possibility that no-free balance transfers from Citi might be coming to an end. So… There’s not better time to apply for a 0% bala…

  3. Mighty Bargain Hunter » Roundup for week of 18 March 2007 - March 26, 2007

    […] All Financial Matters has several formulas for predicting future returns of the S&P 500. […]