Summary MA270 - Financial Math WEBWORK 2 Q&A

Dhari Gandhi MA270 W21
Assignment WebWork 2 due 02/02/2021 at 11:59pm EST



• 2.9
1. (1 point) • 0.024*100
Consider a 2-year $2500 par value bond that pays semi-annual • 0.034*100
coupons at a rate of c(2) = 8 • 0.0145*2*100
• 2746.02-2748.93
(a) Use the method of averages to approximate the effective • 0.024*100
• 0.0145*2*100
yield rate compounded semi-annually. State the result as a per-
• 0.01325*2*100
cent to 1 decimal place. • 2758.86854575-2748.93
• 0.01325*2*100
y(2) ⇡ • 0.0145*2*100
• 0.013875*2*100
(b) Complete the chart below by performing 2 iterations of • 2752.43-2748.93
the bisection method to approximate the effective yield rate • 0.0141875*2*100
compounded semi-annually. (correct)
[Note: For the initial interval [a(0), b(0)] use the percent- Correct Answers:
age result y(2) in part (a) as follows: a(0) = y(2) 0.5 and • 2.9
b(0) = y(2) + 0.5 .] • 2.4
• 3.4
• 2.9
• -2.91233
• 2.4
• 2.9
n • 2.65
a(n) (as a 0 • 9.938546
• 2.65
• 2.9
• 2.775
• 3.503391
• 2.8375
1
2. (1 point)
Consider a bond that pays a semi-annual coupon of 13

(a) Use the method of averages to approximate the bond’s yield.
2 Express your answer as a percent, to nearest basis point.



(b) Estimate the bond’s price, and the derivative of price with
respect to (per-period) yield, using the rounded result from part
(a). Express your answers in dollars, to the nearest cent. Note
that you may have to divide your answer from (a) by the com-
(c) Use the last line in the table above to find the bracket pounding frequency, before you plug it into the appropriate
[a(3), b(3)] and the midpoint c(3) to approximate the effective formula.
yield rate compounded semi-annually. State the final result as a
percent to 4 decimal places. Price = $

y(2) ⇡ c(3) = Derivative of Price = $

(c) Use the rounded results in parts (a) and (b) to complete
Answer(s) submitted: 1 iteration of Newton’s method to approximate the bond’s yield.
1

, Express your answer as a percent, to the nearest basis point. • 1.83
• 84.22
• 930.17
• 4635.21

4. (1 point)
Answer(s) submitted: A 6-month zero coupon bond with a face value of $100 is trad-
• 2.9297 ing at $99.03. A 12-month zero coupon bond with a face value
• 2388.10 of $400 is trading at $390.96. An 18-month coupon bond, pay-
• 752143.62
ing a semi-annual coupon of 5 i. Compounded semi-annually '
• 2.93 25
on a fu of $5000 , is
trading at $5178 .
.




(score 0.5)
Correct Answers: (a) What is the yield on the 6-month zero-coupon bond? Ex-
• 2.93 press your answer as a percent, to the nearest basis point.
• 2388.10
•
•
-23587.43
2.86
Yield =
1.94%
ytpq-lnCFIBI.tn (100/99.03)
642
-



( )
3. (1 point) = 1.94%
The continuously compounded yield curve is y(T ) = 0.05 (b) What is the yield on the 12-month zero-coupon bond?
0.035e 0.4T . Express your answer as a percent, to the nearest basis point.

Yield = 2.29% yqoy = Inf 4001390.96 ) = 2.29%
(a) What is the yield on a zero-coupon bond that matures in 3 1-
months? Express your answer as a percent, to the nearest basis
(c) What should the yield on an 18-month zero-coupon bond
y( 3421=0.05-0.03580-4%4
point.
be? Express your answer as a percent, to the nearest basis point.
1.83%
Yield = $125.00
Yield = 2.5Gt iv. ( sooo =
1.83%
.

. =
=

0.510.01941
(b) Determine the price of a zero coupon bond that matures 5178-25=12 g. e- t
in 4 years and has face value is $100. Express your answer in Answer(s) submitted:
dollars, to the nearest cent. • 1.94 -
9- ( 0.02929 )
125 @
YT • 2.29 +


Price = $ 84-22 D= f- e- 0.0183141 • 2.56 1842 ( Y )
e- g , zg e-
=
, (correct)
= 84.22 Correct Answers:
(c) Consider cash flows [ C1 , C2 , C3 ] = [ $350, $250, $450] 0.0256
y
-



• 1.95
'
-

.
.




to be received at times [ T1 , T2 , T3 ] = [ 1.5, 3, 4.25] (in years). • 2.29
Determine the present value of the cash flow stream. Express • 2.56 y
-

-
2. SGT .




your answer in dollars, to the nearest cent. 5. (1 point) Lo LI
Consider the Nelson-Siegel yield curve y(T ) = 0.085 0.06 ·
Present Value = $ 1 e 0.9T
4.2T
. LR Lo
-




+2508
-
's
rysoe
pV=3SOE 0.9T
LR SR =L ,
(d) Consider a 2-year bond that pays a semi-annual coupon
-




0¥ of 5 % (a) What is the long rate? Express your answer as a percent,
to the nearest basis point.
"'


q
Price = $
Answer(s) submitted:
(
It
I = @ Yield = g. Sy . Lr
-10=0.085--8.5-1
• 1.83 .


•
• 84.22 = 0.01838
• 930.17 i.
y, (b) What is the short rate? Express your answer as a percent,
• 4635.20 to the nearest basis point.
(correct)
ftp.zos-0-0838/An.y )
2.5 " SR -_ di
Correct Answers: Yield = LR
:p 4S
-


a
-
2
8. S
-
SR
=
G
D=
SR
= 2.5%