r p1 p2e 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: (a) -2 percent one year from now, and (b) a higher inflationary rate of 4 percent one year from now. Assume the real rate is 2 percent for each. In addition, define and compute the implied forward yield on an one year default free security one year from now, assuming the current two year yield is 5.0 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. What is the implied expected rate of inflation if the real rate remains at 2 percent? Use the following definitions and values: 0.02 (constant real rate of interest) 0.02 (period 1 rate of inflation) (a) -0.02 (expected period 2 rate of inflation) (b) p2e 0.04 (expected period 2 rate of inflation) 1y1 current yield on one year securities 2yle Expected period 2 yield on one year securities 1y2 current yield on two year securities Unbiased Expectations Hypothesis In general, (1 + lym) = [(1 + 1y1)(1 + 2yle)...(1 + myle)]1/m and jyle = the expected future short-term spot rate in period j for a term of 1 year and is the implied forward rate, jfl. Fisher Relationship: (1 + jy1) = (1 +jr1)(1+jple), where jple is the expected rate of inflation for period for 1 year, and jr1 is the real rate of interest for period j for 1 year. Specifically, (1 + 1y2) = [(1 + 1y1)(1 + 2yle)]1/2 and 2yle = the forward rate, 2f1. The expected future 1-year yield factor is: Problem 2.c: Draw the yield curves under expected inflation assumptions (a) and (b) concerning 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?). r p1 p2e 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: (a) -2 percent one year from now, and (b) a higher inflationary rate of 4 percent one year from now. Assume the real rate is 2 percent for each. In addition, define and compute the implied forward yield on an one year default free security one year from now, assuming the current two year yield is 5.0 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. What is the implied expected rate of inflation if the real rate remains at 2 percent? Use the following definitions and values: 0.02 (constant real rate of interest) 0.02 (period 1 rate of inflation) (a) -0.02 (expected period 2 rate of inflation) (b) p2e 0.04 (expected period 2 rate of inflation) 1y1 current yield on one year securities 2yle Expected period 2 yield on one year securities 1y2 current yield on two year securities Unbiased Expectations Hypothesis In general, (1 + lym) = [(1 + 1y1)(1 + 2yle)...(1 + myle)]1/m and jyle = the expected future short-term spot rate in period j for a term of 1 year and is the implied forward rate, jfl. Fisher Relationship: (1 + jy1) = (1 +jr1)(1+jple), where jple is the expected rate of inflation for period for 1 year, and jr1 is the real rate of interest for period j for 1 year. Specifically, (1 + 1y2) = [(1 + 1y1)(1 + 2yle)]1/2 and 2yle = the forward rate, 2f1. The expected future 1-year yield factor is: Problem 2.c: Draw the yield curves under expected inflation assumptions (a) and (b) concerning 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?)