It is January 1, 2008. Inflation currently is about 2 percent; throughout 2007 t

Question

It is January 1, 2008. Inflation currently is about 2 percent; throughout 2007 the Fed took action to maintain inflation at this level. Now the economy is starting to grow too quickly and reports indicate that inflation is expected to increase during the next five years. Assume that at the beginning of 2008, the rate of inflation expected for 2008 is 4 percent; for 2009 it is expected to be 5 percent; for 2010 it is expected to be 7 percent; and for 2011and every year thereafter, it is expected to settle at 4 percent

A. what is the average expected inflation rate over the 5 year period 2008-2012 (use the arithmetic average)
B. what average nominal interest rate would over the 5 year period be expected to produce a 2 percent real risk free rate of return on 5 year treasury securities
C. Assuming a real risk-free rate of 2 percent and a maturity risk premium that starts at 0.1 percent and increases by 0.1 percent each year, estimate the interest rate in January 2008 on bonds that mature in one, two, five, 10, and 20 years. Also, draw a yield curve based on these data.
D. Describe the general economic conditions that could be expected to produce an upward-sloping yield curve.
E. if the consensus among investors in early 2008 had been that the expected rate of inflation for every future year was 5 percent, what do you think the yield curve would have looked like? consider all factors that are likely to affect the curve. does your answer here make you question the yield curve you drew in part c

Explanation / Answer

c) According to the given information, Inflation rate in 2008 = 4% 2009 = 5% 2010 = 7% 2011 = 4% 2012 = 4% Real risk free rate (r*) = 2% Maturity risk premium = 0.1% increases every year. Interest rate in 1,2,5,10,20 years? r1 = r* + IP + MRP + LP + DRP where IP = Inflation premium MRP = Maturity risk premium LP = Liquidity premium DRP = Default risk premium r1 = 2% + 4% = 6% r2 = 2% + 4.5% + 0.1% = 6.6% {IP2 = (4% + 5% ) / 2 = 4.5%} r5 = 2% + 4.8% + 4(0.1%) = 7.2% {IP5 = 4.8%} r10 = 2% + 4.4% + 9(0.1%) = 7.3% {IP10 = (IP5 + 4% + 4% + 4% + 4% + 4%) / 10 = 4.4%} r20 = 2% + 4.2% + 19(0.1%) = 8.1% Therefore, the interest rates in 1,2,5,10 & 20 is 6% , 6.6% , 7.2% , 7.3% & 8.1% d) If in the future we expect that the inflation will be higher than the current one, then we will obtain an upward sloping yield curve.

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