Question

Suppose the real risk-free rate is 2.3%, the average future inflation rate is

2.1%, and a maturity premium of 0.05% per year to maturity applies, i.e., MRP =

0.05%(t), where t is the years to maturity. What rate of return would you

expect on a 5-year Treasury security, assuming the pure expectations theory is

NOT valid?

Group of answer choices

4.65%

4.30%

5.35%

5.00%

5.70%

Your portfolio consists of $31,232 invested in a stock that has a beta = 1.9,

$45,024 invested in a stock that has a beta = 1, and $93,754 invested in a

stock that has a beta = 1.8.  The risk-free rate is 5%.  Last year this portfolio had

a required return of 8.3%.  This year nothing has changed except that the market

risk premium has increased by 3.8%. What is the portfolio’s current required rate

of return?

Group of answer choices

14.6%

14.3%

14.4%

14.7%

14.5%

Answer 1

5 year treasury security

Real Risk-Free Rate = 2.3%
Average Inflation Rate = 2.1%
Maturity Premium = 0.05% * 5 = 0.25% (0.05% * t and maturity is 5 years)

Expected Returns for the 5 year treasury is
= Real Risk-Free Rate + avg inflation Rate + Maturity Premium
= 2.3% + 2.1% + 0.25%
= 4.65%
Hence, Expected Returns for the 5 year treasury is 4.65% or option A.

Portfolio Name	Beta	Portfolio Amount	Portfolio Weight	Beta Weight
A	1.9	31,232.00	0.184	0.35
B	1.0	45,024.00	0.265	0.26
C	1.8	93,754.00	0.551	0.99
Total		170,010.00	1.00	1.61

Please note, the name of the portfolios have been assigned by me for the simplification process. I have assumed that risk-free rate and portfolio beta for last year is also same for this year too

Portfolio Weight = Portfolio A (amount) / Total Portfolio Amount
Beta Weights = Beta of Portfolio A * Weightage of the portfolio A

Required Rate of Return = Risk-Free Rate + Beta * market Risk Premium
Required Rate of Return (last year) = 8.3%

8.3% = 5% + 1.61 * Market Risk Premium (last year)
8.3% - 5% = 1.61 * Market Risk Premium (last year)
Market Risk Premium (last year) = 3.3%/1.6
Market Risk Premium (last year) = 2.05%

Market Risk Premium for current year = Market Risk Premium (last year) + 3.8%
Market Risk Premium for current year year = 2.05% + 3.8% = 5.85%

Required Rate of Return (current year) = 5% + 1.61 * 5.85%
= 5% + 9.42%
Required Rate of Return (current year) = 14.42% ~ 14.4%

Hence, the Required Rate of Return (current year) is 14.4%.