2006 CORRECTION FIXED INCOME FINAL
1. 800 - (800 x 0.02x) - 240 = 300MM
x= 16.25
2. Sell the 1x3 @5.00%
What amount do you deal ? $1,000,000 (1+4.75%)31/365 = $1,003,950
Eurodollar futures contract trades at 94.40 means the 3-month futures trades at 100 - 94.4 = 5.60%
Loss on the FRA is therefore : 5.60 - 5.00 = 0.60% and ($1,003,949 ( 0.60%)) / 6 = $1003.95 paid by you. Rollover the deposit for the remaining 2-month :
1,003,950 - 1,003.95 = $1,002,950 invested for 2-month (1+ 4.90%)61/365 =
$1,011,000
Borrowing cost : $1,000,000 (1+0.05)92/365 = $1,012,400 Overall loss = 1,012,400 - $1,011,000= $1,400.
3. Clients after 4-years wants 50MM(1+6%)4 = $63.12MM
The structurer can work at 8% and his safety cushion is therefore: 3.60MM found this way (50 - (63.12/1.08)4).
If all the funds are invested in a zero coupon 10-year bond yielding 8%, the duration of his investment will be 10/1+(0.08/2) =9.61
His safety cushion will reach zero once he’d lose $3.60MM. he will lose 3.60MM if rates increase to 3.60/9.61 =0.3746% x 2 =75BP. With that is if the YTM reaches 8% + 0.75 = 8.75%
Therefore market value +AI = 8,103,000 + 49,760 =$8,152,760
b) Average duration =[(132.6 x 3 x 9.34) + (126.4 x 2 x 10,50) + (106,9 x 1.5 x 15,4)]/mkt value= 10.89
Average convexity = =[(132.6 x 3 x 120) + (126.4 x 2 x 155) + (106,9 x 1.5 x 350)]/mkt value = 176
c) Decrease duration by 20% to 8.70.
You must sell (10.89 - 8.70) x 8,152,760/ (12 x 109,187)= 14 contracts.
d) Dollar duration of WMT bond = 1069.4 x 1500 x 15.40% = 247,000 average modified duration of PG & XOM = 9.82
e) Use the Tbonds futures contract which, from the handout, trades at 109-06 that is 109 and 6/32 = 109.19
To hedge my WMT position the amount of contracts that must be shorted is : Hedge ratio x (par value to be hedged/par value of contract):
17/12 [(2352 + 1500) x 1000)/100,000)] = 55 contracts need to be shorted.
5.
TIME (years)
P(default) Recovery amount
Risk free value ($)
Loss given default ($)
PV of expected
loss
0.5 Q 40 99.84 59.84 58.41Q
1.5 Q 40 101.94 61.94 57.62Q
2.5 Q 40 102.04 62.04 55.01Q
3.5 Q 40 102.20 62.20 52.56Q
4.5 Q 40 102.31 62.31 50.18Q
---274Q
