Question

A​ 2-year Treasury bill currently offers a

22​%

rate of return. A​ 3-year Treasury note offers a

44​%

rate of return. Under the expectations​ theory, what rate of return do investors expect a​ 1-year Treasury bill to pay 2 year from​ now?

The rate of return investors expect a​ 1-year Treasury bill to pay 2 years from now is

Answer 1

Dear student before sloving this we will firstly understand what is Expectations Theory for conceptual clarity and then we will look at the steps for solving this problem

Expectations Theory refers to the theory to attempt to predict that the short term interest rates will be in the future based on the current long term interest rates.According to this theory it suggest that the investor earns the same interest by investing in 2 consecutive one year bond as an when compared to one two year bond today. This theory i will explain by taking the example from question only.

In the given question we are asked to here in this question we need to anlayise that if you as an investor you will invest in T bill then for what you should opt investing in a 1 T bill for 2 years or investing in 2 consecutive Tbills for consecutive year. Technically in both STRATERGY you will receive same rate (IF RISK IS SAME) of interest otherwise there will be an arbitrage opportunity.

Now to analyse this type of question we use expectation theory

So now lets solve the question:

Step 1: The first step of this calculation is to add 1 in the three years T bill = The result is 1.44

Step 2: Next is to cube the result =1.44*1.44*1.44= 2.985984

Step 3:Next is to divide it from square of (1.22*1.22)=1.4884 we will get 2.006

step 4 : now substract from the result we will get 1.006 or 6%