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Finance · level 2

Put–call parity

Two portfolios with identical payoffs must have identical prices. That single sentence prices a put from a call, and explains why equity is a call on the firm's assets.

Worked example: Stock $69, a six-month call with strike $69 costs $6, risk-free 4%. No dividends. Price of the put with the same strike and expiry?

call$6
stock$69
PV(K)$67.66
put$4.66

Step by step

  1. 1

    Parity

    P = C − S + PV(K)

  2. 2

    PV of strike

    $69 / 1.04^0.5 = $67.66

  3. 3

    Put

    $6 − $69 + $67.66 = $4.66

  4. 4

    Why

    Stock + put and call + risk-free bond pay the same at expiry, so they must cost the same today or an arbitrage exists.

Stock $69, a six-month call with strike $69 costs $6, risk-free 4%. No dividends. Price of the put with the same strike and expiry? = 4.66

The theory behind it

Intuition

Finance is time and risk applied to cash: move every cash flow to the same date at a rate that reflects its risk, then compare.

Common pitfalls

  • ×Discounting a nominal flow at a real rate (or vice versa).
  • ×Mixing enterprise-value and equity-value numbers in the same ratio.

In the interview

Valuation, WACC, LBO and accretion rounds — where a wrong bridge is a wrong answer.