Question

GIC’s (Guaranteed Investment Contracts) are often issued by the insurance companies and are widely used by individuals saving for their retirement. A GIC is essentially a zero-coupon bond (recall that in the U.S. the Zeroes are treated as semi-annuals) that pays a predetermined sum of money at its maturity. For instance, a three-year GIC carrying a guaranteed interest rate of 10% and a price of $10,000, will pay $13,400 at maturity. Therefore, the issuer knows in advance, that in three years, they will need $13,400 to cover that future obligation. Insurance companies often fund such future obligations by buying par-value coupon bonds and reinvesting the coupon payments, as they are received, at the then-prevailing interest rates.

1. Assume that the market interest rates remain at the current level of 10% for the next 3 years and assume that the issuer of the GIC referred to above, uses the $10,000 received to purchase a 5-yer, par-value coupon bond. Calculate the future values of the coupon payments and the proceeds from the sales of the bond at the end of the third year to show how this obligation-matching strategy works.
2. Now assume that the market interest rates change to 12% and calculate the impact on the re-invested coupons and the market value of the bond at the end of three- year period. What do you conclude?

Answer 1

a) For a coupon bond to sell at par value, the coupon rate should be the same as the discount rate i.e. 10% compounded semiannually

Now, the issuer purchases 10% coupon bond at $10000 which pays $500 coupon amount at the end of each of thesix-month periods and amount got by selling the bond at the end of 6 periods (4 coupons remaining)

Six month rate (1 period ) = 10%/2 =5%

Now, the coupons' (1st one received six-months from now and reinvested for 5 six-month periods) future value will be

= 500*1.05^5+ 500*1.05^4 + .... + 500

=500/0.05*(1.05^6-1)

=$3400.96  

Value of bond at the end of 3 years

= 500/1.05+500/1.05^2+..+500/1.05^4+10000/1.05^4 = 500/0.05*(1-1/1.05^4)+10000/1.05^4= $10000

So, the final amount available with the Issuer = $10000 + $3400.96 =$13400.96

Obligation to redeem GIC = 10000*1.05^6 = $13400.96

Thus the obligation and the Future value  of proceeds from Investment matches

b) If after purchase of coupon bond market interest rates increase to 12%, the coupons are reinvested at 12% (6% every 6 months)

So, Future value of coupons

= 500/0.06*(1.06^6-1)

=$3487.66

Value of bond at the end of 3 years

= 500/1.06+500/1.06^2+..+500/1.06^4+10000/1.06^4 = 500/0.06*(1-1/1.06^4)+10000/1.06^4= $9653.49

So, final amount available with the Issuer = $9653.49+ $3487.66 =$13141.15

Obligation to redeem GIC = 10000*1.05^6 = $13400.96

Thus the obligation and the Future value  of proceeds from Investment do not match

Thus, in this case, obligation is more than the Future value  of proceeds from Investment and the Issuer loses by an amount of $259.81 at the end of 3 years

Thus, it can be concluded that with the increased interest rates, the coupons could be reinvested at a higher rate but, the price of the bond also gets reduced much more creating an overall loss.

In this case, to match , a bond with a duration of 3 years (same as duration of GIC obligation) must be chosen to completely hedge and match the obligation with proceeds of investment.