Transcript Derivatives - Matt Will Web Page

Lecture 12
1
2
3
4
5
6
-
The Duration Model
Naive Hedging Model
Conversion Factor Model
Basis Point Model
Regression Model
Yield Forecast Model

Duration Model
Cash Price
Duration Cash 1  ErCash
HR =


Futures Price Duration CTD 1+ ErCTD
1  ErCash
 Usually tossed out due to poor forecsating
1+ ErCTD
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
96.87x10.14
= 659.04 = .671
982.26
(1,000,000 / 100,000) x .671 = 6.71 or 7 contracts
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
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
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
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
Example - Conversion Factor Model
CF = PV of 5.1875 @ 3% for 43 periods / 100 = 1.52
1.52 x (1mil/100,000) = 15
Today
6 mths
Cash
Own $1mil
@ 100.5363
($1,005,363)
Futures
Short 15 K
@ 79.718 (given)
+ $1,195,770
Sell @ 87.63
+ $876,301
(129,062)
buy 15 K @ 71.07 (given)
($1,066,050)
+129,720
Basis Point Model
BVCCASH
HR 
 B # of Ks
BVCCTD CFCTD
BVCcash = $ change in value per basis point of
cash position
B = Relative yield volatility of cash to CTD
= (Vcash / Vctd)
BVCctd = $ change in value per basis point of
CTD
CFctd =conversion factor of CTD
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%.
Basis Point Model
9.00%
9.01% BVC.
Bond Value 108.737 108.630 107
CT D Value
82.442 82.356
86
Use Calculator bond functions for calcualtions
example - continued
Cash value @ 9% = 108.737
BVCcash = $107
(PV @ 9% - PV @ 9.01)
BVCctd = $86
B = .6 / .5 = 1.20
CF = .1.16 (PV of CTD @ 6% / 100)
HR* = (
107
) x1.20
( 86 / 1.16)
= 1.73
1 mil / 100,000 x 1.73 = 17 contracts
example - continued (10%)
Today
Cash
Futures
$1mil @ 108.737
-$1,087,370
17K @ 82.44 (given)
+1,401,480
3 months (YTM = 10%)
$1 mil @ 98.82
+$ 988,212
17K @ 76.45 (given)
- $1,299,650
Net Position
$101,830 gain
net gain of $2,672
$99,158 loss
example - continued
Assume YTM = 8%
Today
Cash
Futures
$1mil @ 108.737
-$1,087,370
17K @ 82.44 (given)
+ 1,401,480
3 months (YTM = 8%)
$1 mil @ 120.30
+$ 1,203,034
17K @ 89.56 (given)
- $1,522,520
Net Position
$121,040 loss
net loss of $5,376
$115,664 gain
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
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 CV YTM FC
12.65
11.25
12.85
11.40
13.55
12.05
13.75
12.20
CV
101.72
100.14
94.99
93.62
FC
75.06
74.14
70.37
69.54
CVdiff
3.77
2.20
-2.95
-4.33
FCdiff
2.56
1.64
-2.13
-2.96
HR
1.48
1.34
1.36
1.47