Problem 2: You are the financial adviser to three individuals, a Young person wi

Question

Problem 2:

You are the financial adviser to three individuals, a Young person with high risk tolerance, a Middle aged person with medium risk tolerance and an old person with low risk tolerance.

Here are the current conditions: Risk free asset is earning 12 % per year . Risky asset ( or market portfolio ) has expected return o f 30% per year and standard deviation of 40%. Using the mutual fund theorem or Separation theorem.

: a. Construct an appropriate portfolio (Mix of risky asset and risk free asset) for your young client and estimate the expected return and standard deviation of your young client for the coming year .

b. Construct an appropriate portfolio for your middle aged client and estimate the expected return and standard deviation of your middle aged client.

c. Construct an appropriate portfolio for your old client and estimate the exp ected return and standard deviation of your old client.

d. If your middle aged client requires a portfolio with a standard deviation of 30%, what is i ts expected rate of return?

Explanation / Answer

You are the financial adviser to three individuals, a Young person with high risk tolerance, a Middle aged person with medium risk tolerance and an old person with low risk tolerance.

Here are the current conditions: Risk free asset is earning 12 % per year . Risky asset ( or market portfolio ) has expected return o f 30% per year and standard deviation of 40%. Using the mutual fund theorem or Separation theorem.

: a. Construct an appropriate portfolio (Mix of risky asset and risk free asset) for your young client and estimate the expected return and standard deviation of your young client for the coming year .

Answer

Since Young client is high risk tolerence therefore he would invest 100% in Risky asset than

Expected return = 30%

Standard deviation = 40%

b. Construct an appropriate portfolio for your middle aged client and estimate the expected return and standard deviation of your middle aged client.

Since middle aged client is medium risk tolerence therefore he would invest 50% in Risky asset and 50% in Risk Free Asset

Expected return = 30*50% + 12*50% = 21%

Standard deviation = 40*50% = 20%

c. Construct an appropriate portfolio for your old client and estimate the exp ected return and standard deviation of your old client.

Since old aged client is less risk tolerence therefore he would invest 100% in Risk Free Asset than

Expected return = 12%

Standard deviation = 0

d. If your middle aged client requires a portfolio with a standard deviation of 30%, what is i ts expected rate of return?

If your middle aged client requires a portfolio with a standard deviation of 30%

Standard Deviation of portfolio in case where investment in two asset which comprise risk free asset formula because Standard Deviation of Risk free asset is 0 will be

Standard Deviation of portfolio = Weight of Risky asset * Standard Deivation of Risky asset

30 = Weight of Risky asset * 40

Weight of Risky asset = 30/40

Weight of Risky asset = 0.75

Weight of Risk free asset = 1- 0.75 = 0.25

Expected rate of return will be = Weight of Risky asset*Expected rate of return of Risky asset +Weight of Risk free asset*Expected rate of return of Risk free asset

Expected rate of return will be = 0.75*30 + 0.25*12

Expected rate of return will be = 25.50%

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