Financial Markets & Expectations

Stock Pricing & the Fundamental Value

coreExam · medium

The fundamental value of a stock is the expected present discounted value of future dividends, discounted at the required return (risk-free rate + equity risk premium). With constant dividend D and required return k: Q = D/k. With expected dividend growth g, Gordon formula: Q = D/(k − g). Bubbles arise when price deviates persistently from fundamental value.

Derivation

Step 1 / 7

1Press Space or click Reveal next
(hidden)
2Press Space or click Reveal next
(hidden)
3Press Space or click Reveal next
(hidden)
4Press Space or click Reveal next
(hidden)
5Press Space or click Reveal next
(hidden)
6Press Space or click Reveal next
(hidden)
7Press Space or click Reveal next
(hidden)

The Fundamental Value

A stock is a claim on a perpetual stream of dividends. Its fundamental value is the PDV of expected dividends, discounted at the required return $k$ :

Q_t = \sum_{n=1}^{\infty} \frac{E_t[D_{t+n}]}{(1 + k)^n}

The Gordon Growth Model

With constant growth $g < k$ :

Q_t = \frac{E_t[D_{t+1}]}{k - g}

Rearranged:

k = \frac{D_{t+1}}{Q_t} + g

The required return equals the dividend yield plus expected dividend growth. For the S&P 500 (yield ~2%, expected growth ~4%), $k \approx 6\%$ .

Two Channels for Price Movements

| Channel | Variable | Mechanism | |---------|----------|-----------| | Discount rate | $k$ | Higher $r$ or risk premium lowers $Q$ | | Cash flow | $g$ | Higher expected growth raises $Q$ |

Why Stocks Are Long-Duration Assets

Dividends are spread over many years. A change in $k$ affects every term, compounding into a big price move. This is why equity prices swing sharply with central-bank rate changes even when near-term earnings are unchanged.

Bubbles

A bubble $B_t$ is a deviation from fundamental value that grows at rate $k$ :

Q_t = Q^{\text{fund}}_t + B_t, \quad E_t[B_{t+1}] = (1+k) B_t

This is an equilibrium as long as investors expect $B$ to keep growing — a self-fulfilling belief. Eventually, the bubble bursts when expectations shift.

Worked Example

A stock pays D = 3 next year, expected to grow at g = 3% per year. Required return k = 8%. (a) Compute Q. (b) The Fed raises rates → k rises to 10%. Compute new Q and % drop.

(a) Q = D/(k − g) = 3/(0.08 − 0.03) = 3/0.05 = 60.
(b) New Q = 3/(0.10 − 0.03) = 3/0.07 ≈ 42.86. Drop ≈ (60 − 42.86)/60 ≈ 28.6%.
Interpretation: a 2 pp rise in k causes a ~29% equity loss via the discount-rate channel.

Initial Q = 60. After rate hike: Q ≈ 42.86, a 28.6% loss. Stocks are long-duration assets — very sensitive to discount rates.

Common Mistakes

—Using D_t instead of E[D_{t+1}] in the Gordon formula — the denominator references next year's expected dividend.
—Forgetting the convergence condition g < k: if g ≥ k, the PV diverges and Gordon doesn't apply.
—Confusing k (required return) with the risk-free rate r — k = r + equity premium.
—Attributing all price movements to fundamentals — much of short-run volatility is discount-rate driven.

Exam Cues

→Gordon: Q = D/(k − g). Yield + growth: k = D/Q + g.
→Discount-rate channel: ↑k → ↓Q. Cash-flow channel: ↑g → ↑Q.
→Bubbles: price above fundamental, growing at rate k. Self-fulfilling until they burst.
→Equity risk premium ≈ 4–6 pp historically. Adds to the risk-free rate to give k.