Question

2. You want to know what 2-year spot rates will be one year from now. According to the pure expecta- tions theory, this unknown forward rate of interest is implied by current spot rates. The simplest method of calculating this forward rate is to use today's 1-year and 3-year spot rates; i.e., the spot rates that take you out to the start of, and to the end of the forward period of time you are interested in. Thus: (1 + R2 ) = (1 + R ). (1+F2): (1.0650) = (1.0575). (1+F212 F2 = [(1.0650) / (1.0575) 112-1 = 6.88% Notice that this is consistent with the upward-sloping current term structure: 2-year rates are 6.25% today, and the market expects this same spot rate to increase to 6.88% next year. Using the same logic as above, for the 1-year forward rate two years from now: (1 + R= (1 + R ). (1+2F): (1.0650) = (1.0625). (1 + 2) 2F1 = [(1.0650) / (1.0625)) - 1 = 7.00%

Answer 1

Expectations theory help us to predict what short-term interest rates will be in the future based on current long-term interest rates, if there is difference between short term (Spot+future) and long term rate is the arbitrage opportunity.

Formula to calculate forward rate from long term spot rate, if there is two year bond and one year bond.

(1+r)²= (1+r)*(1+f₁)

now come to the solution part

Part 1^st - (1.0625)²=(1.0575)*(1+₂f₁)

= (1+₂f₁)= (1.0625)²/(1.0575)

= ₂f₁= 6.75% rate second year forward rate one from now.

Part 2^nd - (1.0650)³=(1.0625)²*(1+₂f₁)

= (1+₂f₁) = (1.0650)³/(1.0625)²

= ₂f₁ = 7% rate one year forward rate tow from now.