FIXEDINCOMEMSCINFMI - Knowledge FINAL__CORRECTION
FINAL CORRECTION
1. 360/90 (100- Y) = 6 Therefore T-bill cvash price, Y, is 98.5 or $985
2. 5/1.061 + 5/1.062 + 5/1.063 + 105/1.064 = 96.53 that is $965.30
3. Modified duration of Bond XYZ is 3.71 modified duration = 3.71/1.06= 3.49
4.
BOND
TBILL
ABC
XYZ
AMOUNT
50 million
100 million
250 million
DURATION
0.5
8.5
3.49
The portfolio duration is 50/400 * 0.5 + 100/400 * 8.5 + 250/400 * 3.49 = 4.37
5. Unit Cost of Bond ABC : number of days since last coupon : Jan 20 to April 9th = 78
Number of days between each coupon date = 180
Accrued interest is therefore (78/180) * $35 = $15.17 Cost = 1020 + 15.17 = $1035.17
6. If rates increase by 200Bp, the value of the portfolio will decrease.
Using duration and convexity, the value of each bond would be :
Tbill would decrease by 0.02 x 0.5= 1% using duration and ½ * 7 * 0.022 =
0.14% using convexity
Net decrease for Tbill= -1% + 0.14% = -0.86%
Bond ABC would decrease by 0.02 x 8.5 = 17% using duration and ½ * 52*
0.022 = 1.04%
Net decrease for Bond ABC = -17% + 1.04% = -15.96%
Bond XYZ would decrease by 0.02 x 3.71 = 7.42% using duration and ½ * 21
*0.022 = 0.42%
Net decrease for Bond XYZ = -7.42% + 0.42% = -7%
The portfolio would therefore decrease by:
0.86 x (50/400) + 15.96 x (100/400) + 7 x (250/400) = 8.36% or $34.24 million
another way to derive the answer would be to calculate the convexity of the overall
portfolio that is :
0.125 x 7 + 0.25 x 52 + 0.625 x 21 = 27
and then derive the percent age change of the prtfolio using both duratin and
convexity :
4.37 x (-0.02) = -8.76%
27 x ½ x (0.02)2 = 0.54%
the answer is close enough to the one using the other formula that is –8.76 = 0.54 =
8.22% decrease due to a 2% increase in rates
7. Dollar duration of Bond ABC = 100 000 000 x 0.085 = 8,670,000
Duration of Bond XYZ is 3.49 (see above)
MDXYZ
From the formula seen in class
$DABC = ----------- MVXYZ
100
MVXYZ = 233,692,722 Number of bonds to be purchased : 243,553,008 / 965.30 =
252,308 bonds
Students finding an approximate measure , depending on duration calculation ( or use
of modified duration) close to this number will get full credit.
8. Fixed leg :
3/(1+0.05)3/12 + 3/(1+0.05)9/12 + 3/(1+0.05)15/12 + 103/(1+0.05)21/12
= 103.24
Floating leg : (100 + 5.5+0.9)/(1 + 0.05)6/12 = 103.83
DB is paying Libor and receiving fixed so its net position from this swap is :
103.24 - 103.83 = -$0.59 million
9. DB runs the risk of having Sahan Bank default on its swap. SB is net debtor on the
swap but keep in mind that its risk lays with the investment bank it’s doing business
with.
10.
SAHAN BANK
DEUTSCHE BANK
FIXED
9%
6%
FLOATING
Libor + 0.9%
Libor + 0.4%
SB has a comparative advantage in floating rates as the difference in floating rate
(0.5%)between the 2 banks is less important than the difference in the fixed rates (3%).
11. Difference between 9% - 6% = 3% and Libor + 0.9% - Libor + 0.4% = 0.5%
That is 2.5% - 0.3% (fees) = 2.2%
2.2%/2 =1.1%
SB will borrow fixed at 7.9% (that is 9% - 1.1%)
DB will borrow floating at Libor –0.7% (that is Libor+0.4% - 1.1%)
12. The minimum requested future value by the client is 25 (1+0.05)6 = 33.50 million
13. 33.50/(1+0.065)6 = $22.95 million
Safety cushion = 25 million - 22.95 million = $2.05 million
14. If rates decrease by 1% and the bond’s duration is 6, the bond should appreciate by 6%
that is $1060. The 1-year interest on each bond provided by the coupon is $120
Therefore, the value of the portfolio after 1 year is 1180 x 25 000 = $29 500 000
15. The need of immunization can be mathematically defined when the safety cushion
reaches zero or becomes negative.
