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IAI Actuarial Core Principles · Actuarial Mathematics for Modelling · Duration, convexity and immunisation

Which statement about volatility (modified duration) is correct for a bond with fixed positive cashflows?

Volatility is approximately the proportional fall in price for a unit rise in yield, defined as minus (1/V) times dV/di. It differs from Macaulay duration by the factor 1/(1+i), falls with higher coupons, and never exceeds the final term.

  1. AIt is the proportional fall in price for a unit rise in yield, approximatelyCorrect
  2. BIt equals the weighted mean term of payments without any adjustment
  3. CIt increases when coupons are raised, other terms unchanged
  4. DIt is unaffected by the level of the yield
  5. It is always greater than the term to maturity

Explanation

Volatility = -(1/V)dV/di, the proportional price fall per unit yield rise. The mean term is Macaulay duration, not volatility. Higher coupons shorten duration, and duration never exceeds term for positive cashflows.

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