Consider a risky portfolio. The end-of-year cash flow derived from the portfolio will be either $50,000 or $150,000, with equal probabilities of 0.5. The alternative riskless investment in T-bills pays 5%. (a) If you require a risk premium of 10%, how much will you be willing to pay for the portfolio? (b) Suppose the portfolio can be purchased for the amount you found in (a). What will the expected rate of return on the portfolio be? (c) Now suppose you require a risk premium of 15%. What is the price you will be willing to pay now? (d) Comparing your answers to (a) and (c), what do you conclude about the relationship between the required risk premium on a portfolio and the price at which the portfolio will sell?

Kindly check explanation

Explanation:

Given the following :

Risk free return (risk less investment) = 5%

Cashflow derived from portfolio = $50,000 or $150,000 each at a probability of 0.5

(a) If you require a risk premium of 10%, how much will you be willing to pay for the portfolio?

Risk premium = 10%

Required return on portfolio = risk premium + risk free return = (10% + 5%) = 15%

Expected value of cashflow:

(0.5 × $50,000) + (0.5 × $150,000)

$25,000 + $75,000 = $100,000

Value of portfolio = Amount paid(a) × (1 + required return)

100,000 = a( 1 + 0.15)

100,000 = 1.15a

a = (100,000 / 1.15)

a = 86956.521

a = $86,956.5

B) If amount paid for portfolio = $86,956.5

Expected rate of return :

(Expected value - amount paid) / amount paid

= ($100,000 - $86,956.5) / $100,000

= $13043.5 / $100,000

= 0.130435 = 13.04%

C.) Now suppose you require a risk premium of 15%. What is the price you will be willing to pay now?

Risk premium = 15%

Required return on portfolio = risk premium + risk free return = (15% + 5%) = 20%

Value of portfolio = Amount paid(a) × (1 + required return)

100,000 = a( 1 + 0.20)

100,000 = 1.20a

a = (100,000 / 1.20)

a = 83333.333

a = $83,333.3

D.)

At a required risk premium of 10%, portfolio will sell at $86,956.5

At a required risk premium of 15%, portfolio will sell at $83,333.3

Hence, the price at which a portfolio will sell decreases as risk premium increases.

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