Question

Interest rates on 3 year treasury securities are currently 7%, while 5 year treasury securities yield 8%. If the pure expectations theory is correct what does the market believe that 2 year securities will be yielding 3 years from now?

Answer 1

9.52 percent on annual compounding assumption

9.509 percent on semiannual compounding assumption

Step-by-step explanation:

Based on annual compounding assumption

Yield on three year security = 7%

Yield on five year security = 8%

If the markets are in equilibrium, the yield on two years security three years from now should be as under

[(1+0.08)^5/(1+0.07)^3]^(1/2) - 1

[1.46933/1.225]^0.5 - 1

1.0952 - 1 = 0.0952 or 9.52%

Based on semiannual compounding assumption

Yield on three year security = 3.5%

Yield on five year security = 4%

If the markets are in equilibrium, the yield on two years security three years from now should be as under

[(1+0.04)^10/(1+0.035)^6]^(1/4) - 1

[1.4802/1.2292]^0.25 - 1

1.04755 - 1 = 0.04755 = 4.755% semiannual

4.755 x 2 = 9.509%