4. You have $10,000 to invest and you put $8,000 in stock C and $2,000 in stock

Question

4. You have $10,000 to invest and you put $8,000 in stock C and $2,000 in stock D (the two stocks listed in Question 3). What is the beta of your portfolio? What is the expected return rate of your portfolio?

5. You have observed GE stock for a long time. The stock has an expected return of 14% and a beta is 1.2. If risk free rate is 2%, what is the expected return rate from the market portfolio?

6. You also considered Google stock for your investment portfolio. The stock has an expected return of 20% and a beta is 2. If the expected return rate from the market portfolio is 12%, what is the risk free rate in the economy?

1. Definition: (i for every possible scenario)

2. Sharpe Ratio: S= E(r)-rf/ o

3. Coefficient of Variation: CV= / E(r)

4. Portfolio situation. The expected return and standard deviation of return for A and B are and respectively, and wA wB are investment weights on asset A and B:

1)Portfolio Expected Return Rate:

2)Portfolio Standard Deviation:

3)Portfolio Beta:

5. Capital Asset Pricing Model (CAPM):

            Expected Return: E(r) = rf+risk premium = rf + B [E(rm)-rf]

Explanation / Answer

(5) Computation of the expected return rate from the market portfolio.We have,

Risk-free rate(Rf) =2 %

Expeced rate of return of stock(E(r)) = 14%

Beta =1.2

Using the capital asset pricing model(CAPM).We have,

E(r) = rf + B [E(rm)-rf]

14 = 2 + 1.2[E(rm) - 2]

1.2[E(rm) - 2] = 14 - 2 = 12

E(rm) - 2 = 12/1.2

E(rm) = 10 + 2 = 12%

Hence, the expected return rate from the market portfolio is 12%.

(6) Computation of the risk free rate in the economy.We have,

Risk-free rate(Rf) = ?

Expected rate of return of stock(E(r)) = 20%

Beta =2

Expected rate of return on market portfolio = 12%

Using the capital asset pricing model(CAPM).We have,

E(r) = rf + B [E(rm)-rf]

20 = rf + 2 ( 12 - rf)

20 = rf + 24 - 2rf

20 = - rf + 24

rf = 24 - 20 = 4 %

Hence,the risk free rate in the economy is 4%.

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