The other valuation gauges compare a price to a past. The implied premium compares a price to a future, and it is the only forward-looking instrument on the dashboard. The logic inverts a discounted cash flow: the market shows you the price every day, the cash flows can be estimated, so solve for the discount rate that makes them consistent, and subtract the risk-free rate.
Three implementation choices carry all the weight. Cash flow to shareholders is dividends plus net buybacks, because in a market where buybacks exceed dividends a dividend-only model understates the cash yield and therefore the premium. Growth runs at an aggregate expectation for five years and then at a terminal rate. The terminal rate is capped at the risk-free rate, on the reasoning that a market's cash flows cannot outgrow the economy forever and the risk-free rate is a serviceable proxy for the economy's nominal growth.
Run it on the illustrative Indian index. Level 26,000, dividend yield 1.30 percent, net buyback yield 0.25 percent, so the first year's cash flow is 403.00. Grow it at 12.00 percent for five years, then at the risk-free rate of 6.90 percent forever. The discount rate that reproduces the level is 8.7540 percent, which is an implied premium of 1.85 percentage points.
Run it on the illustrative United States index. Level 6,800, dividend yield 1.25 percent, net buyback yield 1.80 percent, so the first year's cash flow is 207.40. Grow it at 10.50 percent for five years, then at the risk-free rate of 4.25 percent. The solved rate is 8.0304 percent and the implied premium is 3.78 percentage points.
Advertisement
How sensitive is the implied premium to its inputs?
Now the caveat that decides whether you can use either figure. In the Indian solve, 92.44 percent of the index level is coming from the terminal value, because the solved rate of 8.75 percent sits only 1.85 points above the terminal growth rate and the perpetuity denominator is tiny. In the United States solve the terminal share is 85.22 percent. A model that puts nine-tenths of its answer in a perpetuity is exquisitely sensitive to the perpetuity's assumptions, and here is the size of it:
| Terminal growth convention | India implied premium | US implied premium |
|---|---|---|
| Risk-free rate less 150 bp | 0.46 pp | 2.48 pp |
| Risk-free rate less 100 bp | 0.92 pp | 2.91 pp |
| Risk-free rate less 50 bp | 1.39 pp | 3.35 pp |
| Risk-free rate (the convention used) | 1.85 pp | 3.78 pp |
| Risk-free rate plus 25 bp | 2.09 pp | 4.00 pp |
A 150-basis-point change in a convention nobody debates moves the Indian reading from 1.85 to 0.46, a four-fold swing. By contrast, moving the five-year growth assumption by 200 basis points either way moves India only from 1.73 to 1.98 and the United States from 3.54 to 4.04. The stage-one growth forecast that everyone argues about barely matters. The terminal convention that nobody mentions dominates.
Which gives the rule for using the number. Never quote an implied premium without its terminal convention and its cash-yield definition in the same sentence, and never compare two implied premiums computed under different conventions. Fix your convention once, write it into your policy, and then read the series rather than the level, because a convention error that is constant through time cancels out of the change.
The premium also responds to the risk-free rate in a way the other gauges do not. Hold the illustrative United States inputs fixed and vary the risk-free rate: at 3.00 percent the premium is 3.95 points, at 4.25 percent it is 3.78, at 5.00 percent 3.68, at 6.00 percent 3.56. So the premium falls as rates rise, but by far less than one for one, because the price is held fixed and most of the rate move passes through into the solved discount rate. That is the mechanical reason a market can look dear on an absolute gauge and reasonable on a relative one at the same time.
Is there a quick way to estimate the implied premium?
The Gordon one-liner is worth keeping for the back of an envelope. Expected return equals cash yield plus growth. On the Indian inputs, 1.55 percent plus 6.90 percent gives 8.45 percent and a premium of 1.55 points against the solved 1.85. On the United States inputs, 3.05 percent plus 4.25 percent gives 7.30 percent and a premium of 3.05 points against the solved 3.78. Both are within about half a point of the full model, which tells you where the answer actually comes from: the cash yield and the terminal growth rate, not the five-year forecast.