2006 CORRECTION FIXED INCOME FINAL
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%
4.
a) Mkt value = 3MM x 1.326 + 1.5MM x 1.07 + 2MM x 1.26 = $8,103,000
+AI
Accrued = (48/360 x 86.25)3M + (5/360 x 50)1.5M
+ (32/360 x 80 )2M =
49,760
Therefore market value +AI = 8,103,000 + 49,760 =$8,152,760
b) Average duration =[(132.6 x 3 x 9.34) + (126.4 x 2 x 10,50) + (106,9 x 1.5 x
15,4)]/mkt value= 10.89
Average convexity = =[(132.6 x 3 x 120) + (126.4 x 2 x 155) + (106,9 x 1.5 x
350)]/mkt value = 176
c) Decrease duration by 20% to 8.70.
You must sell (10.89 - 8.70) x 8,152,760/ (12 x 109,187)= 14 contracts.
d) Dollar duration of WMT bond = 1069.4 x 1500 x 15.40% = 247,000 average
modified duration of PG & XOM = 9.82
247,000 = (9.82 x MVWMT)/100 Therefore MVWMT = 2,515,300 which
corresponds to 2,515,300/1069 =2352 bonds WMT
e) Use the Tbonds futures contract which, from the handout, trades at 109-06 that
is 109 and 6/32 = 109.19
To hedge my WMT position the amount of contracts that must be shorted is :
Hedge ratio x (par value to be hedged/par value of contract):
17/12 [(2352 + 1500) x 1000)/100,000)] = 55 contracts need to be shorted.
5.
TIME
(years)
P(default)
Recovery
amount
Risk free
value ($)
Loss given
default ($)
0.5
1.5
2.5
3.5
4.5
Q
Q
Q
Q
Q
40
40
40
40
40
99.84
101.94
102.04
102.20
102.31
59.84
61.94
62.04
62.20
62.31
PV of
expected
loss
58.41Q
57.62Q
55.01Q
52.56Q
50.18Q
-----------274Q
Expected loss from default is price Risk free – price Corp = 99 22/32 - 96.80 =2.8875
or $28.875
274Q = 28.875 therefore Probability of default Q = 9.48%
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%
4.
a) Mkt value = 3MM x 1.326 + 1.5MM x 1.07 + 2MM x 1.26 = $8,103,000
+AI
Accrued = (48/360 x 86.25)3M + (5/360 x 50)1.5M
+ (32/360 x 80 )2M =
49,760
Therefore market value +AI = 8,103,000 + 49,760 =$8,152,760
b) Average duration =[(132.6 x 3 x 9.34) + (126.4 x 2 x 10,50) + (106,9 x 1.5 x
15,4)]/mkt value= 10.89
Average convexity = =[(132.6 x 3 x 120) + (126.4 x 2 x 155) + (106,9 x 1.5 x
350)]/mkt value = 176
c) Decrease duration by 20% to 8.70.
You must sell (10.89 - 8.70) x 8,152,760/ (12 x 109,187)= 14 contracts.
d) Dollar duration of WMT bond = 1069.4 x 1500 x 15.40% = 247,000 average
modified duration of PG & XOM = 9.82
247,000 = (9.82 x MVWMT)/100 Therefore MVWMT = 2,515,300 which
corresponds to 2,515,300/1069 =2352 bonds WMT
e) Use the Tbonds futures contract which, from the handout, trades at 109-06 that
is 109 and 6/32 = 109.19
To hedge my WMT position the amount of contracts that must be shorted is :
Hedge ratio x (par value to be hedged/par value of contract):
17/12 [(2352 + 1500) x 1000)/100,000)] = 55 contracts need to be shorted.
5.
TIME
(years)
P(default)
Recovery
amount
Risk free
value ($)
Loss given
default ($)
0.5
1.5
2.5
3.5
4.5
Q
Q
Q
Q
Q
40
40
40
40
40
99.84
101.94
102.04
102.20
102.31
59.84
61.94
62.04
62.20
62.31
PV of
expected
loss
58.41Q
57.62Q
55.01Q
52.56Q
50.18Q
-----------274Q
Expected loss from default is price Risk free – price Corp = 99 22/32 - 96.80 =2.8875
or $28.875
274Q = 28.875 therefore Probability of default Q = 9.48%