The current oneyear Tbill rate is 50 percent and the expecte

The current one-year T-bill rate is .50 percent and the expected one-year rate 12 months from now is 1.20 percent. According to the unbiased expectations theory, what should be the current rate for a two-year Treasury security? (Do not round intermediate calculations. Round your answer to 2 decimal places. (e.g., 32.16))

Solution

According to Pure Expectation theory, short term interest rates are indicator of long term interest rates.

Based on this theory, if you invest in a two year bond, you would generate equal returns as you would have generated if you would have invested in a 1 year bond and then reinvested the proceeds in another 1 year bond.

(1 + 2yr Rate)² = (1 + 1Yr Rate) * (1 + 1 Yr rate 1 Yr from now)

(1 + 2yr Rate)² = (1 + 0.50%) * (1 + 1.2%)

(1 + 2yr Rate)² = (1.0050) * (1.012)

(1 + 2yr Rate)² = 1.01706

1 + 2yr Rate = 1.008494

2 Yr Rate = 0.85%