Question

Can you please provide a solution all the information is as under:-

Treasury Bonds Term-structure of Interest Rates Code Coupon Maturity (years) Face value Maturity (years) Zero-Coupon Yields Coupon Payment Bond Price

Treasury Bonds					Term-structure of Interest Rates
Code	Coupon	Maturity (years)	Face value		Maturity (years)	Zero-Coupon Yields	Coupon Payment		Bond Price
GSBS18	3.25%	0.50	100		0.5	1.860%	1.625		$100.6929
GSBE19	5.25%	1.00	100		1.0	1.870%	2.625		$103.3421
GSBS19	2.75%	1.50	100		1.5	1.945%	1.375		$101.1998
GSBG20	4.50%	2.00	100		2.0	2.005%	2.25		$104.8939

Suppose there is a zero-coupon bond (ZCB) with a face value of $100 and 2 years to maturity, which currently trades at $95. Construct an arbitrage portfolio by trading in the ZCB and also in the first four treasury bonds to show how you can make an arbitrage profit. You need to indicate your portfolio in terms of weights and dollar amounts of the bonds and explain your answer.

Answer 1

In this que, we need to understand that what is yield in Zero coupon bond. Here is the calculation

Category	Values
PMT	0
PV	95
FV	100
N	2
Rate	2.5978%

(Use Rate formula in excel)

Since all the yeild rates in table (given) are less than yeild from ZCB. Hence to create arbitrage profit, you should buy ZCB and sell any on the bond given in table.

It would make more snese to sell the bond where maturity on the bond bought and sold are same. so we will sell GSBS20 and buy ZCB.

By selling GSBG20, we will recieve a cash which can be used to buy ZCB. Yeild we ean from ZCB would be used to pay the yield and since yield of ZCB is higher, we will end up saving good profit.

Now we need to understand how many bonds we need to buy or sell.

This can be identified by deviding the curren prices of bonds

=104.8939/95

=1.104

So for every 1 GSBG20 sold, we should purchanse 1.104 ZCB.

By this method, lets assume we are selling 100 bonds of GSBG20, which would mean we buy 110 ZCB 9since bonds can be bough/sold in whole number)

Portfolio weights should be

ZCB - 110/210 = 52.38%

GSBG20 = 47.62%

No of bonds	Price of bond	Value of bond - Buy/sell
100	104.8939	10489.39
110	95	10450