Unbiased Expectations Theory Oneyear Treasury bills currentl

Unbiased Expectations Theory One-year Treasury bills currently earn 2.55 percent. You expected that one year from now, one-year Treasury bill rates will increase to 2.85 percent and that two years from now, one-year Treasury bill rates will increase to 3.15 percent. If the unbiased expectations theory is correct, what should the current rate be on 3-year Treasury securities?

3.15 percent

2.55 percent

2.85 percent

2.93 percent

Solution

r1 = 2.55%
1r1 = 2.85%
1r2 = 3.15%

(1 + r₃)^3 = (1 + r₁)*(1 + ₁r₁)*(1 + ₁r₂)
(1 + r₃)^3 = (1 + 0.0255) * (1 + 0.0285) * (1 + 0.0315)
(1 + r₃)^3 = 1.0255 * 1.0285 * 1.0315
(1 + r₃)^3 = 1.087951
1 + r₃ = 1.0285
r₃ = 0.0285
r₃ = 2.85%

So, rate on 3-year Treasury Securities is 2.85%