The model I use for determining whether the stock market is attractively valued today doesn't seem to be widely followed, but unlike popular valuation models such as Robert Shiller's CAPE model, it's forward looking and considers the impact of interest rates. The model is most appropriate for long-term investors - those with an investment horizon of about ten years or more, let's say. Here are the steps.

First, take the price of an S&P500 index fund, such as the SPDR S&P500 Trust, trading under ticker symbol SPY. Let's assume the price today is around $165 a share.

2) Second, assume a holding period that makes sense for you, the investor. For example, let's assume your investment horizon is ten years.

3) Third, take the interest rate on a ten year U.S. Treasury (or longer dated Treasury, if you're using a longer holding period for your investment). Let's assume that the interest rate is 2.83% today for a ten-year U.S. Treasury.

4) Forth, take the dividend yield on SPY. Over the last year, the fund has paid about $3.33 in dividends, for a yield of around 2%.

5) Fifth, look at the annual growth rate for the dividends on SPY over the last decade. In 2003, SPY paid a grand total of $1.63 in dividends, so the dividend growth for SPY over the last decade has been about 7.4% on average.

6) Sixth, assume that if you buy one share of SPY today and hold it for the next ten years, you will receive an annual dividend of $3.33 that will grow at 7.4%. The future value of all those payments will amount to around $47 in future dollars. Now let's pick an assumed inflation rate of 2%. We see that the present value of this ten-year future income stream, discounted by 2%, is $38.56.

7) Seventh, compare that with the future value of the interest payments you'd get if you invested $165 into a ten-year U.S. Treasury. At an interest rate of 2.83%, that comes to $4.67 a year, with zero growth. Over ten years, that means you'd accumulate around $46.7 in future dollars. Discounted back to present value at an assumed inflation rate of 2%, that equals a present value of $38.31.

8) Eighth, in addition to cash flow, the investment in SPY offers the potential for future appreciation or future losses. The question is, what is the value today of that potential future appreciation, taking into account the cost of future losses? The answer is the value is equal to the price of a ten-year call option minus a ten-year put option. The reason why is that if a Treasury investor wanted to mimic the returns of a security like SPY, he or she would have to buy Treasuries PLUS a call option on SPY. By the same token, if the stock investor wanted to mimic the returns on a ten year U.S. Treasury, which will not lose any value if held to maturity, he'd have to purchase a ten-year put option on SPY.

9) Ninth, figure out the price of these long-term options using a Black Scholes calculator (or other similar such options pricing tool). For example, you can go to the CBOE homepage and use the free options calculator there to see that the price of a call option on SPY with an assumed risk-free interest rate of 2.83% and 3650 days to expiration is about $37, whereas the price of the put option is $28. The disparity between the price of the call option and the put option is $9. Meaning, if you buy a share of SPY today, the expected value of the potential future capital appreciation, balanced with the risk of future capital depreciation, equals $9. Add that to the present value of the future expected cash flow (about $38.56), and we see that the total return an investor could expect on a ten-year investment in SPY is $47.56. That's $9.25 better than the $38.31 present value you'd earn if you invested $165 into ten year U.S. Treasuries. All told, that implies that SPY is about $9.25 undervalued, relative to bonds, and the stock market is about 6% undervalued currently.

The main assumption behind the model is that the "value" of an investment is entirely and exclusively relative to other investment alternatives readily available to an investor. The main benefit of the model is that it does not rely on subjective guesses about future earnings growth based on past earnings, future demand for stock, or other factors that could impact future stock prices. In that sense, it's a useful adjunct to stock pricing models such as CAPE.

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