There are a number of theories of the term structure of interest rates including the unbiased expectations hypothesis, preferred habitat hypothesis, and market segmentation hypothesis. Discuss the implications of the unbiased expectations hypothesis within the context of the following problem. Problem 1: For a two year, default free, zero coupon security, compute its yield to maturity and draw the respective yield curves assuming two different expectations of inflation employing the Fisher Effect and the data below: (a) 4 percent one year from now, and (b) 2 percent one year from now. In addition, define and compute the implied forward yield on a one year security one year from now, assuming the current two year yield is 6.0 percent. Discuss the assumptions underlying this calculation and how it can be used to evaluate the implied forward yield on a 1-year loan, next year. (c) What is the implied expected rate of inflation if the real rate remains at 3 percent?
Use the following definitions and values:
R = 0.03 (constant real rate of interest)
p1 = 0.02 (period 1 rate of inflation)
(a) p2e = 0.04 (expected period 2 rate of inflation)
(b) p2e = 0.02 (expected period 2 rate of inflation)
1y1 = current yield on one year securities
2y1e = Expected period 2 yield on one year securities
1y2 = current yield to maturity on two year securities
Unbiased Expectations Hypothesis
In general, (1 + 1ym) = [(1 + 1y1)(1 + 2y1e). . .(1 + my1e)]1/m and jy1e = the forward rate, jf1.
Fisher Relationship: (1 + jy1) = (1 + jR1)(1+ jp1e ), where jp1e is the expected rate of inflation for period j for 1 year, and jR1 is the real rate of interest for period j for 1 year.
Specifically, (1 + 1y2) = [(1 + 1y1)(1 + 2y1e)]1/2 and 2y1e = the forward rate, 2f1.
The expected future 1-year yield factor is:
Don’t forget to draw the yield curves under assumptions (a) and (b), above, for each of the expected rates of inflation. Give the reasons for the shapes of these yield curves (HINT: are forward rates on future short-term securities equal to, greater than, or less than current short-term interest rates).