you have two investmwnts, each of which has a 0.8% chance if a loss $12 million and a 99.2% chance of loss of $2 million. these two incestments ate independent of each other. what is 99% vaR for a portfolio consisting of these two investments
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suppose that you have two investmwnts, each of which has a 0.8% chance if a loss $12 million and a 99.2% chance of loss of $2 million. these two incestments ate independent of each other. what is 99% vaR for a portfolio consisting of these two investments ?
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- Suppose that each of two investments has a 4% chance of a loss of $10 million, a 2% chance of a loss of $1 million, and a 94% chance of a profit of $1 million. They are independent of each other. What is the VaR for a portfolio consisting of the two investments when the confidence level is 95%? Also calculate the expected shortfall. (show steps)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.)An investor invests 75% of his wealth in a risky asset with an expected rate of return of 28% and a standard deviation of 30% and 25% in a treasury bill that pays 3%. What is the EXPECTED RETURN of the combined portfolio of t-bills and the risky asset?
- Suppose you are considering investing your entire portfolio in three assets A, B and C. You expect that after you invest, four possible mutually exclusive scenarios will occur, with associated returns (in %) for each of the three assets as listed below. The probability of each scenario is given below. A B C Probabilities return 0.05 0.50% -3.60% 3.60% 0.35 0.60% 2.75% 0.15% 0.45 3.66% 1.45% 0.45% 0.15 -4.80% -0.60% 6.30% Find the expected returns and standard deviations of Asset A, B & C. (HINT: the expected return is given by the probability-weighted sum of returns in each scenario. The expected standard deviation is given by the square root of the probability-weighted sum of squared deviations from the expected return.) Is there any reason to invest in Asset A given its low expected return and high standard deviation?Jamie has wealth of $10,000 to invest. The market portfolio consists of three stocks with 20% being Stock A, 40% being Stock B and the remainder Stock C. The expected return on this market portfolio is 14%. The risk free rate is 5%. The CAPM holds. Suppose Jamie's optimal portfolio has an expected return of 23%, what are the dollar values of her investments in A, B. C and the risk free asset?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?
- Ms. B has $1000 to invest. She is considering investing in the common stock of company M. In addition, Ms. B will either borrow or lend at the risk-free rate. Ms. B decide to invest $350 in common stock of company M and $650 placed in the risk- free asset. The relevant parameters are 1) What is the expected return? 2) What is the variance of the portfolio? 3) What is the standard deviation of the portfolio?One of our clients, Mr. Choi, currently has an investment portfolio value of $1mil. His portfolio consists of 70% risky portfolio and 30% risk-free asset. If Mr. Choi has now extra $100,000 cash to invest, and if he is a constant relative risk aversion, how do you think he wants to allocate his extra $100,000 over the risky and the risk-free asset? Assume that Mr. Choi’s utility is a power function with gamma= 2 If another client, Mr. Smith, also has a power utility function but has a larger risk preference parameter value of gamma than Mr. Choi does, how does Mr. Smith want his money to be allocated relative to Mr. Choi?An investor invests 30 percent of his wealth in a risky asset with an expected rate of return of 0.14 and a standard deviation of .35 and 70 percent in a T-bill that pays 3 percent. His portfolio's expected return and standard deviation are __________ and __________, respectively. Please show the formula
- You have invested $1,000 in a risky asset with an expected rate of return of 0.17 and a standard deviation of 0.40 and a T-bill with a rate of return of 0.04. What percentages of your money must be invested in the risky asset and the risk-free asset, respectively, to form a portfolio with an expected return of 0.11? What percentages of your money must be invested in the risk-free asset and the risky asset, respectively, to form a portfolio with a standard deviation of 0.20? Calculate the slope of CAL. If the degree of risk aversion A=4, what proportion of the money should be invested in risky asset. Sub Parts to be solvedYou have invested $1,000 in a risky asset with an expected rate of return of 0.17 and a standard deviation of 0.40 and a T-bill with a rate of return of 0.04. What percentages of your money must be invested in the risky asset and the risk-free asset, respectively, to form a portfolio with an expected return of 0.11? What percentages of your money must be invested in the risk-free asset and the risky asset, respectively, to form a portfolio with a standard deviation of 0.20? Calculate the slope of CAL. If the degree of risk aversion A=4, what proportion of the money should be invested in risky asset.Consider three investments. You are given thefollowing means, standard deviations, and correlations for the annual return on these three investments.The means are 0.12, 0.15, and 0.20. The standarddeviations are 0.20, 0.30, and 0.40. The correlationbetween stocks 1 and 2 is 0.65, between stocks 1 and3 is 0.75, and between stocks 2 and 3 is 0.41. Youhave $10,000 to invest and can invest no more thanhalf of your money in any single stock. Determine theminimum-variance portfolio that yields a mean annualreturn of at least 0.14
