Average Annual Rates Standard Deviation Inflation 4.07 5.95 2.89 T-Bills Inflati

Question

Average Annual Rates Standard Deviation Inflation 4.07 5.95 2.89 T-Bills Inflation 2.25 1.68 3.53 Real T-Bill T-Bills All months First half Recent half 3.46 1.04 4.45 0.56 0.29 0.90 3.12 1.29 3.11 Real T-Bill 3.81 6.27 2.13 (1926-2016) Mean excess return (annualized) Standard deviation (annualized) Market Index 0.83 18.64 Big/ Growth 7.98 18.50 Big/ Value 11.67 24.62 Small/ Growth 8.79 26.21 Small/ Value 15.56 28.36 Suppose that the inflation rate is expected to be 2.25% in the near future using the data provided above, what would be your predictions for the following? (Round your answers to 2 decimal places.) a. The T-bill rate? b. The expected rate of return on the Big/Value portfolio? c. The risk premium on the stock market? 3.31

Explanation / Answer

We derive the answer using CAPM model which provide the below:

Expected Rate of Return on a Portfolio = Risk free rate + Beta *(Market Return-Risk free rate)

Assumptions:

1. Data is correct and so derived data is also correct

2. Mean Excess Return actually means return above risk free rate but in this case assuming it's the nominal rate of return

3. There's no use of inflation in this case as we usually take nominal rates while calculating expected return unless explicitly asked for real rate of return

11.67 = 3.46 + Beta * (0.83 - 3.46)

Using the above, Dervied value of Beta is -3.12167.

With nominal T Bill rate as now 3.31% and using the above calculated value of Beta, Expected Rate of return on the portfolio is as below:

E (Ri) = 3.31 + (-3.12167) * (0.83-3.31)

E (Ri) = 11.05175%

Risk premium on stock market is Beta * (Market return - RIsk free rate)

=  (-3.12167) * (0.83-3.31)

= 7.741749%

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