Inputs
Answer
1) a Treasury bills
2) e Negatively Related
YTM- yield to maturity
Bond A Bond B
Par Value $ 1,000.00 Par Value $ 1,000.00
interest Annually $ 120.00 interest Annually $ 120.00
Before YTM 12% Before YTM 12%
After YTM 10% After YTM 10%
Mature Years 5 Mature Years 6
Bond A Bond B
Bond A Increases in Value Bond B Increases in Value
Bond B has more change 3) A
Logic:
If yield to maturity drops, bonds increase in value and the longer duration bond will change higher as we
ond will change higher as well
Bond F Bond G
Par Value 1000 Par Value 1000
Interest 90 Interest 90
Before YTM 9% Before YTM 9%
After YTM 10% After YTM 10%
Mature Year 15 Mature Year 26
Bond F Bond G
Bond F decreases in value Bond F decreases in value
4) E
more change in bond G
Inflatiion
in year
just
Time ended Par Value Coupon Payment Principle payment
0 $ 1,000.00
1 1% $ 1,010.00 $ 40.40 $ -
2 2% $ 1,025.15 $ 41.01 $ -
3 3% $ 1,050.78 $ 42.03 $ 1,050.78
Second Year Third Year
Nominal Return 5.56% 6.60%
Real Return 4% 4%
Possible Alternate Way:
Coupon rate is real rate of return, so 8% for both
Use fishere equation to find nominal returns.
total Payment coupon rate 4%
$ 40.40
$ 41.01
$ 1,092.81
key 5%
Year 2
FV/ Par Value $ 1,000.00
PV $ 1,000.00
Coupon Payment $ 120.00
YTM 12.0%
r Proceeds Realized YTM
7% $ 1,248.40 11.73%
9% $ 1,250.80 11.84%
11% $ 1,253.20 11.95%
YTM CHECK
12.0% $ 1,254.40 12.00%
YTM correct
7E
8B
1 Year zero Coupon bond
YTM Year 1 7.50%
Government of Canada
Year 2
Coupon Rate 10.0%
FV $ 100.00
Coupon Payment $ 10.00
a) $102.74
b) 8.453%
c) forward rate f2 9.509%
Price year 1 $ 100.45
d) Liquidity Premium 1.50%
Forward Rate 2 9.51%
Expected return Year 2 8.0%
Price $ 101.84
2- Year zero coupon bond
YTM Year 2 8.50%
(1+fn)=(1+yn )n)/(1+yn-1)n+1
Forward Rate n = (pricen-1)/ (pricen -1)
priceN+1/(1+E(r2)) = priceN
-$99.08
Maturity Years YTM
1 10.50%
2 11.50%
3 12.50%
Face Value $ 1,000.00
A) Maturity Forward Rate
1 Year 10.50%
2 years 12.51%
3 years 14.53%
B) Next Year . PV YEAR 1
2 YEAR BOND
PV next year $ 888.82
2-year bond 12.51%
the slope shifts upwards, as the yield curive is increasing and upward sloping. Shifts upwards a
C) PV=FV/(1+r)n
PV of first year bond PV of second year bond
$ 904.98 $ 804.36
Next year, two year coupon bond is a one year bond and sell for:
E(r) Two year bond in one year 10.50%
E(r) Three year bond in one year 10.50%
D) coupon rate 10%
Coupon Payment $ 100.00
PV $ 943.50
Expected price 1 year $ 942.57
Total Expected Return 10.50%
(1+fn)=(1+yn)n/[(1+fn-1)*(1+fn-2)*…]
Price= FV/(1+forward rate)1*(1+forward rate)2
3 Year Bond
PV next year $ 776.08
3-year bond 13.51%
ing and upward sloping. Shifts upwards according to hypothetis.
