ZuoTi.Pro
Question

9. You are currently holding stock A which has expected return of 10% and standard deviation of 3%. You would like to add one
business   finance   
0 0
Add a comment Improve this question Transcribed image text
Next > < Previous
Sort answers by oldest

Homework Answers

Answer #1

(a) All the three stocks A, B & C have the same expected return of 10%. However they have different standard deviation. Since, all the stocks are uncorrelated, we should choose the stock with least standard deviation for the given level of expected return, for inclusion in the portfolio. Hence, we should choose stock C.

(b) Variance of a portfolio of A & B = (WAσA)2 + (WBσB)2 + 2ρA,B(WAσA)(WBσB) = (WAσA)2 + (WBσB)2 + 2 x 0.5 x (WAσA)(WBσB) = (WAσA)2 + (WBσB)2 + (WAσA)(WBσB)

Variance of a portfolio of A & C = (WAσA)2 + (WCσC)2 + 2ρA,C(WAσA)(WCσC) = (WAσA)2 + (WCσC)2 + 2 x 0 x (WAσA)(WCσC) = (WAσA)2 + (WCσC)2

Since, σB > σC; the variance of the portfolio of A, B will be higher than that of A, C even though the expected return will remain the same. Hence, we will choose the stock that will give rise to the portfolio with lower variance if the expected return is constant. Hence, this time also, we will choose stock C.

(c) Variance of a portfolio of A & C = (WAσA)2 + (WCσC)2 + 2ρA,C(WAσA)(WCσC) = (WAσA)2 + (WCσC)2 + 2 x (-1) x (WAσA)(WCσC) = (WAσA)2 + (WCσC)2 - 2 x (WAσA)(WCσC) = (WAσA - WCσC)2

Hence, the optimal portfolio = minimum variance portfolio = Portfolio for which (WAσA - WCσC)2 = 0

i.e. (WAσA - WCσC) = 0 i.e WAσA = WCσC

Hence, WA x 3% = WC x 2%

WA + WC = 1

Hence, WA x 3% = (1 - WA) x 2%

Hence, WA = 2% / 5% = 0.4; Wc = 1 - 0.4 = 0.6

Hence, the optimal portfolio will invest 40% in stock A and the balance 60% in stock C.

The variance of such a portfolio will be zero, hence it's risk will be zero. Hence, this portfolio is risk free portfolio. And hence the return of this portfolio = WA x RA + WC x RC = 0.4 x 10% + 0.6 x 10% = 10% = risk free return in this economy.

0 0
Add a comment
Know the answer?
Add Answer to:
9. You are currently holding stock A which has expected return of 10% and standard deviation of 3%. You would like...
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Log In

Sign Up

Not the answer you're looking for? Ask your own homework help question. Our experts will answer your question WITHIN MINUTES for Free.
Similar Homework Help Questions

  • 9. You are currently holding stock A which has expected return of 10% and standard deviation...

    9. You are currently holding stock A which has expected return of 10% and standard deviation of 3%. You would like to add one of the following two stocks (so you would like to have a portfolio with two stocks): В 10% 10% E(r) o(i) 4% 2% a. Which stock should you buy assuming that all three stocks are uncorrelated and you can only purchase one of the stocks B or C? b. Now assume that p(A,B) 0.5 and p(A,C)...

  • 6. Consider the following information for Stocks 1 and 2: Expected Standard Stock Return Deviation 1...

    6. Consider the following information for Stocks 1 and 2: Expected Standard Stock Return Deviation 1 20% 40% 2 12% 20% NE a. The correlation between the returns of these two stocks is 0.3. How will you divide your money between Stocks 1 and 2 if your aim is to achieve a portfolio with an expected return of 18% p.a.? That is, what are the weights assigned to each stock? Also take note of the risk (i.e., standard deviation) of...

  • Compute the expected return, standard deviation, beta, and nonsystematic standard deviation of the portfolio. 4. Assume...

