Dr. Sudhakar Raju
FN 6700
ASSIGNMENT 2 – ANSWERS TO FIXED INCOME MARKETS
1.) First, determine the MMY (Money Markey Yield). Note that the ASKED is the selling
price of the dealer. This is therefore the price that the investor will pay for the T-Bill.
Face Value = $1000; Discount Rate = 4.1125%; Maturity = 360 days.
Purchase Price
= Face Value - Discount Amount
= $1000 – [$1000 × .041125 × (360/360)]
= $1000 - $41.25
= $958.875
FV = PV [1 + r n]
$1000 = $958.875 [1 + r (360/360)]
1.0429 = 1 + r
r = .0429 or 4.29% (MMY)
Thus, the MMY (or 360 day yield) is 4.29%. The BEY (or 365 day yield) is given by:
BEY = .0429 × (365/360) = 4.35% p.a.
The Ask Yield for T-Bills is the same thing as the BEY (Bond Equivalent Yield).
Notice the following sequence: BEY>MMY>Discount Rate (or Asked Price).
2.) The selling price of the dealer = 80:12 (80 points and 12 ticks) or 80 + (12/32) =
80.375. (This is the buying price for the investor). For a $100 face value T-bond, the
purchase price is $80.375. For a $1000 face value T-bond, the appropriate price is
$803.75.
To solve for the yield to maturity (YTM) do the following:
2 shift P/Yr
1000 FV
803.75 +/- PV
32.50 PMT (Semi-annual coupon payment of $65/2 = $32.50)
30 N [Sept. 2040 – Sept. 2010 = 30 years]
Shift N
I/YR = > 8.28% p.a. [ASK YLD]
1
3.) Discount Amount = $13,119.17
Price of T-Bill
= Face Value – Discount Amount
= $1 m - $13,119.17
= $986,880.83
Money Market Yield: FV = PV [1 + r n]
$1m = $986,880.83 [1 + r (91/360)]
$1m = $986,880.83 [(1 + 2528 r)
1.01329 = 1 + .2528 r
r = [.01329 /.2528]
r = .0526 or 5.26% (MMY)
The Bond Equivalent Yield (BEY) is given by: .0526 × [365/360] = 5.33% p.a.
4.) FV = $1000; CIR (Coupon Interest Rate) = 9%; N (Number of Years/Periods) = 15
years; Annual Bond.
When bonds are first issued, they are issued at face value or par. If interest rates rise,
the price of the bond will decline. Thus:
1 Shift P/YR
1000 PV
90 PMT
15 N
15 I/YR
PV = $649.16
Thus, the price of the bond drops from $1000 to $649.16
5.) 1 shift P/yr
70 PMT
11 N
8.50 I/YR
1000 FV
PV = $895.47
6.) 1Shift P/yr
1000 FV
102.50 PMT
14 N
1225 +/- PV
2
I/YR = 7.59%
Current Yield (CY)?
CY = Annual Coupon
PB
CY = $102.50 = 8.37%
$1225
7.) 2 shift P/yr
350 +/- PV
1000 FV
O PMT (since these are zero coupon bonds)
10 N
Shift N
I/YR = 10.78% [YTM]
8.) 2 shift P/yr
350 +/- PV
650 FV
O PMT
5N
Shift N
I/YR = 12.77% [Yield to Call]
9.) 2 Shift P/yr
1000 FV
860 +/- PV
10 I/YR
10.50 N
Shift N
PMT = 39.08 (This is the semi-annual payment. Since the annual coupon is $78.16, the
coupon rate is [$78.16 / $1000] or 7.816%
10.) 2 Shift P/yr
1000 FV
43.75 PMT [$87.50 / 2 = $43.75]
7.25 I/YR
9 N [10 year bonds issued one year ago. Thus, remaining maturity is 9 years].
Shift N
PV = $1097.91
11.) 2 Shift P/yr
1000 FV
10 N
Shift N
3
47.50 PMT
960 +/- PV [96% of par implies .96 x $1000 = $960]
I/YR = 10.15%
12.) 2 Shift P/yr
1000 FV
10 I/YR
0 PMT
15 N
Shift N
PV = $231.38
2 years later [13 years remaining to maturity] the price of the bond remains the same.
This means that the YTM must have changed to keep the price the same. The new YTM
is:
2 Shift P/yr
1000 FV
0 PMT
13 N
Shift N
231.38 +/- PV
I/YR = 11.58%
The YTM must have increased to 11.58% from 10%.
13.) First, analyze Bond X.
Bond X
1 Shift P/yr
1000 FV
90 PMT
7 I/YR
15 N
PV = $1182.16
14 N (1 year from now remaining maturity is 14 years)
PV = $1174.91
10 N
PV = $1140.47
1N
PV = $1018.69
0N
PV = $1000
Bond Y
1 Shift P/yr
1000 FV
60 PMT
9 I/YR
4
15 N
PV = $758.18
14 N
