The two year zero rate is 4.00% and the three year zero rate is 4.30%, both annually compounded. Compute the one year forward rate starting in two years, and describe a position that expresses the view that the forward is too high.

The two year zero rate is 4.00% and the three year zero rate is 4.30%, both annually compounded. Compute the one year forward rate starting in two years, and describe a position that expresses the view that the forward is too high.

Approach: Set a two year investment rolled at the forward equal to a three year investment, solve for the forward, then think about which pair of zero coupon exposures isolates that single year.

4.90%. No arbitrage requires (1.043)^3 = (1.04)^2 * (1 + f), so 1 + f is 1.134627/1.0816, which is 1.049026 and gives f of 4.90%. The forward sits well above both zero rates because the three year rate is 30 basis points above the two year and that whole increment lands on the third year alone. To express the view that 4.90% is too high, buy the three year zero and short the two year zero in duration-matched size, which is long the third year of the curve and roughly flat to a parallel move. In swap form the same position is a two year forward starting one year receiver, and the profit and loss is approximately notional times the change in the forward times one year of duration.

Follow-up: Both zero rates rise 40 basis points in a parallel move. What happens to the forward rate and to the profit and loss of the duration-matched position?

Key concepts: forward rate, zero curve, no arbitrage, duration matching.