The VaR on a Portfolio with a one-day time horizon is £100 million. What is the VaR using a ten-day horizon? Assuming 250 trading days in a year, how many “back-testing” exceptions or VaR events should you expect with 90% confidence interval?
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- You want to calculate the 30 Day 95% VaR for the following portfolio. You invest $5 million in the NADAQ composite and short $4 million of Bitcoin. The NASDAQ composite has standard deviation of returns of 15% pa; Bitcoin has standard deviation of returns of 20%. The two assets have a correlation of 0.8. Assuming a 250 day year, what is the 30 day VaR? What is the expected return of a portfolio that has $8,000 invested in S and $2,000 invested in T? The risk-free rate is 6% and the market portfolio's return is 14%. Do you expect the investment to be a good one for the coming year if betas for the two portfolio components are 0.6 and 1.3, respectively?Suppose that you have $1 million and the following two opportunities from which to construct a portfolio:a. Risk-free asset earning 12% per year.b. Risky asset with expected return of 30% per year and standard deviation of 40%.If you construct a portfolio with a standard deviation of 30%, what is its expected rate of return?
- If the one year ahead forecasted return on a portfolio is always 3% and dividends on the portfolio are known to be 2 per year in the future what is the efficient markets price of the portfolio?Consider a risky portfolio. The end-of-year cash flow derived from the portfolio will be either $110,000 or $280,000 with equal probabilities of .5. The alternative risk-free investment in T-bills pays 6% per year. Now suppose that you require a risk premium of 10%. What is the price that you will be willing to pay? (Round your answer to the nearest whole dollar amount.)Suppose Carol's stock price is currently $20. If the standard deviation of the continuously compounded returns (σ) on a stock is 60 percent per year. The monthly risk-free rate is 1 percent. Using one-step binomial tree, what is the current value of a six-month call option with an exercise price of $15?
- Assume the riskless rate of interest is 2% per year, and the expected rate of return on the market portfolio is 8% per year. According to the CAPM, what is the efficient way for an investor to achieve an expected rate of return of 5% per year? If the standard deviation of the rate of return on the market portfolio is 4%, what is the standard deviation of the portfolio producing the 5% expected return? • Plot the CML and locate the foregoing portfolios on the same graph. • Plot the SML and locate the foregoing portfolios on the same graph.Suppose Carol's stock price is currently $20. If the standard deviation of the continuously compounded returns (σ) on a stock is 60 percent per year. The annual risk-free rate is 12%, compounded every 6 months. A. Using one-step binomial tree, what is the current value of a six-month call option with an exercise price of $25?B. Using two-step binomial tree, what is the current value of a one-year put option with an exercise price of $25?Security F has an expected return of 10 percent and a standard deviation of 43 percent per year. Security G has an expected return of 15 percent and a standard deviation of 62 percent per year. Required: (a) What is the expected return on a portfolio composed of 30 percent of Security F and 70 percent of Security G? (b) If the correlation between the returns of Security F and Security G is .25, what is the standard deviation of the portfolio described in part (a)?
- Stock A has expected return of 10 percent per year and stock B has expected return of 20 percent. If 40 percent of a portfolio funds are invested in stock A and the rest in stock B. What is the expected return on the portfolio of stock A and Stock B? (please state the formula and show your workings)Consider a risky portfolio. The end-of-year cash flow derived from the portfolio will be either $110,000 or $280,000 with equal probabilities of .5. The alternative risk-free investment in T-bills pays 6% per year. a. If you require a risk premium of 4%, how much will you be willing to pay for the portfolio? (Round your answer to the nearest whole dollar amount.) b. Suppose that the portfolio can be purchased for the amount you found in (a). What will be the expected rate of return on the portfolio? (Round your answer to the nearest whole number.)A respected analyst forecasts that the return of the S&P 500 index portfolio over the coming year will be 10%. The one-year T-bill rate is 5%. Examination of recent returns of the S&P 500 Index suggest that the standard deviation of returns will be 18%. What does this information suggest about the degree of risk aversion of the average investor, assuming that the average portfolio resembles the S&P 500?