Macaulay, Modified, and Effective Durations
The duration of a bond measures the sensitivity of the bond’s full price (including accrued interest) to changes in the bond’s yield-to-maturity or, more generally, changes in benchmark interest rates. Bond duration estimates changes in bond price assuming that variables…
Effective Duration-Measure of Interest Rate Risk
Another approach to assessing interest rate risk of a bond is to estimate the percentage change in price against a change in the benchmark yield curve, such as the government par curve. The effective duration is defined as the sensitivity…
Interest Rate Risk Given a Bond’s Maturity, Coupon, and Yield
Duration – whether it’s Macaulay duration, effective duration, or any other kind of duration – is a measure of interest rate risk. Some factors affect duration and consequently affect interest rate risk. Time to Maturity Longer maturity bond prices are…
Portfolio Duration and its Limitations
Like equities, bonds are typically held in a portfolio. Therefore, bond portfolio managers need to measure the whole portfolio duration. There are two methods for calculating the duration of a bond portfolio: the weighted average of time to receipt of…
Money Duration and Price Value of a Basis Point
The modified duration is a measure of the percentage price change of a bond given a change in its yield-to-maturity. On the other hand, the money duration of a bond is a measure of the price change in units of…
Calculate and Interpret Convexity
The Modified Duration provides an estimate of the percentage price change for a bond given a change in its yield-to-maturity. A secondary effect is measured by the convexity statistic. Approximate Convexity The true relationship between the bond price and the…
Duration and Convexity Effect on the Price Change of a Bond
The change in the price of a bond can be summarized as follow: $$\text{Change in price} = \text{Duration effect} + \text{Convexity effect} $$ $$≈(\text{-AnnModDur}×ΔYield)+(\frac{1}{2}×\text{AnnConvexity}×(ΔYield)^2)$$ Example: Change in Price of the Bond when Interest Rate Falls Suppose the yield-to-maturity is expected…
Term Structure of Yield Volatility and Interest Rate Risk
Time horizon is an important aspect of understanding interest rate risk and the return characteristics of a fixed-rate investment. The primary concern for an investor is the change in the price of a bond given a sudden change in its…
Bond’s Holding Period Return, Duration, and Investment Horizon
Although short-term interest rate risk is a concern to some investors, other investors have a long-term horizon. Day-to-day changes in bond prices cause unrealized capital gains and losses. A long-term investor is concerned mostly with the total return over the…
Effect of Credit Spread on Yield-to-maturity
The yield-to-maturity on a corporate bond comprises a government benchmark yield and a spread over that benchmark. The building-blocks approach implies that the yield-to-maturity changes can be broken down further. The benchmark yield could change either because of a change…