PV = $766.42
10 N
PV = $807.47
1N
PV = $972.48
0N
PV = $1000
As the bonds get closer to maturity, the price of the bonds will tend to get closer
to the face value of $1000.
14 a.) Since the bond as trading at par, the coupon rate must equal the YTM (Market
Rate/Discount Rate). Thus, coupon rate = YTM = 8%.
b.) The reinvestment rate drops from 8% to 5%. The bond is also not held to maturity
and is sold off after 10 years. The lower reinvestment rates will lower return to the
investor. However, the effect of the lower reinvestment rate will be offset by the higher
price received when the bond is sold off after 10 years. Calculating both these effects we
have:
Year
1
2
3
4
5
6
7
8
9
10
10
CFs
$80
$80
$80
$80
$80
$80
$80
$80
$80
$80
$1373.87
(selling
price of
bond in
year 10 See
explanation
below)
Value of CFs at Yr 10 Assuming Reinv Rate = 10%
FV = $80(1+.05)9 = 124.11
FV = $80(1+.05)8 = 118.20
FV = $80(1+.05)7 = 112.57
FV = $80(1+.05)6 = 107.21
FV = $80(1+.05)5 = 102.10
FV = $80(1+.05)4 = 97.24
FV = $80(1+.05)3 = 92.61
FV = $80(1+.05)2 = 88.20
FV = $80(1+.05)1 = 84.00
FV = $80(1+.05)0 = 80.00
FV = $1373(1+.05)0 = 1373.87
$2380.11
The selling price of $1373.87 can be figured out thus. At year 10, the investor gets the
coupon payment of $80 and then sells off the bond. The selling price of the bond
reflects the PV of its remaining cash flows and can be determined thus:
5
1 Shift P/yr
1000 FV
80 PMT
20 N [Remaining life of a 30 year bond after it is sold off in year 10]
5 I/YR
PV = $1373.87
Realized Yield?
The bond was purchased for $1000 and the value of its coupons plus its selling price
totals $2380.11 at year 10. What is the rate of return (r) on an investment of $1000
which yields $2380.11 in 10 years? This can be computed as:
FV = PV (1 + r)n
$2380.11 = $1000 (1 + r)10
r = 9.06%
1 shift P/yr
1000 +/- PV
2380.11 FV
10 N
I/YR = 9.06%
NOTE: A quick way to get at the $2380.11 is to recognize that the coupons constitute
an annuity. The FV of a fixed payment of $80 for 10 years at 5% is given by:
1 shift P/yr
80 PMT
10 N
5 I/YR
FV = $1006.23
Add the above to the selling price of $1373.87 to get $2380.11
The reinvestment rate is 5% and the YTM is 8%. The realized yield should lie between
5% and 8%. Why is it much higher at 9.06%? The reason is that the bond is not held to
maturity but is sold off before maturity. Had the bond been held to maturity and the
reinvestment rate of 5% had held for 30 years, then the realized yield would have fallen
between 5% and 8%.
15.) This problem compares long maturity bonds with short maturity bonds.
Bond A
FV = $1000
CIR = YTM = 8%
(priced at par)
N = 2 years
Pb=$1000
PB = $1000
6
New Rate=10%
New PB = $965.29
To solve for $965.29 do the following:
1 shift P/yr
1000 FV
80 PMT
2N
10 I/yr
PV => 965.29
% Decrease in value of bond can be computed as:
=>
965.29  1000
1000
=> -3.47%
Thus, the 2 year bond drops in value by 3.47% when interest rates rise by 2%.
Bond B
FV = $1000
CIR=YTM=8%
N=15 Years
PB=$1000
New Rate= 10%
New PB=$847.88
% Decrease:
=>
847.88  1000
1000
= -15.21%
Thus, while the shorter maturity bond (Bond A) declines by only 3.47%, the longer
maturity bond (Bond B) declines by much more (15.21%). This implies that longer term
bonds are more susceptible to interest rate risk as compared to shorter term bonds.
If rates decrease by 2% (rather than increase) then the price of Bond A increases to
$1036.67 while Bond B’s price goes up to $1194.24. The price increase of the longer
1194.24  1000

