Question

Consider price quotes and characteristics for two different bonds:

	Bond A	Bond B
Par Value	$100	$100
Coupon Payment	Annual	Annual
Maturity	3 years	3 years
Coupon Rate	9%	5%
Yield to Maturity	10.75%	10.85%
Price	$95.70	$85.67

At the same time, you observe the spot rates for the next three years:

Term	Spot (Zero-Coupon) Rates
1 year	4%
2 years	7%
3 years	10%

Demonstrate whether the price for either of these bonds is consistent with the quoted spot rates. Under these conditions, recommend whether Bond A or Bond B appears to be the better purchase. Do not round intermediate calculations. Round your answers to the nearest cent.

The non-arbitrage price of Bond A: $____

The non-arbitrage price of Bond B: $____

____ appears to be the better purchase.

Answer 1

The price of a bond is given by the sum of future cash flows discounted at the YTM. This price should be the same if the cash flows are discounted at the given respective spot rates. The cash flows comprise of coupon payments and par value, at maturity.

Bond A: Coupon = 9%*100 = 8

Non-arbitrage price of A = 9/(1+4%) + (9/(1+7%)^2) + ((100+9)/(1+10%)^3) = 98.41

This is different from the quoted price of 95.70 so there is an arbitrage opportunity here.

Non-arbitrage price - quoted price = 98.41 - 95.70 = 2.71

Bond B: Coupon = 5%*100 = 5

Non-arbitrage price of B = 5/(1+4%) + (5/(1+7%)^2) + ((100+5)/(1+10%)^3) = 88.06

In this case also, the price is different from the quoted price of 85.67 so there is an arbitrage opportunity here.

Non-arbitrage price - quoted price = 88.06 -85.67 = 2.39

Bond A is a better purchase because it is more undervalued than Bond B so margin of profit is more whenever the market corrects to its non-arbitrage price.