1. 360/90 (100- Y) = 6 Therefore T-bill cvash price, Y, is 98.5 or $985
2. 5/1.061 + 5/1.062 + 5/1.063 + 105/1.064 = 96.53 that is $965.30
3. Modified duration of Bond XYZ is 3.71 modified duration = 3.71/1.06= 3.49
4.
BOND
TBILL
ABC
XYZ
AMOUNT
50 million
100 million
250 million
DURATION
0.5
8.5
3.49
The portfolio duration is 50/400 * 0.5 + 100/400 * 8.5 + 250/400 * 3.49 = 4.37
5. Unit Cost of Bond ABC : number of days since last coupon : Jan 20 to April 9th = 78
Number of days between each coupon date = 180
Accrued interest is therefore (78/180) * $35 = $15.17 Cost = 1020 + 15.17 = $1035.17
6. If rates increase by 200Bp, the value of the portfolio will decrease.
Using duration and convexity, the value of each bond would be :
Tbill would decrease by 0.02 x 0.5= 1% using duration and ½ * 7 * 0.022 =
0.14% using convexity
Net decrease for Tbill= -1% + 0.14% = -0.86%
Bond ABC would decrease by 0.02 x 8.5 = 17% using duration and ½ * 52*
0.022 = 1.04%
Net decrease for Bond ABC = -17% + 1.04% = -15.96%
Bond XYZ would decrease by 0.02 x 3.71 = 7.42% using duration and ½ * 21
*0.022 = 0.42%
Net decrease for Bond XYZ = -7.42% + 0.42% = -7%
The portfolio would therefore decrease by:
0.86 x (50/400) + 15.96 x (100/400) + 7 x (250/400) = 8.36% or $34.24 million
another way to derive the answer would be to calculate the convexity of the overall
portfolio that is :
0.125 x 7 + 0.25 x 52 + 0.625 x 21 = 27
and then derive the percent age change of the prtfolio using both duratin and
convexity :
4.37 x (-0.02) = -8.76%
27 x ½ x (0.02)2 = 0.54%
the answer is close enough to the one using the other formula that is –8.76 = 0.54 =
8.22% decrease due to a 2% increase in rates
7. Dollar duration of Bond ABC = 100 000 000 x 0.085 = 8,670,000
Duration of Bond XYZ is 3.49 (see above)
MDXYZ
From the formula seen in class
$DABC = ----------- MVXYZ
100
MVXYZ = 233,692,722 Number of bonds to be purchased : 243,553,008 / 965.30 =
252,308 bonds
Students finding an approximate measure , depending on duration calculation ( or use
of modified duration) close to this number will get full credit.
8. Fixed leg :
3/(1+0.05)3/12 + 3/(1+0.05)9/12 + 3/(1+0.05)15/12 + 103/(1+0.05)21/12
= 103.24
Floating leg : (100 + 5.5+0.9)/(1 + 0.05)6/12 = 103.83
DB is paying Libor and receiving fixed so its net position from this swap is :
103.24 - 103.83 = -$0.59 million
9. DB runs the risk of having Sahan Bank default on its swap. SB is net debtor on the
swap but keep in mind that its risk lays with the investment bank it’s doing business
with.
10.
SAHAN BANK
DEUTSCHE BANK
FIXED
9%
6%
FLOATING
Libor + 0.9%
Libor + 0.4%
SB has a comparative advantage in floating rates as the difference in floating rate
(0.5%)between the 2 banks is less important than the difference in the fixed rates (3%).
11. Difference between 9% - 6% = 3% and Libor + 0.9% - Libor + 0.4% = 0.5%
That is 2.5% - 0.3% (fees) = 2.2%
2.2%/2 =1.1%
SB will borrow fixed at 7.9% (that is 9% - 1.1%)
DB will borrow floating at Libor –0.7% (that is Libor+0.4% - 1.1%)
12. The minimum requested future value by the client is 25 (1+0.05)6 = 33.50 million
13. 33.50/(1+0.065)6 = $22.95 million
Safety cushion = 25 million - 22.95 million = $2.05 million
14. If rates decrease by 1% and the bond’s duration is 6, the bond should appreciate by 6%
that is $1060. The 1-year interest on each bond provided by the coupon is $120
Therefore, the value of the portfolio after 1 year is 1180 x 25 000 = $29 500 000
15. The need of immunization can be mathematically defined when the safety cushion
reaches zero or becomes negative.