Question

Using the expectations hypothesis theory for the term structure of interest rates, determine the expected return for securities with maturities of two, three, and four years based on the data. Do an analysis similar to that in the right-hand portion of Table 6-6. 1-year of T-bill at beginning of year 1.....5% 1-year of T-bill at beginning of year 2.....8% 2-year of T-bill at beginning of year 3.....7% 3-year of T-bill at beginning of year 4.....10%

Answer 1

The expectations theory describes the term structure of interest rates where in equilibrium; long-term rates are equal to short term rates. As per this theory expected return for the 2 year security is the average of the expected yields of year 1 and year 2; expected return for the 3 year security is the average of the expected yields of year 1, year 2 and year 3 and so on…..

1 year t bill at beginning of year 1 = 5%

And 1 year t bill at beginning of year 2 = 8%

Therefore, expected return for securities with maturities of two = (5% +8%)/2 = 13%/2 = 6.5%

Similarly,

Expected return for securities with maturities of three = (5% + 8% + 7%)/3 =20%/3 = 6.67%

Expected return for securities with maturities of four = (5% + 8% + 7%+10%)/4 =30%/4 = 7.50%