Duration

1. Define the duration of a bond and discuss its uses 2. Why modified duration is a better measure than maturity when calculating the bond’s sensitivity to change in interest rates 3. Define convexity and explain how modified duration and convexity are used to approximate the bond’s percentage in price, given a change in interest rates Bond: Price-yield relationship 1. Basic concept: price, yield to maturity, current yield, capital yield, coupon. Yield to maturity= (current yield+ capital yield) (Current yield=coupon /current price) 2. Interest rate sensitivity (how interest rate change can affect bond price)-(detailed explanation on PP514, TEXT BOOK) 1) YTM-Price 2) YTM-Price (change rate) 3) Maturity-Interest rate sensitivity 4) Maturity-Interest rate sensitivity (change rate) 5) Coupon- Interest rate sensitivity 6) Current yield-interest rate sensitivity 1)-5): Malkiel’s bond pricing relationship 6): Homer and Martin (1972) 3. Duration (linear approximation of price yield relationship) a. Why use duration (Pros): (1) Simple, effective (2) Tool of immune portfolio (3) Measure interest rate risk i. Maturity is the main determinant of bond risk, while time to maturity is not a perfect measure of long term/short term nature, therefore it is important to apply a more accurate one. ii. Duration is proportion to the price change, but maturity is not. b. Definition: Macaulay Duration: * As a effective maturity concept, weighted average of the time to each coupon or principle payment made by the bonds. * This form of duration measures the number of years required to recover the true cost of a bond, considering the present value of all coupon and principal payments received in the future Modified Duration: * This measure expands or modifies Macaulay duration to measure the responsiveness of a bond’s price to interest rate changes. It is defined as the percentage change in price for a 100 basis point change in interest rates. c. Calculation and measure (1) Duration or Macaulay duration (D or MD) delta P/P = - D x delta (1+y)/(1+y) (2) Modified duration i. (D*=D/(1+y) delta P/P = - D* x delta y ii. Short cut (I), when delta y is know (See ppt Lect 3 p26) D* (per period) (3) Approximate duration (See ppt Lect3, pp 40) d. Determinants of duration (4 rules) (1) Rule1: zero coupon, duration =maturity (2) Rule2: holding maturity constant, duration is lower for higher coupon bond (3) Rule 3: holding coupon rate constant, duration increase with time to maturity (4) Rule 4: other factor constant, duration is high when YTM is lower (5) Rule 5: perpetuity duration is (1=y)/y e. Limitations (Cons) (1) Only appropriate for small changes (2) Direct proportion to change in bond’s yield but not exactly so (3) Lead to bias in estimation i. Underestimate bond price increase when yield decrease ii. Overestimate bond price decrease when yield increase. 4. Convexity (curvature measure of price yield relationship) a. Why use convexity (Pros) (1) The duration is only linear approximation and restricted when the interest rate change is small. Convexity helps to adjust the measure b. Definition: The curvature measure of the price yield relationship. Rate of slope change on price yield curve expressed as the fraction of bond price. c. Calculation: (1) Ordinary (2) Short cut (used when delta y is know) a. Dollar convexity (ppt Lect3, pp36) b. Percentage convexity (ppt Lect3, pp 36) c. Approximate convexity (see ppt pp.43) 5. Passive Bond Management a. Indexing strategy i. Concept: Replicate the performance of a given bond index ii. b. Immunization techniques 6. Issues to notice in bond, duration, and convexity a. Calculation -be clear about the yield and its relevant period, whether it is annual based or not. -need to match each yield with its unit (period; semi-annual; annual) -emphasis the above idea in duration and convexity calculation (especially in short cut application) b. Discussion (general guidance on possible discussion topics) (1) Definition i. What is the bond’s market price ii. What is the difference between duration and convexity iii. Why bond price and yield move in opposite direction iv. Define the duration (2) Evaluations i. Evaluate the benefit and limitation in using duration /convexity ii. Explain why modified duration is better measure than maturity. (3) applications i. in what circumstance, a bond investor should apply duration; when should he/she use convexity ii. explain how the modified duration and convexity are used to approximate bond’s interest rate risk (The questions in boldface are those shown in the past paper and need to concentrate on.)