PV of third year bond
$ 702.33 $ 2,411.67
and sell for:
943.49885823
942.56623834
0
Maturity (Years) Price YTM Forward Rate
1 $ 940.93 6.28%
2 $ 868.39 7.31% 8.35%
3 $ 800.92 7.68% 8.42%
4 $ 735.40 7.99% 8.91%
5 $ 670.48 8.32% 9.68%
A) 1.1945 price of 3 year bond/ price 5 year b
B) Time Cashflow
0 0 Nocashflow
3 $1,000.00 Buyer, positve cashflow
5 -$1,194.55 -$ 1,194.55 Selling, negative cashflow
C) 2-year Interest rate 19.45%
D) Check method 19.45%
19.45%
Coupon Rate 0%
Forward Rate FV 1000
(1+fn)=(1+yn )n)/(1+yn-1)n+1
year bond/ price 5 year bond= how many times bond 5 is neet
sitve cashflow
egative cashflow
Duration- measure of price sensativity 12
Effects:
Coupon Rate
Time to maturity
E
13 D
Semi Annual bond
Coupon Rate 4.40%
Years 3
A) YTM 8.00%
B) YTM 7.0%
FV 100
8 Years
8 Year duration Graph
Time Cashflow PV of CF dscounted 3% Weight
1 $ 2.20 $ 2.115 0.023358
2 $ 2.20 $ 2.034 0.022459
3 $ 2.20 $ 1.956 0.021596
4 $ 2.20 $ 1.881 0.020765
5 $ 2.20 $ 1.808 0.019966
6 $ 102.20 $ 80.770 0.891856
Sums $ 90.564 1
Duration for half years $ 5.66709
A) Duration 8% YTM $ 2.8335
Duration Time Cashflow PV of CF dscounted 5%
$ 0.02336 1 $ 2.20 $ 2.13
$ 0.04492 2 $ 2.20 $ 2.05
$ 0.06479 3 $ 2.20 $ 1.98
$ 0.08306 4 $ 2.20 $ 1.92
$ 0.09983 5 $ 2.20 $ 1.85
$ 5.35113 6 $ 102.20 $ 83.14
$ 5.66709 Sums $ 93.07
Duration of Half years 5.672489
B) Duration 10% YTM 2.8362
FV 100
Weight Duration
0.022838 0.022838
0.022066 0.044132
0.02132 0.063959
0.020599 0.082394
0.019902 0.09951
0.893276 5.359656
1 5.672489
2 Year duration Graph 6% Yield $92
Coupon Payment $ 9,600.00 Time Until Payment (Years) Cashflow
FV $ - 1 $ 9,600.00
Time 2 2 $ 9,600.00
YTM 8% Sums
PV $17,119.34
A) PV $ 17,119.34
Duration 1.4808
B) A zero coupon bond maturing in 1.4808
Duration 1.4808
FV $19,185.80
C) Bond increase/decrease 10%
PV of bond $16,660.46
PV of tuition $ 16,661.16
Net Position decrease
D) Bond increase/decrease 7%
PV bond $17,356.79
PV of tuition $17,356.97
Net Position decrease
ration Graph 6% Yield $9200 PMT
Discout CF at 8% Weight Duration
$ 8,888.89 0.51923077 0.519231
$ 8,230.45 0.48076923 0.961538
$ 17,119.34 1 1.480769
years immunizes obligation
in value by $ 0.70
in value by $0.19
Year 30 YTM
Coupon Rate 8.50% 10.60%
Duration 18.23 11.60%
Convexity 199.2 12.60%
YTM 11.60%
FV 1000
aaa
$811.53 A) YTM of 10.4% $811.53
$742.69 YTM of 12.4% $683.86
$683.86
B) Maturity Falls 10.4%
Duration Rule
Predicted Price Change $121.32
Predicted New Price $864.01
Duration-with-convexity Rule
Predicted Price Change $128.72
Predicted New Price $871.41
Maturity Raises 12.4%
Duration Rule
Predicted Price Change $121.32
Predicted New Price $621.37
Duration-with-convexity Rule
Predicted Price Change -$113.92
Predicted New Price $628.77
Duration Rule Duration- with-
Convexity Rule
YTM Falls to 10.4% $864.01 $871.41
YTM Increases to 12.4% $621.37 $628.77
Duration-with-
c) Duration Rule convexity Rule
Percent Error for 10.4% YTM 6.47% 7.38%
Percent Error for 12.4% YTM -9.14% -8.06%
d) The duaration-with-convexity rule provides more accurate approximations to the true chan
in price.
error 6.47%
error 7.378%
error -9.137%
error -8.056%
proximations to the true change
