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  1. 056Two stocks both have a 10% cost of equity. One grows its dividends at 8% a year, the other at 2%. Using the Gordon growth model, how much does each price fall if the discount rate rises by 50 basis points?Duration and ratesCoreBlackRockNew York · 2026

    Try it first

    Which stock falls more when the discount rate rises half a point?

    Show the worked solution

    The 8% grower falls 20%; the 2% grower falls about 5.9%. Under Gordon growth, price is next year's dividend over r minus g. For the fast grower that gap widens from 2% to 2.5%, so the price falls to 0.02 over 0.025, or 80% of what it was. For the slow grower the gap goes from 8% to 8.5%, and the price keeps 0.08 over 0.085 of its value.

    Why does the fast grower react so much more?

    Think of two ways to be paid Rs 10 lakh: most of it next year, or a trickle that grows for decades. If someone doubles the rate at which you discount the future, the trickle loses far more, because most of its money is far away. A fast-growing dividend is that trickle: its value sits in cash flows many years out. A stock whose value rests on distant cash flows behaves like a long bond, so the same rise in the discount rate cuts its price far more.

    Same 50 basis point rise, very different price falls4060801001201409.5%10.0%10.5%11.0%11.5%12.0%Discount rate (cost of equity)both 100 at 10%g = 2%: 94.1, down 5.9%g = 8%: 80.0, down 20.0%Equity duration = 1 / (r - g)50 years against 12.5 years
    Both stocks are priced at 100 with a 10% cost of equity. A rise to 10.5% takes the 8% grower to 80, a fall of 20%, and the 2% grower to 94.1, a fall of 5.9%, because the fast grower's price rests on a gap of only 2 points between r and g.

    How do you turn this into a duration number?

    Differentiate the price with respect to r and divide by price: the answer is 1 over (r minus g). That gives the fast grower an equity duration of 50 years and the slow grower 12.5 years. Duration times 0.5% predicts falls of 25% and 6.25%; the exact falls are a little smaller, 20% and 5.9%, because the price curve bends, the same convexity a bond has.

    The relationship
    P=D1r−gDeq=−1PdPdr=1r−gP = \frac{D_1}{r-g} \qquad D_{\text{eq}} = -\frac{1}{P}\frac{dP}{dr} = \frac{1}{r-g}
    D_1next year's dividend
    rthe cost of equity, 10%
    gthe constant dividend growth rate, 8% or 2%
    What it says in wordsAn equity's sensitivity to the discount rate is one over the gap between the discount rate and growth.

    The limitation is that Gordon growth assumes growth never changes and runs for ever, which exaggerates duration for a fast grower that will slow. The direction survives any sensible model: growth stocks carry more rate risk than stocks priced on today's cash.

    Where candidates lose it

    The trap is answering that both fall by about the same amount because the rate change is the same. The rate change is the same; the base it lands on is not. The fast grower's r minus g is a quarter of the slow grower's, so the same half point is four times as large relative to it.

    The second slip is quoting the duration answer, 25%, as exact. Give 20% and say duration overstates it because the price curve bends.

    What the interviewer asks next

    • What happens to each price if growth expectations for the fast grower fall to 7% at the same time?
    • Why might a portfolio of growth stocks behave like a long-duration bond fund?
    • What does equity duration mean for a pension fund that holds equities against long liabilities?

    Asked at BlackRock, Risk and Quantitative Analysis, New York, 2026 (Wall Street Oasis): Which equities have duration? Technical and behavioural on VaR, market views and stock valuation.