Solution of investment
BKM CHAPTER 5
1. The Fisher equation tells us that the real interest rate approximately equals the nominal rate minus the inflation rate. Suppose the (expected or realized) inflation rate increases from 3% to 5%. Does the Fisher equation imply that this increase will result in a fall in the real rate of interest? Explain.
The Fisher equation relates nominal rates required by investors to real rates required by investors and inflation. You can think about this from two perspectives:
i. Ex-ante (before) required Nominal Return as a function of required Real Return and Expected Inflation: (1 + rNominal) = (1 + rReal)(1 + E(i))
ii. Ex-post (afterward) realized Real Return as a function of Nominal Return and Realized Inflation: (1 + rReal) = (1 + rNominal)/(1 + i)
Assume the question asks this instead:
Suppose the expected inflation rate increases from 3% to 5%. Does the Fisher equation imply that this increase will result in a fall in the real rate of interest?
The theory is the ex-ante required real return is not a function of inflation. If expected inflation increase, required real return will remain unchanged and the required nominal return will increase (the security will have to pay more).
Now assume the question asks this:
Suppose realized inflation is 5% instead of the 3% expected inflation. Does the Fisher equation imply that this increase will result in a fall in the real rate of interest?
Since the nominal return was set when the asset was purchased, a realized inflation greater than expected inflation will decrease the realized real return.
2. You've just stumbled on a new dataset that enables you to compute historical rates of return on U.S. stocks all the way back to 1880. What are the advantages and disadvantages in using these data to help estimate the expected rate of return on U.S. stocks over the coming year?
If we assume that the distribution of returns remains reasonably stable (same expectation and standard
1. The Fisher equation tells us that the real interest rate approximately equals the nominal rate minus the inflation rate. Suppose the (expected or realized) inflation rate increases from 3% to 5%. Does the Fisher equation imply that this increase will result in a fall in the real rate of interest? Explain.
The Fisher equation relates nominal rates required by investors to real rates required by investors and inflation. You can think about this from two perspectives:
i. Ex-ante (before) required Nominal Return as a function of required Real Return and Expected Inflation: (1 + rNominal) = (1 + rReal)(1 + E(i))
ii. Ex-post (afterward) realized Real Return as a function of Nominal Return and Realized Inflation: (1 + rReal) = (1 + rNominal)/(1 + i)
Assume the question asks this instead:
Suppose the expected inflation rate increases from 3% to 5%. Does the Fisher equation imply that this increase will result in a fall in the real rate of interest?
The theory is the ex-ante required real return is not a function of inflation. If expected inflation increase, required real return will remain unchanged and the required nominal return will increase (the security will have to pay more).
Now assume the question asks this:
Suppose realized inflation is 5% instead of the 3% expected inflation. Does the Fisher equation imply that this increase will result in a fall in the real rate of interest?
Since the nominal return was set when the asset was purchased, a realized inflation greater than expected inflation will decrease the realized real return.
2. You've just stumbled on a new dataset that enables you to compute historical rates of return on U.S. stocks all the way back to 1880. What are the advantages and disadvantages in using these data to help estimate the expected rate of return on U.S. stocks over the coming year?
If we assume that the distribution of returns remains reasonably stable (same expectation and standard