Interest Rate Risk

Interest rate risk has two components that move in opposite directions. When yields rise, the market value of a bond falls, but every coupon received can be redeployed at the new higher rate. When yields fall, capital values rise while future coupons and maturing principal earn less. The net effect on realised return therefore depends on the investor's horizon relative to the timing of the bond's cash flows.

Macaulay duration is the weighted average time to receipt of a bond's cash flows, with each weight equal to that cash flow's present value as a share of total price. It also identifies the horizon at which the two effects roughly cancel for a single parallel shift in yields: hold the bond for a period shorter than its Macaulay duration and price risk dominates, hold it longer and reinvestment risk dominates. This is the analytical foundation of duration matching.

Modified duration converts Macaulay duration into a percentage price sensitivity: divide Macaulay duration by one plus the yield per period. The estimated percentage change in price is then minus modified duration multiplied by the change in yield, expressed in decimal form. Money duration scales this by the bond's full price, giving a currency amount per unit of yield change, and the price value of a basis point is the money change for a one basis point move.

Because the price-yield relationship is curved rather than straight, the duration estimate understates gains when yields fall and overstates losses when yields rise. Adding one half of convexity multiplied by the squared change in yield corrects for this curvature. The convexity term is always positive for a straight bond, so it improves the estimate in both directions and matters most for large yield moves and long-dated, low-coupon issues.

Bond fund factsheets and index summaries quote effective duration precisely because it is the standard unit of interest rate exposure; a portfolio's duration is closely approximated by the market-value-weighted average of its holdings' durations, which makes duration a tradable target rather than just a descriptive statistic. Dealers hedge inventory in duration terms, and futures and swaps are sized by matching money duration.

On balance sheets the exposure appears as an asset-liability mismatch. Banks funding long fixed-rate securities and mortgages with short-dated deposits carry structural duration risk, and the accounting distinction between held-to-maturity and available-for-sale portfolios changes when losses become visible, not whether they exist. Life insurers and defined-benefit pension plans face the mirror problem: their liabilities are long-duration, so falling yields raise the present value of what they owe faster than assets appreciate.

Expect to compute Macaulay, modified and approximate modified duration, convert between them, and produce a full percentage or currency price estimate for a stated yield shift with and without the convexity adjustment. You should also rank bonds by exposure using the standard drivers: longer maturity, lower coupon and lower yield all increase duration, and the coupon effect frequently overturns a naive maturity ranking.

Equally important is knowing which measure applies. Yield duration measures such as modified duration assume fixed cash flows, so bonds with embedded options require effective duration, computed from repricing the bond under small upward and downward shifts of the benchmark yield curve. Non-parallel curve moves call for key rate durations, and for credit-risky bonds empirical duration can differ from analytical duration because spreads often move opposite to benchmark yields.