The 6-month Treasury rate is 5% p.a. The 12-month Treasury rate is 6% p.a. Both rates are semi-annual compounding. Consider a 20-year floating rate bond (FRB), face value $1,000, issued by a risk-free borrower, paying a floating rate equal to the 6-month Treasury rate.(Hint: think of a FRB with semi-annual coupons as equivalent to a 6-month T-bill delivering a cash flow at maturity given by face value + coupon)
(a) Determine its modified duration and convexity at t=0.
(b) What is the approximate change in price (in percentage terms, and in dollars) of the 20-year FRB above, given a 150 basis point increase in the 6-month treasury rate?