Bond Futures Price/Reinvested Coupons

CFA Level II Derivatives
#1

I’m having trouble reconciling two examples in the CFAI text covering bond futures pricing.

Specifically, in the blue box problem on page 109, the following rates are provided in the problem:

  • 7.5% annual yield on the bond

  • 8% coupon on the bond

  • Reinvestment rate of 3.75% (1/2 of the 7.5% annual yield)

  • 7% one-year risk-free rate

To determine the future value of the coupon payments, the solution provided compounds the coupon payments at the reinvestment rate of 3.75% (again, one-half of the 7.5% annual yield). Then, the arbitrage-free price of the bond is determined by compounding the current price of the bond at the risk-free rate.

So far, so good.

However, back on page 107, the text provides another example with a similar fact set (7% coupon, 8% yield, 6.5% risk-free rate). In this example, though, the text determines the future value of the coupon payments based on the 6.5% risk-free rate - NOT one-half of the 8% yield to maturity.

To me, it would make sense to determine the future value of the coupon payments based on the assumed reinvestment rate (which is based on the YTM) - NOT based on the risk-free rate (i.e. it seems to me that the blue box problem is correct).

I’m sure there’s some distinction here that I’m missing but wanted to pose it to the group to see if anyone has any insights.

Thanks so much.

#2

The BB example on page 109 gives the coupon reinvestment rate of 3.75 as part of question A. “Assume a reinvestment rate of 3.75 percent per six-month period.”

Without that assumption, the correct rate for compouding the dividends is the risk free rate as explained on page 107.