1. Finance 300 Financial Markets Lecture 14 Fall, 2001© Professor J. Petry http://www.cba.uiuc.edu/broker/fin300/fin300pp.htm

2. 2 Exam Preparation Mid-term #2 next class –Will be a touch more challenging Chapter IV (Debt Market), Chapter V (Money Market) –True & false, matching, and problems, other MC –All Multiple Choice format; length comparable, but heavier emphasis on problems—I will provide a formula sheet, which I will post by Thursday. –Only covers new material Everything in Ch IV except : –realized yield calculation on page 162. –Immunization calculation done in answers to TTD (IV-18, D) All definitions, concepts in Ch V, including yield definitions—i.e. what is included in Bankers Discount Yield, what is not—but no problems to actually calculate. No bid/ask or auction problems (example on page 192 is out for instance). However, all institutional details of primary, secondary markets and instruments will be on the exam. Series 7 like questions are legit in both chapters.

3. 3 Bond Pricing The Term Structure of Interest Rates (cont’d)

4. 4 Duration & Volatility Volatility –The tendency of a security price or market index to change due to the changes in market conditions. Volatility = Δ price / price Duration –A measure of the effective maturity of a bond, defined as the weighted average of the times until each payment, with weights proportional to the present value of the payment. –Bond price volatility and duration are directly related. –Modified duration measures the volatility in response to a 1% change in interest rates. Volatility = Δ price/price = -[duration / (1 + yield)] * Δi –Duration trading strategies would include increasing duration exposure ahead of expected decreases in interest rates, (or decreasing ahead of interest rate increases) to maximize price impact on your holdings.

5. 5 Duration Calculation Vol=Δprice/price=-[duration/(1+ yield)]*Δi=4.27/1.07*1%=-3.9907% Modified Duration = D* = duration/(1+yield)=3.9907 years Ex: 1% change (decline) in interest rates would result in what change in bond price? From 7% to 6% ; -D* x -.01 =-3.9907 x -.01 = 3.9907% ; 1082 x 1.039907 = $1125.18

6. 6 Pricing Error from Convexity Price Yield Duration Pricing Error from Convexity

7. 7 Correction for Convexity Modify the pricing equation: Convexity is Equal to: Where: CF t is the cashflow (interest and/or principal) at time t.

8. 8 Duration & Volatility Convexity –The curvature of the price-yield relationship of a bond. Duration and volatility are a linear estimate of a convex relationship. Convexity is a correction to the duration formula, which adjusts for the convexity of the relationship. The convexity correction is particularly important for measuring large changes in the price-yield relationship. Convexity increases with lower coupon rates, longer maturity and lower yield. To more properly estimate the price change due to a change in interest rates we add the convexity correction to the duration estimate: ΔP/P = -modified duration Δy + ½ Convexity Δy 2

9. 9 Duration & Convexity Calcs Volatility=Δ price/price =-[duration / (1 + yield)] * Δi = 4.27/1.07*1% =-3.9907% Corrected ΔP/P = -modified duration Δy + ½ Convexity Δy 2 = -3.9907 x –0.01 +.5 (24.22) (-.01) 2 =.039907+.001211=.041118% Check this against actual price change

10. 10 Duration & Convexity Calcs Volatility = Δ price/price = -[duration / (1 + yield)] * Δi = Corrected ΔP/P = -modified duration Δy + ½ Convexity Δy 2

11. 11 Duration & Volatility Example –Assume a 30 year bond, 8% coupon and initial yield to maturity of 8%. The bonds duration is 11.37 years. (What does this mean?) –Convexity for this bond is 212.4. (What does this mean?) –If yields move from 8% to 10%, how much would you expect the price of this bond to move? –What would the price be at the new interest rate? –Check your answer by re-valuing the bond at the new yield.