    Compute the expected return, standard deviation, beta, and nonsystematic standard deviation of the portfolio. 4. Assume that the total market value of an initial portfolio is $300,000. Suppose that the owner of this portfolio wishes to decrease risk by reducing the allocation to the risky portfolio from y = 0.7 to y = 0.56. How do you reallocate your risky portfolio? 5. Which of the following factors reflect pure market risk for a given corporation? a. Increased short-term interest rates....

  • 2. Company A's stock has a beta of BA 1.5, and Company B's stock has a beta of βΒ-2.5. Expected r...

    2. Company A's stock has a beta of BA 1.5, and Company B's stock has a beta of βΒ-2.5. Expected returns on this two stocks are E [rA]-9.5 and E rB 14.5. Assume CAPM holds. At age 30, you decide to allocate ALL your financial wealth of $100k between stock A and stock B, with portfolio weights wA + wB1. You would like this portfolio to be risky such that Bp- 3 (a) Solve for wA and wB- (b) State...

  • Stock A’s expected return and standard deviation are E[rA] = 8% and σA= 15%, while stock...

    Stock A’s expected return and standard deviation are E[rA] = 8% and σA= 15%, while stock B’s expected return and standard deviation are E[rB] = 12% and σB= 21%.  a. Determine the expected return and standard deviation of the return on a portfolio with weights wA=.35 and wB=.65 for the following alternative values of correlation between A and B: pAB=0.6 and pAB= -0.4. b. Assume now that pAB=-1.0 and find the portfolio p of stocks A and B that...

  • 3. Stocks A, B, C and D have the same standard deviation of 10% and the...

    3. Stocks A, B, C and D have the same standard deviation of 10% and the same expected return of 5%. The following table shows the correlation coefficient between the returns on these stocks. (note that correlation with itself is always 1). Stock B Stock C Stock D Stock A Stock B Stock C Stock D Stock A 1.0 -0.4 0.9 -0.1 1.0 0.1 1.0 -0.5 -0.2 1.0 (a) Consider a portfolio P = 0 A+ B+ C, calculate the...

  • 3. The risk-free rate is 0% and the expected return on the market is 10%. You...

    3. The risk-free rate is 0% and the expected return on the market is 10%. You are given the same stocks as in Q 2. Assuming, as in Q 2(b), that you hold the stock as part of a well-diversified portfolio, which stocks would you buy if the expected return on the stocks were as below: Stock Expected return in % Stock o (in %) 20 B 0.5 D 5 2

  • Intro Assume that there are only two stocks in the economy, stock A and stock B. The risk-free asset has a return of 3%...

    Intro Assume that there are only two stocks in the economy, stock A and stock B. The risk-free asset has a return of 3%. The optimal risky portfolio, i.e., the portfolio with the highest Sharpe ratio, is given below: A BC Stock A Stock B Risk-free asset 2 Expected return 0.062 0.075 0.03 3 Variance 0.1521 0.0484 4 Standard deviation 0.39 0.22 5 Covariance 0.02574 D Optimal risky portfolio 8 Weights 9 Expected return 10 Variance 11 Standard deviation 12...

  • A stock has a beta of 1.14 and an expected return of 10.5 percent. A risk...

    A stock has a beta of 1.14 and an expected return of 10.5 percent. A risk free asset currently early 2.4 percent. a. What is the expected return on a portfolio that is equally invested in the two assets? b. If a portfolio of the two assets has a beta of .92, what are the portfolio weights? c. If a portfolio of the two assets has an expected return of 9 percent, what is its beta? d. If a portfolio...

  • 4. Stock A has the expected return of 12%, the standard deviation of 15%, and the...

    4. Stock A has the expected return of 12%, the standard deviation of 15%, and the CAPM beta of 0.5. Stock B has the expected return of 18%, the standard deviation of 20% and the CAPM beta of 1.1. The risk-free rate is 3%. If you have no other wealth could invest in some combination of the risk-free asset and only one of these two stocks, which of the stocks A and B will you choose and why? (1 point)

ADVERTISEMENT
Free Homework Help App
Download From Google Play
Scan Your Homework
to Get Instant Free Answers
Need Online Homework Help?
Ask a Question
Get Answers For Free
Most questions answered within 3 hours.
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT