Question

5. The dollar return for a semiannual bond with the following characteristics assuming that you can earn the same yield on a 9-year certificate of deposit are:

Coupon rate

Time to maturity

Price

YTM (BEY)

6.10%

9 years

$109.79

4.75%

a. Calculate the realized rate of return for the buy and hold investor if market interest rates increase by 50 basis points after purchase and before the first coupon payment.

b. Calculate the realized rate of return of the investor who sells the bond after 5 years, but interest rates decrease by 50 basis point after purchase and before the first coupon payment.

Please help me solve this! please show equations used

Answer 1

First we have to find out the face value of the semiannual bond. In order to find out the same, the following formula is used:

YTM =

Where, YTM = 4.75% / 2 = 2.375% = 0.02375

Current price = $109.79

or, YTM + 1 =

or, 0.02375 + 1 =

or, 1.02375 =

or, 1.02375 / 0.77026 =

or, 1.3291 =

or, (1.3291)¹⁸ = Face Value

or, Face Value = $167.51

a. A 50 basis points increase in market interest rate means 0.50% increase in the coupon rate. Therefore the interest rate becomes 6.10% + 0.50% = 6.60%.

In order to find out the rate of return, the following formula is used:

Rate of return =

Interest = 6.60% of $167.51 = $11.06

So, Rate of Return =

= (-46.66 / 167.51 ) * 100

= -27.86%

b. A decrease of 50 basis point means 0.50% decrease in market rates. So, coupon rate becomes, 6.10% - 0.50% = 5.60%.

Here, interest will be = 5.60% of $167.51 = $9.38

By applying the same formula above, Rate of return =

= (-48.34 / 167.51) * 100

= -28.86%