Explain why an increase in the inflation rate will cause the yield to maturity on a bond to increase.
Answer: When the inflation rate increases, it means that the risk free rate of return will increase. This happens because investors need to make some real return, even on a risk free investment. This means that in order to keep the real rate of return constant, when the inflation rate goes up, the nominal interest rate goes up as well. Consequently, to maintain the same real rate of return, the nominal rate must go up, which in turn raises the required return, or yield to maturity.
What elements determine what the yield to maturity will be for a bond?
Answer: The starting point is the risk free rate, a rate for a bond with no risks. A short term treasury bill reflects the risk free rate. The risk free rate comprises the real rate of return plus an inflation premium, so that the investor can earn the real return. If one knows the nominal risk free rate and the inflation rate, one can determine the real rate through the Fisher effect. When there is a possibility of default, the investor must receive a default premium to reflect that risk. Finally, there is the risk that the yield to maturity of the bond may change over the life of the bond, possibly lowering its value. This risk is reflected by the investor adding a maturity premium to the required return. In summary, the yield to maturity will be the real return, plus premiums for inflation, default, and maturity.
Given the anticipated rate of inflation (i) of 6.3% and the real rate of interest (R) of 4.7%, find the nominal rate of interest (r).
Answer:
r = R + i + iR
r = .047 + 0.63 + (.063)(.047)
r = 11.3%
If provided the nominal rate of interest (r) of 14.2% and the anticipated rate of inflation (i) of 5.5%, what is the real rate of interest (R)?
Answer:
r = R + i + iR
.142 = R + .055 + (.055)(R)
.142 - .055 = 1.055R + .055 - .055
.087 = 1.055R
R = 8.2%
Given the anticipated rate of inflation (i) of 6.13% and the real rate of interest (R) of 7.56%, what is the true inflation premium?
Answer: We know the inflation premium to equal i + iR or = 0.0613 + (.0613)(.0756) = 6.59%
