Determinants of Interest Rate for Individual Securities The Wall Street Journal

Question

Determinants of Interest Rate for Individual Securities The Wall Street Journal reports that the rate on 3-year Treasury securities is 8.80 percent, and the 6-year Treasury rate is 9.20 percent. From discussions with your broker, you have determined that expected inflation premium is 3.75 percent next year, 3.15 percent in Year 2, and 4.10 percent in Year 3 and beyond. Further, you expect that real interest rates will be 4.20 percent annually for the foreseeable future. What is the maturity risk premium on the 6-year Treasury security?

a) .50%

b) .90%

c) 1.25%

d) 1.85%

Explanation / Answer

The correct solution is b (0.90%). Working is provided below:

The nominal interest rate of a security can be described as:

((1+r)=((1+r*)×(1+IP)×(1+MRP))-1…..(1)

where    r=nominal interest rate=9.20

             r*=Real Rate of interest=4.20

IP= Inflation Premium=(1.0375×1.0315×1.0410×1.0410×1.0410×1.0410)1/6-1=1.038827-1=0.038827=3.8827%

MRP=Maturity Risk Premium=?

Therefore, plugging in values in equation 1:

(1.0920= (1.0420×1.038827×MRP))-1

(1.0920=1.082458MRP)-1

MRP= (1.0920/1.082458)-1

            =0.90%

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