You manage a portfolio worth $10M, you estimate the volatility is 20% per annum, if log rate of return is normally distributed, what is 99% two weeks VaR
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- Suppose you invest Rs 600 in IBM and Rs 400 in Merc for a month. If the realized return is 2.5% on IBM and 1.5% on Merc over the month, what is the return on your total portfolio? a. 3.4% b. 1.4% c. 8.7% d. 2.1%Suppose the next month rate of return on a portfolio (worth $1M) is distributed as follows. Return Rate -0.05 -0.03 -0.01 0.00 0.01 0.03 0.04 0.07 0.10 0.12 Probability 1% 1.5% 2.5% 5% 10% 20% 25% 20% 10% 5% What is the expected rate of return given that the return is known to be greater than or equal to 4%?11. Consider $10m invested in a stock. The annual volatility of the rate of return is 25%. Assuming that the return is IID and normally distributed with p=0. a. What is the 99% 1-day VAR? b. What is the 95% 1-day VAR? c. What is the 95% one-week VAR? d. What is the 95% 1-day ES? e. What is the 99% 10-day ES?
- Suppose you have the following investments: Security Amount Invested Expected Return Beta A $2,000 5% .80 B $4,000 10% .95 C $6,000 15% 1.10 D $8,000 18% 1.40 What is the expected return on this portfolio?Consider the following information State Probability X Y Boom .25 15% 10% Normal .60 10% 9% Recession .15 5% 10% What is the expected return for a portfolio with an investment of $6000 in asset X and $4000 in asset Y?with a probability of 95 %, what is the maximum amount that a $1 million portfolio is expected to lose in a given year if its annual returns are normally distributed with a mean of 10% and standard deviation of 25% ?
- Question 5 a) The change in the value of a portfolio in 10 days is normally distributed with a mean of (i) GHS500,000 and (ii) GHS0 (zero). The standard deviation is GHS3 million in each case. Calculate the VaR (for both cases) for a confidence level of 99% and a time horizon of 10 days. Deduce the daily VaR.Consider a stock currently priced at $40. Assume that in each period of one month, the stock could either appreciate or depreciate by 10% . The risk - free rate is 2% per annum. What would be the value of a 2 - month ATM Asian put?Value of the portfolio today is $100. Annual mean μ= 20%, variance ?2=10%. Time horizon is one year. What is the V@R at R% probability?
- Consider a position consisting of a $100,000 investment in asset A and a $100,000 investment in asset B. Assume that the daily volatilities of both assets are 1% and that the coefficient of correlation between their returns is 0.3. What is the 5-day 99% VaR for the portfolio?You are going to invest $20,000 in a portfolio consisting of assets X, Y, and Z, as follows: Asset Annual Return Probability Beta Proportion X 10% 0.50 1.2 0.333 Y 8% 0.25 1.6 0.333 Z 16% 0.25 2.0 0.333 Given the information in Table 5.2, The beta of the portfolio in Table 8.2, containing assets X, Y, and Z is ________. Select one: a. 1.6 b. 2.0 c. 1.5 d. 2.4Suppose you have the following investments: Security Amount Invested Expected Return Beta A $2,000 5% .80 B $4,000 10% .95 C $6,000 15% 1.10 D $8,000 18% 1.40 What is the expected return on this portfolio? Select one: