Relative Expected Value Analysis (REVA) is a tool investors can use to evaluate whether the broad stock market is overvalued or undervalued relative to risk-free bonds. Unlike various other stock valuation models, REVA evaluates the impact of possible future dividend growth, prevailing interest rates, and the optionality component of stock returns by comparing the price of call options on a stock to the price of put options on the same stock. REVA can evaluate whether the broad market is overvalued or undervalued, and can also ascertain whether an individual stock is overvalued or undervalued relative to the broad market or to a more specific benchmark.

To evaluate an individual stock, REVA consists of 16 separate steps. I'll use stock in McDonald's (NYSE:MCD) as my example.

1) Take the stock price for MCD, which is around $95.50 a share today.

2) Pick a holding period that makes sense for your situation. Since REVA tends to work best for longer-term holding periods, I'm picking a 10-year investment horizon for this example.

3) Take the interest rate on a U.S. Treasury, the duration of which matches your investment horizon. Let's assume that the interest rate on a 10-year U.S. Treasury is 2.9% today.

4) Since value is relative, decide what you're going to compare MCD to -- perhaps the broader market, a risk-free asset like a U.S. Treasury held to maturity, a sector ETF, another restaurant stock, or some other security. For this example, I'll compare MCD to the SPDR S&P 500 ETF Trust (NYSEARCA:SPY). Today, SPY trades around $166 a share.

5) Find the most up-to-date annualized dividend for MCD stock. At the moment, MCD pays a quarterly dividend of $0.77 a share, for an annual dividend of $3.08 per share.

6) Take the most up-to-date annual dividend for a share of SPY. Over the last year, the fund has paid about $3.33 in dividends.

7) Look at the annual growth rate for the dividends on MCD stock over the last decade. In 2003, MCD paid an annual dividend of $0.40, compared to the annualized $3.08 MCD pays today, so the dividend growth for MCD over the last decade is an impressive 22.6%. It's tough to expect a repeat performance for the next 10 years, but for illustration's sake, I'll use the past as my guide for McDonald's future dividend growth over the next 10 years.

8) 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 for that year, compared to the $3.33 the fund has paid over the last four quarters, so the dividend growth rate for SPY over the last decade is about 7.4%.

9) Since the stock prices for MCD and SPY differ and we want to compare apples to apples, figure out how many shares of each you could buy for the same dollar value. Since I don't want to use fractional shares in this analysis, I'm going to pick a hypothetical portfolio of $1,000,000. At current prices, for $1,000,000 I can buy about 10,470 shares of MCD and 6,024 shares of SPY, so those are the number of shares I will use in this example.

10) Assume that if you buy 10,470 shares of MCD today and hold them for the next 10 years, you will receive an annual dividend of about $32,250 that will grow at 22.6% per year. The future value of all those payments will amount to around $952,000 in future dollars. Now, let's pick an assumed inflation rate of 2%. We see that the present value of this 10-year future income stream, discounted by 2%, is $781,000. We'll come back to that number in a moment.

11) Assume that if you buy 6,024 shares of SPY today and hold them for the next 10 years, you will receive an annual dividend of about $20,059 that will grow at 7.4% per year. The future value of all those payments will amount to around $282,436 in future dollars. The present value of this 10-year future income stream, discounted by 2%, is about $231,000.

12) We see that in terms of cash flow, buying McDonald's will result in an extra $549,000 in dividends in today's dollars. Put that number aside for a moment and move on to step 13.

13) In addition to cash flow, an investment in either MCD or SPY offers the potential for future appreciation or future losses. The question is: What is today's value of that potential future appreciation, taking into account the potential for future losses? The answer is that the value is equal to the price of a 10-year call option (which is what you'd pay for possible future appreciation on the options market) minus a 10-year put option (which is what you'd pay in the options market to avoid downside risk to the stock price). To price out those long-term options, I will use a free Black Scholes calculator that you can find on the CBOE homepage. In both cases, I will use an assumed risk-free interest rate of 2.9%, which is what the 10-year U.S. Treasury yields today, and 365 days to expiration. Finally, I will set the strike price at today's price.

14) Starting with MCD, I calculate the price of a 10-year call option at $15.05, and the price of a 10-year put option at $17.41. The spread between the price of a 10-year put option and a call option on MCD stock is a negative $2.36. I multiply that by my number of shares in MCD, and come out with a total cost of $24,700. That's the value of future appreciation in MCD stock, taking into account the price of potential for future losses in the stock. I subtract $24,700 from the present value of the dividends I expect to earn on MCD stock over a 10-year time period, which we found in step 10 to be $781,000, and I come to a final number equal to about $756,000. This is my expected value on a $1,000,000 investment in MCD stock over a 10-year time frame.

15) I look at the options calculator for SPY, where I calculate the price of a 10-year call option at $36.19, and the price of a 10-year put option at $27.09. The spread between the price of a 10-year put option and a 10-year call option on SPY stock is a positive $9.10. I multiply that by my number of shares in SPY, and come out with a total amount equal to about $55,000. That's the value of future appreciation in SPY stock, taking into account the price of potential future losses in the stock. I add that to the present value of the dividends I expect to earn on SPY stock over a 10-year time period, which we found was about $231,700, and I come to a final number equal to around $287,000. This is my expected value on a $1,000,000 investment in SPY stock over a 10-year time frame.

16) I compare the total expected value of my MCD investment, $756,000, to the total expected value of my SPY investment, $287,000, and find that the MCD investment produces total expected returns of $469,000 more than the total expected returns of a comparably sized investment in SPY. I divide that figure by the total $1,000,000 worth of my hypothetical investment, and see conclude that MCD is trading at a nearly 47% discount relative to the broader market.

So, that's the basic approach for using REVA to evaluate the relative value of one security to another. In practice, though, an investor would be well advised to "stress test" the assumptions used in this example. For instance, what if MCD doesn't grow dividends at the hefty rate it has in the past? What if the interest rate on a 10-year U.S. Treasury fluctuates above 2.9%, which would impact the price of the stock options on both SPY and MCD? Finally, what if you believe the Black Scholes model doesn't work very well when it comes to valuing very long-term options? An investor can run a REVA analysis using a range of possible outcomes (such as rising interest rates or slower dividend growth) and come up with a range of possible relative expected values of a security, which could give a more complete picture than a single, specific relative expected value.

**Disclaimer:** This article is not a recommendation to either buy or sell any security. No investor should rely on any statement contained in this article in making any investment decisions.

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