Question

Consider a one-year maturity, $100,000 face value bond that pays a 6 percent fixed coupon annually. If the bond is selling at par, what is the percentage price change for the bond if interest rates increase 50 basis points from 6 percent

Answer 1

Answer:

7.7% of price change for the bond if interest rate increases.

Explanation:

When the bond is selling at par, the yield of the bond is same as the coupon rate of the bond. So the increase in the interest is the the increase in the yield with same value.

50 basis point means 0.5% ( 50/ 100 ), Increase in the 50 basis point from six percent means the interest will increase by 0.5% to 6.5%

Percentage of price change = Change in price / initial interest rate

Percentage of price change = 0.5% / 6.5% = 0.077 = 7.7% change

Answer 2

Answer:

The price decrease by 0.469%

We determiante the new market value of the bond:

In one year we are going to receive:

100,000 maturity

and 6,000 interest

We discount this at 6.50% (6% plus 50 points which means half of a percentage) to get the present value

$\frac{Maturity}{(1 + rate)^{time} } = PV$  

Maturity  $106,000.00

time  1.00

rate  0.06500

$\frac{106000}{(1 + 0.065)^{1} } = PV$  

PV   99,530.5164

at par it would sale at 100,000

now it is being sold at 99,530.5164

Now, we divide each term:

99,53.5134 - 100,000 / 100,000 =

-469.4836 / 100,000 =  -0.00469  

The price decrease by 0.469 percent