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Investment Management Inc. (IMI) uses the capital market line to make asset allocation recommendations. IMI derives the
following forecasts:

• Expected return on the market portfolio: 12%.
• Standard deviation on the market portfolio: 20%.
• Risk-free rate: 5%.

Samuel Johnson seeks 'Ml's advice for a portfolio asset allocation. Johnson informs IMI that he wants the standard deviation of the portfolio to equal half of the standard deviation for the market portfolio. Using the capital market line, what expected return can IMI provide subject to Johnson's risk constraint?

Respuesta :

funmilaciousfunmie78

Answer:

The expected return that IMI can provide subject to Johnson's risk constraint is 8.5%

Explanation:

Capital Market Line (CML)

Expected return on the market portfolio, E([tex]r_m[/tex]) = 12 %

Standard deviation on the market portfolio, σ[tex]_p[/tex] = 20%

Risk-free rate, [tex]r_f[/tex] = 5%

E([tex]r_c[/tex]) =  [tex]r_f[/tex] + [  E([tex]r_p[/tex])  - [tex]r_f[/tex] ] × ( σ[tex]_c[/tex] ÷ σ[tex]_p[/tex])

         = 0.05 + [ 0.12 - 0.05] × (0.10 ÷ 0.20)

= 8.5%

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