Question

Below are hypothetical prices and maturities of STRIPs, which are zero-coupon bonds that pay $100 at maturity. The prices are quoted in 32nds. Maturity Price 3 months 98:20 9 months 95:19 (a) (b) Calculate annualized bond-equivalent yields for each STRIP. (4 marks) Imagine that there is a Treasury coupon bond, issued 9 14 years ago, that matures in nine months. The coupon is 82 percent, paid semiannually. What price should the bond have to be consistent with the STRIPs prices above? (Calculate the total price, including accrued interest.) (6 marks)

Answer 1

(a) Calculation of Annualized Bond-equivalent yields for each STRIP.

Generally, Zero-Coupon Bonds (Strip Bonds) have shorter durations so we have to apply Bond Equivalent Yield formula to determine what Zero-Coupon Bonds would pay annually and it also helps us in comparison with Traditional Bonds to make an informed decision.

Step - 1: Calculate the price of the Bonds.

Here prices are quoted in 32nds. So, we have first to convert them into a percentage to determine the dollar amount required to be paid to purchase a bond.

For, Bond with 3 months maturity price is 98:20. Here, 98 is called "Handle" and 32nds are 20. So, we divide 20 by 32 which is 0.625 and we add this amount to the Handle which is 98.625. So, 98:20 is equal to 98.625%.

So, Price of Bond with 3 months maturity is $ 98.625 ($100*98.625%)

The same way we calculate Price of Bond with 9 Months maturity = 19/32 =0.59375+95 =95.59375% =$ 95.59375.

Step - 2: Calculate the annualized bond equivalent yield.

Formula = (Return on Bonds/Purchase Price of Bonds)*100*(12/Maturity Period in months)

So basically we are calculating simple return on bonds and by multiplying it with (12/Maturity Period in months) we are calculating annual return so that we can compare returns of bonds and make an informed decision.

Now, For the Strip bond with 3 Months Maturity,

Annualized bond equivalent yield = (($100-$98.625)/$98.625) * 100 * (12/3) = 5.576%

Now, For the Strip bond with 9 Months Maturity,

Annualized bond equivalent yield = (($100-$95.59375)/$95.59375 *100 * (12/9) = 6.146%

(b) Calculation of the price of the Treasury Coupon Bond which is Consistent with the prices of above Two Strips.

Now, Treasury Coupon Bond is required to be consistent with the Strips. For that, the return of both Treasury Coupon Bond and Strips must be the same.

Further, whenever the maturity price is not given, it assumed that bonds are matured at par. So, here we assume that Treasury Coupon Bonds will mature at par i.e. $ 100.

So, Price (including Accrued Interest) of Treasury Coupon Bond which in Consistent with Strip Bond with 3 Months Maturity can be calculated as under:

5.576% = (($100-Price of Treasury Coupon Bond)/Price of Treasury Coupon Bond) * 100 * (12/9)

Solving the above equation, we will get the price of the Treasury Coupon Bond= $ 104.24 (including accrued interest) which is consistent with Strip Bond with three months maturity.

So, Price (including Accrued Interest) of Treasury Coupon Bond which in Consistent with Strip Bond with 9 Months Maturity can be calculated as under:

6.146% = (($100-Price of Treasury Coupon Bond)/Price of Treasury Coupon Bond) * 100 * (12/9)

Solving the above equation, we will get the price of the Treasury Coupon Bond= $ 103.83 (including accrued interest) which is consistent with Strip Bond with 9 months maturity.