 19.42% is greater than that of the shorter term bond
1000


term bond 
7
1036.67  1000

 3.67% . Thus, if rates decrease you are better off with a longer

1000

term bond since you experience a sharper price appreciation (see diagram below).
Bond
Prices
Bond B
Bond A
$1000
$965.29
Bond A [S-T Bond]
$847.88
Bond B [L-T Bond]
8%
Yields
10%
(YTM)
16.) This problem compares low coupon bonds with high coupon bonds.
Original
YTM=9%
Bond J (Low Coupon Bond)
Bond K (High Coupon Bond)
FV = 1000, CIR = 4%, N=10 yrs
FV=1000, CIR=10%, N=10 yrs
Original PB = $679.12
Original PB = $1064.18
New PB =$587.75
New PB = $941.11
% change = (941.111064.18)/1064.18
New YTM=11%
% change=(587.75679.12)/679.12
= -11.56%
= -13.45%
New YTM=7%
New PB =$789.29
% change = (789.29-679.12)/
(679.12)
New PB =$1210.71
% change = (1210.71-1064.18) /
(1064.18)
= +16.22%
= + 13.77%
Notice that the low coupon bond (Bond J) is much more price sensitive as compared to
the high coupon bond (Bond K). This is consistent with the principles of duration which
state that low coupon bonds have greater price risk as compared to high coupon bonds.
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17.) The rate of return on the investment can be determined thus:
1 Shift P/yr
1000 FV
100 PMT
1100 +/-PV
10 N
I/YR = 8.48%
Thus, the rate of return you expect to receive on this bond, provided you hold it to
maturity and yields do not change over the life of the bond, is 8.48%
Selling price of bond?
FV = $1000; CIR=10%; PMT=$100, N=8 yrs (2 years later implies N=8year), New
YTM = 8.48%-2.50% = 5.98% (yields are 2% lower). The new price of the bond turns
out to be $1249.83
What is the realized yield on this investment? The details of this investment are as
follows:
Purchase price of bond = $1100
Selling price of bond = $1249.83
Time Horizon (holding period) = 2 years
Two coupon payments of $100 each
1 Shift P/yr
1100 +/- PV
1249.83 FV
100 PMT
2N
I/Yr = 15.41%
Notice that the realized yield is now higher than 8.48% because interest rates have
dropped leading to a higher selling price of the bond.
18 a.) YTM?
1 Shift P/Yr
98.25 +/- PV
100 FV
18 N
8 PMT
I/Yr = 8.19%
Thus, the YTM is 8.19%
b.) Realized Yield?
Time
1
CFs
$8
FV of CFs reinvested at 7.35%
9
2
.
.
.
17
18
$8
.
.
.
$8
$8 + $100
FV  $8(1  0.0735)17  $26.71
FV  $8(1  0.0735)16  $24.88
.
.
.
FV  $108(1  0.0735) 0  $108
__________________________
$381.31
It’s too tedious to compute the FV of each cash flow component. It’s simpler to recognize
that we are dealing with an annuity of $8m for 18 years invested at a yield of 7.35%. The
FV of this annuity is:
1 Shift P/yr
8 PMT
18 N
7.35 I/yr
FV = 281.31
Thus, the 18 annuity payments of $8 invested at 7.35% sum to $281.31. To this add the
principal of $100 at year 18. Thus, the FV of all cash flows sum to $381.31.
The realized yield can then be computed thus:
Purchase price of bond = $98.25
Compounded value of coupons and principal at Year 18 = $381.31
Time horizon of Investment = 18 years
1 Shift P/yr
98.25 +/- PV
381.31 FV
18 N
I/YR = 7.82%
Thus, the realized yield is 7.82%
c.) The relationship between the YTM, realized yield and reinvestment rate is as follows:
YTM = 8.19%
Reinvestment Rate = 7.35%
The realized yield of 7.82% lies between the YTM and the reinvestment rate. Note that
this will be true only if the bond is held to maturity.
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