3. Suppose that you have two investments, each of which has a 0.9% chance of a loss of S10 million and a 99.1% chance of a loss of $1 million. These two investments are independent of each other. a. What is the VaR for one of the investments at the 99% confidence level? b. What is the expected shortfall for one of the investments at the 99% confidence level? c. What is the 99% VaR for a portfolio consisting of the two investments? d. What is the 99% expected shortfall for a portfolio consisting of the two investments?

3. Suppose that you have two investments, each of which has a 0.9% chance of a loss of S10 million and a 99.1% chance of a loss of $1 million. These two investments are independent of each other. a. What is the VaR for one of the investments at the 99% confidence level? b. What is the expected shortfall for one of the investments at the 99% confidence level? c. What is the 99% VaR for a portfolio consisting of the two investments? d. What is the 99% expected shortfall for a portfolio consisting of the two investments?

FINANCIAL ACCOUNTING

10th Edition

ISBN:9781259964947

Author:Libby

Publisher:Libby

Chapter1: Financial Statements And Business Decisions

Section: Chapter Questions

Problem 1Q

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Consider two different assets. Asset A has a mean expected return of 6% with a standard deviation of 22%. Asset B has a standard deviation of returns of 32%. What should be the mean expected return on asset B for a rational investor to be indifferent about these two investments? Answer only if you are 100% sure, other wise i will report your answer.
An investor has an opportunity to invest in two risky assets and a risk-free asset. Theexpected return of the two risky assets are μ1 = 0.12, μ2 = 0.15. Their standarddeviations are σ1 = 0.05 and σ2 = 0.1, and the correlation coefficient between theirreturn is 0.2. The risk-free rate is 0.05. Suppose the investor has $1000 and he wantsto hold a portfolio with expected return of 0.1. If the investor is risk averse, how muchshould he invest in the two risky assets and the risk-free asset?
Suppose the risk-free rate is 5%. The expected return and standard deviation of a risky asset are 10% and 20%, respectively. a. What is the slope of the capital allocation line (CAL) constructed using the risk-free asset and the risky asset? A. 0.30 B. 0.15 C. 0.25 D. 0.20 b. If an investor has a risk aversion coefficient of A=2, what is the optimal fraction of the money that she invests in the risky asset? A. 62.5% B. 42.5% C. 30% D. 20% c. If an investor invest 25% of her money in the risky asset, which is the investor’s risk aversion coefficient? a. 5 b. 1 c. 3 d. 4
Supposing the return from an investment has the following probability distribution Return Probability R (%) 8 0.2 10 0.2 12 0.5 14 0.1 Required: What is the expected return of the investment? What is the risk as measured by the standard deviation of expected returns?
b. Suppose that you have the following information of three risky assets. Security Return (%) Standard Covariance with Deviation (%) A B A 11 10 4 14 6. 30 17 Risk free rate = 6%, (assume that A = 6). Requirement: Find the optimal portfolio weight of risky assets. How do you allocate the capital between optimal portfolio of risky asset and risk-free assets.
What is the expected return of a portfolio of two risky assets if the expected return E(Ri), standard deviation (SDi), covariance (COVij), and asset weight (Wi) are as shown below? Asset (A) E(R₂) = 10% SDA = 8% WA = 0.25 COVAB = 0.006 Select one: A. 13.75% B. 7.72% C. 12.5% D. 8.79% Asset (B) E(RB) = 15% SDB = 9.5% WB = 0.75
Suppose there are two investments A and B. Either investment A or B has a 4.5% chance of a loss of $15 million, a 2% chance of a loss of $2 million, and a 93.5% change of a profit of $2 million. The outcomes of these two investments are independent of each other. (a) What is the 95% VaR of investment A? How about investment B? (b) What is the 95% for a portfolio consisting of both investments A and B?(Hint: write out the probabilities of all possible portfolio outcomes.) (c) Is the summation of the 95% VaRs of the individual investments greater or smaller than the 95% VaR of the portfolio? If we measure the risk of an investment or portfolio using VaR, does this suggest that diversificationmust decrease risk? (Intuitively, putting A and B in a portfolio is a form of diversification.)
What is the expected return of a portfolio of two risky assets if the expected return E(Ri), standard deviation (SDi), covariance (COVij), and asset weight (Wi) are as shown below? Asset (A) E(R₁) = 10% SDA = 8% WA = 0.25 COVAB = 0.006 Asset (B) E(R₂) = 15% SDB = 9.5% WB = 0.75
D6) Suppose that an investment has 0.5% chance of a loss of $10 million and a 99.5% chance of a loss of $1 million. What is the Value-at-Risk (VaR) for this investment when the confidence level is 99%?
4. Suppose that there are 2 assets with ri 012 = 0.005. = 0.20, 01 = = 0.40, 2 = 0.10, 02 = 0.25 and (a) If ro = 0.02, what are the market portfolio return and variance? What are the corre- sponding weights (i.e. how much to invest in asset 1, asset 2, and the risk-free asset to get the market portfolio)? Answer. (b) If ro 0.05, what are the market portfolio return and variance? What are the corre- sponding weights? Answer.
Two assets, A and B, have the same expected return (10%) and the same level of risk (average). Which of the following statements is true? Select one: a. A rational investor will either put 100% of her funds into asset A or 100% of her funds into asset B because the return same but the investor will not have to track two separate investments. b. A combination of assets A and B will have the same expected return (10%) as either asset A or asset B, but may have less than average risk depending on how the cash flows from each asset move together. c. A rational investor is indifferent between investing 100% in A, 100% in B, or a combination of A and B, because the return and risk will be the same. d. A combination of assets A and B will result in the same expected return (10%) as investing 100% in A or 100% in B, but the risk will increase because now two investments are at risk.
Consider the following financial market with two risky assets x and y as well as a risk-free asset f: E[r]. x (10%, 8%) •z (6.6%, 6.3%) y (8%, 5%) (0%, 3%) f Is it possible to construct portfolio z with existing assets? Explain.