Question

Alpha Insurance has investment horizon of 3 years. If it invests in a 5 year, 6% annual coupon bond with YTM of 8%, what will be its realized rate of return

1. If interest rates don’t change
2. If interest rate increases by 100 bps immediately after buying the bond
3. If interest rate decreases by 100 bps immediately after buying the bond
4. Is the difference between (a) and (b) the same as the difference between (a) and (c)? why or why not?

Answer 1

Buying price of the bond:

Let us assume that the face value of the bond is $100.

Coupon payment = Face value * Coupon rate = $100 * 6.00% = $6.00

Function "PV" will be used in excel to calculate the buying price of the bond:

Buying price = $92.01

Answer a)

Investment holding period = 3 years

Time to maturity after 3 years = 5 years - 3 years = 2 years

Sale proceeds from the bond after 3 years will be calculated by using the function "PV":

Sale proceeds = $96.43

Coupon payments in 3 years = $6.00 * 3 = $18.00

Realized rate of return = (Sale proceeds + Coupon payments - Buying price) / Buying price

= ($96.43 + $18.00 - $92.01) / $92.01

= 24.37%

Answer b)

100 basis points = 1.00%

New yield = 8.00% + 1.00% = 9.00%

Sale proceeds:

Sale proceeds = $94.72

Coupon payments in 3 years = $6.00 * 3 = $18.00

Realized rate of return = ($94.72 + $18.00 - $92.01) / $92.01

= 22.51%

Answer c)

New yield = 8.00% - 1.00% = 7.00%

Sale proceeds:

Sale proceeds = $98.19

Coupon payments in 3 years = $6.00 * 3 = $18.00

Realized rate of return = ($98.19 + $18.00 - $92.01) / $92.01

= 26.28%

Answer d)

Differnece between the realized rate of return of part (a) and part (b) = 24.37% - 22.51% = 1.86%

Differnece between the realized rate of return of part (a) and part (c) = 26.28% - 24.37% = 1.91%

No, the difference between (a) and (b) is not same as the difference between (a) and (c). The reason for this is that the change in price in all three parts are symmetrical in nature, but the coupon payments remain the same in all three cases; therefore, the change in the realized rate of return is not symmetrical.