What is equity duration and why do growth stocks have higher duration than value stocks?

Question

AcadiFi · Accepted Answer

Equity duration measures the sensitivity of a stock's price to changes in interest rates (or discount rates). It borrows the fixed-income concept but applies it to the stream of expected future cash flows from owning equity.

**Conceptual Definition:**

Equity duration = -(1/P) × (dP/dr) -- the percentage change in stock price for a 1% change in the discount rate.

**Why Growth Stocks Have Higher Duration:**

Growth companies generate most of their value from cash flows far in the future. Like a zero-coupon bond, these distant cash flows are heavily discounted and therefore more sensitive to rate changes.

**Worked Example -- Two Fictional Companies**

**Bedrock Industries (Value):** Pays $10 dividend today, growing at 2% forever, r = 8%
- V = $10 / (0.08 - 0.02) = $166.67
- If r rises to 9%: V = $10 / (0.09 - 0.02) = $142.86 → **-14.3%**

**Zenith Innovation (Growth):** No dividends for 10 years, then $5 growing at 5%, r = 8%
- V = [$5 / (0.08 - 0.05)] / 1.08^10 = $166.67 / 2.159 = $77.20
- If r rises to 9%: V = [$5 / (0.09 - 0.05)] / 1.09^10 = $125 / 2.367 = $52.81 → **-31.6%**

| Company | Price Impact from +1% Rate | Implied Duration |
|---|---|---|
| Bedrock (Value) | -14.3% | ~14 years |
| Zenith (Growth) | -31.6% | ~32 years |

\`\`\`mermaid
flowchart LR
    A[Interest Rates Rise] --> B[Higher Discount Rate]
    B --> C[Value Stocks: Near-Term Cash Flows]
    B --> D[Growth Stocks: Distant Cash Flows]
    C --> E[Moderate Price Decline -- Low Duration]
    D --> F[Severe Price Decline -- High Duration]
\`\`\`

This explains the growth-to-value rotation during tightening cycles. Portfolio managers use equity duration to construct interest-rate-neutral equity portfolios by balancing long-duration growth with short-duration value or dividend stocks.

What is equity duration and why do growth stocks have higher duration than value stocks?

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