Question

1. Relationship between YTM and price

(a) Calculate the price of each bond and fill up the blank cells in the following table (3 points) –

Maturity	PMT	Face value	YTM	Price
10	100	1000	20%
10	100	1000	18%
10	100	1000	16%
10	100	1000	14%
10	100	1000	12%
10	100	1000	10%
10	100	1000	8%
10	100	1000	6%
10	100	1000	4%

(b) Based on above table, draw a graph with horizontal axis showing the YTM and vertical axis showing prices. Show the graph below. (3 points)

(c) Explain intuitively why we do see a negative relationship between YTM and bond prices. (3 points)

Answer 1

a]

Price of a bond is the present value of its cash flows. The cash flows are the coupon payments and the face value receivable on maturity

Price of bond is calculated using PV function in Excel :

rate = (YTM of bond)

nper = (Years remaining until maturity)

pmt = -(annual coupon payment)

fv =   -(face value receivable on maturity)

b]

c]

There is a negative relationship between YTM and bond prices because :

If the interest rates rise, it means that the required return has increased. To make the required return of the bond equal to the market interest rate, the bond price must fall, so that the investor's return increases.

Similarly, if the interest rates fall, it means that the required return has decreased. To make the required return of the bond equal to the market interest rate, the bond price must rise, so that the investor's return decreases.