Exercise . The purpose of this exercise is to show that the claim of the gross return pure expectation hypothesis is inconsistent with interest rate uncertainty.

In the following we consider time points t < t < t.

(a) Show that if the hypothesis holds, then



B t

t

= 

B t

t

Et

, Bt

t

-

.

Hint: Compare two investment strategies over the period [t, t]. The first strategy is to buy at time t zero-coupon bonds maturing at time t. The second strategy is to buy at time t zero-coupon bonds maturing at time t and to sell them again at time t.

(b) Show that if the hypothesis holds, then



B t

t

= 

B t

t

Et

"



Bt

t

#

.

(c) Show from the two previous questions that the hypothesis implies that Et

"



B t

t

#

= 

Et

, Bt

t

-