Question

Debt & Bonds

1. The table below presents the spot rates an investor faces.

Year	Spot Rate
1	2%
2	3%
3	4%
4	5%

Assume that, for each maturity, there is a zero-coupon bond traded in the market. These zeros pay $1,000 at their respective maturity.

a. Is the term structure positive, inverted, or flat?

b. What is the forward rate from t=1 to t=2?

c. Suppose that the investor is expecting to receive $1 million at t=1. This is a future cash inflow. He is planning to do the following investment strategy for this future cash inflow. He will borrow $980392.16 (this is $1 million / (1+2%)) now, and use this borrowing to buy a two-year zero. At t=1, the one-year zero matures, and he will make the payment to the one-year zero lenders. At t=2, the two-year zero matures, and he will receive the payment from the two-year zero. Fill the below cash flow table (the unit is $1 million).

	t=0	t=1	t=2
One-year zero	${\color{Red} \frac{1}{1+0.02}}$
Two-year zero	${\color{Red} -\frac{1}{1+0.02}}$
Others (The $1 million that the investor is expecting to receive at t=1)	0	1	0
Total	0

d. What is the net return that this investor will get from his $1 million future cash flow from t=1 to t=2? Compare it with the forward and comment on what you find.

2. Suppose that we have two Treasury securities traded in the market, and we need to use them to calculate the theoretical spot rates. The first Treasury is a one-year zero, which pays $1,000 at t=1, and the current price is $950. The second Treasury is a two-year maturity, 5% coupon bond, and its current price is $900. The par value of the second Treasury is $1,000. Calculate the one-year spot rate and two-year spot rate, assuming that coupon payments are annual.

3. The table below presents the spot rates an investor faces.

Year	Spot Rate
1	2%
2	3%
3	4%
4	5%

a. What is the price of a two-year maturity 5% annual coupon bond? Par value is $1,000. What is its YTM?

b. What is the price of a two-year maturity 10% annual coupon bond? Par value is $1,000. What is its YTM?

Answer 1

1 (a)  

Чея shot Rate 2 ). 3 % 4% 5% 4 for each maturity there is ZCB, o to plat on graph we get Yield Curve or term structure of bond ie Yield Curve पर o spot 3 į s naxis 0 Term structure es positive,

1 (b)

1 6 forward rate will be Itta = Bigger factor Ilgar - 1 smaller factor) fue = [(1 + ros) 27 -1 from @ 802= 3% La trol)' 801 = 2% 14+ 0.03) - Ito.o2 = 11.06097 -1 = 100401–1 = Ooyo 100 T 1002 J - 4 % AD

1(c)

1 © Innestor w planning a investment Strategy :- w Borrow amount & 980392 016 at t=0 entflow ofter 2 years Intion Invest in a year a CB at t=0 = $980392.16 Now at tale one year z CB matures he will make payment = $ 1 million Nowat t=2 1 two year 2 6 metures and he will recine $ 1 million Cash Flow Table tell t =2 to (980392.16) 980392.16 R Borrow . guest Receine Payment Receined million (1 million) wo million o d ova million

2

Calculation of shot Rates: - Bond Maturity / Couson Rete Price face value 1000 900 000 One year spot rate Bond ist toto spot rete of z cB is 4TM YiM = In Face Value By RO 100 ". I 950 10526 -! = 0.05 26 = 5.26 %. two year shot date Bondan go0oR 1 1050 (100D + 5°). 1000 Shar 900 = 50 + 1050 105261 + roz) = Too & 47.50 + 1050 (1+roz) 2 852.5 = logo (1+roz) hoz ž (loso 1852.5 ½-1 ro2 = (1023167155/21 = 101098-1 = Vol098 rate = 10098 % An Shot

  

3(a)

Strata four Values Coupon Pete on 5% so + OSD 10-20% PS_1 D ISTO I+ 0.02) +0.02) (1 + 0.03) 999.7257 = 49.0196 1 Bice 1032.75 YTME I + F-P Sot 1000 - 1038.7 30625xlub 1519.375 1000 + 1038.75 2 = 2:015%

3(b)

3 year shot 21. 3% 4 a 1000 fore vale Coupon = ns2 10% = Ow Ισυ δε, - ν tor-3 % P= 100 1100 1 1.02 (1003)2 = 98.04 + 1036.85 Price = 1134.90 YTM = 100 + 1000 - 1134.90 2 1000 + 1134 075 de 2 - 32.55 x100 1567.375 YTM = 2008%