**Quick Summary**

1. Find the TTM dividend and buyback yield of the S&P 500.

2. Find consensus earnings growth estimates of the S&P 500 over the next five years and the current ten-year treasury yield.

3. Use a two-stage dividend discount model to estimate the intrinsic value of the S&P 500, using consensus estimates for the short-term growth rate and the ten-year treasury yield as the long-term growth rate. Solve for the implied equity risk premium by setting the current S&P 500 price equal to the intrinsic value estimate.

**1. Dividend and Buyback Yield**

If we already know the expected dividends and price of an asset today, then we can solve for the implied rate of return that equity investors require by using a dividend discount model (DDM), also referred to as the Gordon Growth Model (GGM). Expected dividends (and stock buybacks) can be calculated by taking the current dividend and buyback yield, multiplying it by the current price, and then multiplying that by a growth rate.

If using the S&P 500 as your index, a good online source for looking up the current dividend and buyback yield is the S&P 500 Dow Jones Indices website. Click the *Additional Info* drop-down and select *S&P 500 Stock Buybacks*. The downloaded spreadsheet will have a column named *Dividend & Buyback Yield* that can be referred to for this information.

**2. Consensus Earnings and Treasury Yield**

For a short-term growth rate, we can rely on analysts’ consensus estimates of growth in earnings. A logical place to begin research would be to look up the S&P 500 ticker (^GSPC) on Yahoo Finance and search for analyst estimates. This, however, leads to a dead end. The much less intuitive – but successful – method is to look up absolutely any other stock on Yahoo Finance, select the *Analyst Estimates* link on the leftmost banner, and scroll down to *Growth Estimates*. There you will find a column with the S&P 500 serving as a benchmark with its own *Next 5 Years* earnings estimate.

The risk-free rate should be based on the current ten-year treasury bond yield. This can be found under the *Resource Center* of the *U.S. Department of the Treasury website* (here). Use the drop-down to select the *Daily Treasury Yield Curve Rates*.

**3. Implied Equity Risk Premium (ERP)**

At the time of writing this (7/22/2015), the most recent dividend and buyback yield was 4.92%, consensus estimate of growth in earnings for the next five years was 7.15%, the ten-year treasury yield was 2.33%, and the S&P 500 index was priced at $2,114.15. Expected dividends and buybacks for the next year were therefore 2,114.15 * 4.92% * (1 + 7.15%) = $111.45. Continuing this same logic for the subsequent four years, dividends and buybacks were $119.42, $127.96, $137.11, and $146.91. We assume the second stage of growth is equal to the risk-free rate, or 2.33% in this case. The terminal value of the index was therefore equal to [146.91 * (1 + 2.33%)] / [ERP + 2.33% – 2.33%] = [150.33 / ERP].

At this point, all you need to do is set the current index price ($2,114.15) equal to the present value of the expected dividends and back out the implied premium. This can also be accomplished by trying different values for the ERP until you get a result equal to the market price. A far easier method involves setting an arbitrary value for the premium of, say, 5.0% and using Excel’s Goal Seek to automatically iterate through different premiums until the correct value is found. Using the above example, the implied equity risk premium was equal to 6.19%.

**Concluding Thoughts**

In a valuation context, what ultimately concerns us is the *future* equity risk premium. Since implied premiums adjust in response to changing market fundamentals, the current implied equity risk premium typically yields the best forecast of future returns. Moreover, the current implied premium is ideally suited for equity research since you are valuing an individual company rather than forming an opinion on whether the market as a whole is over- or under-valued (i.e. you’re taking the current level of the index as a given).

As an alternative to using the current dividend and buyback yield, a multi-year average could also be used. The resultant value will better reflect historical premiums but may have less predictive power if market fundamentals have changed.

**Suggested Reading**

Aswath Damordaran. *Equity Risk Premiums (ERP): Determinants, Estimation and Implications*.