Duration MGT 4850 Spring 2008 University of Lethbridge

Fixed Income Securities Bonds and Pricing Term Structure of Interest Rates Risk – Credit –Interest rate Price Reinvestment Risk Measuring and Hedging Interest rate Risk

3 Pricing of Treasury Bonds Bond Pricing Example (cont’d) This corresponds to a newspaper price of about 100 8/32nds.

Interest Rate Term Structure

Bootstraping and Forward rates Non-arbitrage in Interest rate futures Trading the Yield curve Trading Spreads

The NOB Spread The NOB spread is “notes over bonds” Traders who use NOB spreads are speculating on shifts in the yield curve –If you feel the gap between long-term rates and short-term rates is going to narrow ( yield curve slope decreases or flattens), you could sell T-note futures contracts and buy T-bond futures

NOB spread (trading the yield curve) slope increases (long term R increases more than short term or short term even decreases) buy notes sell bonds

TED spread (different yield curves) The TED spread is the difference between the price of the U.S. T-bill futures contract and the eurodollar futures contract, where both futures contracts have the same delivery month (T-bill yield<ED yield) –If you think the spread will widen, buy the spread (buy T-bill, sell ED)

Trading Spreads

10 Bond Risks Credit risk is the likelihood that a borrower will be unable or unwilling to repay a loan as agreed –Rating agencies measure this risk with bond ratings Interest rate risk is a consequence of the inverse relationship between bond prices and interest rates –Duration is the most widely used measure of a bond’s interest rate risk

11 Sensitivity to interest rate changes Maturity Coupon LowerHigher LowerAmbiguous Lower Higher Ambiguous

Definition Measure of the sensitivity of the price of a bond to changes in the interest rate at which bond is discounted Macauley duration measure Basic Duration Calculation

Using Excel Formula Settlement (purchase date) Maturity (bond’s maturity date) Coupon Yield (to maturity) Frequency (# coupons per year) Basis (day count) 0 30/360 1 act/actual 2 act/360 3 act/365 4 Eur 30/360

14 Duration Matching Duration matching selects a level of duration that minimizes the combined effects of reinvestment rate and interest rate risk Bullet immunization Bank immunization

Bullet Immunization When we want to ensure that the money invested in bonds will grow at a target compound rate over the next target period years we need to find a bond with current YTM matching our expected yield and duration equal to the target period.

Meaning of Duration Weighted Average of the bond’s payments Bond’s price elasticity with respect to its discount rate Discount factor elasticity Price volatility

Babcock’s Formula Weighted average of “current yield” and PVIF

Duration Patterns Maturity

Duration Patterns Coupon