Question

An investor with an investment horizon of two years has two investment opportunities:

1.The first investment opportunity is to invest in two-year Treasury bond, yielding 5% per year.

2.The second opportunity is to invest in one-year Treasury bond and then after one year, to roll over an investment into another one year bond. If one year Treasury bond yields 4% and assuming that Expectation Theory holds what should one year bond yield one year from now? Explain fully and show your work. Initial response 250-300 words

Answer 1

Since expectation theory holds good, the spot rates and forward rates of yield of the bonds should be related in such a amanner that there is no arbitrage. (arbitrage is the activity of simultaneous borrowing and investment such that a profit is generated)

We have been given the following information

r02=5%

r01=4%

and we have to calculate r12

Because we know that expectation teory holds good we know that the yield are related such that

r12 = (((1+r02)^t)/1+r01)-1

Therefore r12 = ((1.05^2)/1.04) - 1

   r12 = 0.06 or 6%

Therefore one year bond yeild one year from now should be 6%

At the yield rates calculated above, no arbitrage opportunity exists and this is demonstrated as below

Step 1 : Borrow $1000 today for 1 year @ 4%, So the outflow after 1 year = 1000 x 1.04 = 1040

Step 2: Enter into a contract to borrow today to borrow $1040 after 1 year at 6%. So outflow after 2 years = 1040 x 1.06 = 1102.5

Step 3: Invest the borrowed $1000 today in a bond yielding 5% for 2 years getting 1000 x 1.05 x 1.05 = 1102.5

Thus, Outflow = Inflow and hence proved.