In a perfect world, there are only two interest rates: one-year maturity or two-year maturity. Both annual coupon rates are at 6%. The yield curve is flat at 6%. Investors expect a 120bp increase for the one-year interest rate at the end of one year. Assume all investors have a short-term (one-year) investment horizon.

Question: Prove that investors pure expectation can change the yield curve from flat to upward sloping.