Question

Assume that the yield on a 5 year security is 2.75% , the one year yield is 1.20%, and your expectations for the next 4 year one year yields are 1.55%, 2.19%, 2.98%, and 3.10%. Determine whether you should invest in the 5 year security or 5 consecutive one year securities according to the un-bias expectations theory. Depending upon your answer what should happen to the long term and short yields in the market?

Answer 1

Let us assume that the initial investment amount available is $ 100

Investment Value when Invested in the 5 year security = 100 x (1.0275)^(5) = $ 114.53 approximately

Investment Value when Invested in 5 consecutive 1 year securities = 100 x (1.012) x (1.0155) x (1.0219) x (1.0298) x (1.031) = $ 111.50 approximately

As is observable the single 5-year security gives a greater final investment value and hence the same should be preferred for investment. As according to the expectations hypothesis short-term rates are a predictor of long-term rates, a rising trend of short-term one-year expected rates (1.55%, 2.19 %, 2.98 % and 3.1 %) should imply a rising trend of long-term rates as well. However, as the single long-term investment gives greater yield as compared to multiple short-term investments, the demand for the former should increase, thereby pushing up its prices and pushing down its yield. The opposite should be true for the latter, In such a scenario, the short-term rates should rise and the long-term rates should fall.