1. Lecture 12

2. 1 - The Duration Model 2 - Naive Hedging Model 3 - Conversion Factor Model 4 - Basis Point Model 5 - Regression Model 6 - Yield Forecast Model

3.  Duration Model

4. Duration Model  Your cash position is $1,000,000 10% coupon, 26year bonds, with YTM=12.64% and duration of 8.24 years.  The 6%, 20year, TBill has a duration of 10.14 years, YTM=8.5%  The FC on this bond is priced at 96.87 HR = 79.98x8.24 = 659.04 =.671 96.87x10.14 982.26 (1,000,000 / 100,000) x.671 = 6.71 or 7 contracts

5. Duration Example  In 3 months, you will receive $3.3 mil in cash and must invest it for 6 months. The current 6 month rate is 11.20%. You like that rate, and wish to lock it in.  6 month tbills have a.50 duration, while 3 month bills have a.25 duration.  If the 3 month futures price is 97.36, what number of Ks are required to lock in the rate? HR = 100 x.5 = 2.05 x (3.3 /.1) = 67.8 contracts 97.36 x.25

6. Naive Model HR = 1.0 (all previous examples were naive hedges) Conversion Factor Model HR = conversion factor CF = Price of deliverable bond @ 6% YTM 100

7. Conversion Factor Model Example  You own a $1mil portfolio you wish to hedge. Your are considering a 3 month futures K. The bond that could be delivered against the contract is a 9.5%(semiannual) bond with a 30year maturity. The bond is callable in 15 years. How many Ks should you use to hedge the position? CF = 134.30/100 = 1.34 x (1mil/.1) = 13 contracts

8. Example - Conversion Factor Model  You have a $1mil portfolio, containing 21.5 year 10 3/8 bonds. Price = 100.5363 (YTM = 10 5/16)  CTD 20year, 8% bond has YTM = 10.43  Create the hedge.  Assume that in 6 months YTM on your portfolio rises to 12 % and YTM on CTD rises to 12.217%  Create a table showing your position/profit/loss

9. Example - Conversion Factor Model CF = PV of 5.1875 @ 3% for 43 periods / 100 = 1.52 1.52 x (1mil/100,000) = 15 CashFutures TodayOwn $1mil Short 15 K @ 100.5363@ 79.718 (given) ($1,005,363)+ $1,195,770 6 mthsSell @ 87.63buy 15 K @ 71.07 (given) + $876,301($1,066,050) (129,062)+129,720

10. Basis Point Model BVC cash = $ change in value per basis point of cash position B = Relative yield volatility of cash to CTD = (V cash / V ctd ) BVC ctd = $ change in value per basis point of CTD CF ctd =conversion factor of CTD

11. Example  YTM = 9% on semi-annual bonds  Your cash portfolio consists $1mil of 26 year 9 7/8 bonds, that have a yield volatility of.60  Futures CTD is a 7.25% 26.5 year note with a yield volatility of.50  Use the basis point model to create a hedge and show the position table for a 3month time period and a change in YTM to 10%.

12. Basis Point Model Use Calculator bond functions for calcualtions

13. example - continued Cash value @ 9% = 108.737 BVC cash = $107 (PV @ 9% - PV @ 9.01) BVC ctd = $86 B =.6 /.5 = 1.20 CF =.1.16 (PV of CTD @ 6% / 100) HR* = ( 107 ) x1.20 = 1.73 ( 86 / 1.16) 1 mil / 100,000 x 1.73 = 17 contracts

14. example - continued (10%) CashFutures Today $1mil @ 108.73717K @ 82.44 (given) -$1,087,370+1,401,480 3 months (YTM = 10%) $1 mil @ 98.8217K @ 76.45 (given) +$ 988,212- $1,299,650 Net Position$99,158 loss$101,830 gain net gain of $2,672

15. example - continued Assume YTM = 8% CashFutures Today $1mil @ 108.73717K @ 82.44 (given) -$1,087,370+ 1,401,480 3 months (YTM = 8%) $1 mil @ 120.3017K @ 89.56 (given) +$ 1,203,034- $1,522,520 Net Position$115,664 gain$121,040 loss net loss of $5,376

16. Regression Model HR = Covariance of Cash & Futures Variance of futures best model if HR =.90, then we know that a $1 change in futures prices correlates to a $0.90 change in cash value. requires constant monitoring because HR changes with duration

17. Yield Forecast Model Given various yield forecasts, the HR changes Term Structure can forecast yields HR = CVdiff / FCV diff Example Cash Value = 97.94 & Futures = 72.50 Forecasted YTM YTM CVYTM FCCVFCCVdiffFCdiffHR 12.6511.25101.7275.063.772.561.48 12.8511.40100.1474.142.201.641.34 13.5512.0594.9970.37-2.95-2.131.36 13.7512.2093.6269.54-4.33-2.961.47