9) The local bank that you are a risk manager has a portfolio of options on a traded asset.The delta of the options is -30 and the gamma is -5.i) Explain what these numbers mean.i) The asset price is 20 and its daily volatility is 1%. Use the quadratic model to calculatethe first three moments of the change in the portfolio value.i) Calculate a one-day 99% Value at Risk using the first two moments.iv) From your answer to point ii above, what can you say about the third moment's impacton value at risk calculation?v) Calculate a one-day 99% Value at Risk using all three moments.

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EBK CONTEMPORARY FINANCIAL MANAGEMENT

14th Edition

ISBN:9781337514835

Author:MOYER

Publisher:MOYER

Chapter8: Analysis Of Risk And Return

Section: Chapter Questions

Problem 14P

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An analyst has modeled the stock of a company using the Fama-French three-factor model. The market return is 10%, the return on the SMB portfolio (rSMB) is 3.2%, and the return on the HML portfolio (rHML) is 4.8%. If ai = 0, bi = 1.2, ci = 20.4, and di = 1.3, what is the stock’s predicted return?
What makes for a good investment? Use the approximate yield formula or a financial calculator to rank the following investments according to their expected returns. Buy a stock for $30 a share, hold it for three years, and then sell it for $60 a share (the stock pays annual dividends of $2 a share). Buy a security for $40, hold it for two years, and then sell it for $100 (current income on this security is zero). Buy a one-year, 5 percent note for $1,000 (assume that the note has a $1,000 par value and that it will be held to maturity).
As a portfolio manager for Bank of America Merrill Lynch, you are managing a portfolio of $33.90 million. You would like to estimate how much your portfolio might be losing over the period of next 81 trading days. Suppose the portfolio has a daily volatility of 3.0%. a. What is 81 day volatility?b. What is the VaR (in dollars) over a 81 day time period at a 95% confidence level?c. What is the VaR (in dollars) over a 81 day time period at a 99% confidence level?
Suppose you have $375,000 in cash, and you decide to borrow another $63,750 at a 7% interest rate to invest in the stock market. You invest the entire $438,750 in a portfolio J with a 20% expected return and a 28% volatility. a. What is the expected return and volatility (standard deviation) of your investment? b. What is your realized return if J goes up 39% over the year? c. What return do you realize if J falls by 19% over the year?
Suppose that one year ago, you invested in a stock market portfolio, which is currently worth £62,000. You are convinced the portfolio is well-diversified and fitted to your profile as an investor, and the beta of your portfolic is 0.9. You are planning to hold this portfolio for at least another three years. Suppose that the current level of FTSE100 is 1850, and the risk - free interest rate is 1.5% a) Iderdify any relevant risk that you may be facing in reference to your investment portfolio. b) Suppose there is a two year FTSE100 futures contract available. The futures price is 1855, and one contract is for £10 times the index: How many contracts would you need to eliminate the exposure to the market over the next two years? What position in these contracts would you take today? c) Evaluate the out comes of your hedging strategy if FTSE100 in two years'time is 1842. Comment on your results.
Consider a position consisting of a K200,000 investment in Asset A and a K300,000 investment in Asset B. Assume that the daily volatilities of the assets are 1.5% and 1.8% respectively, and that the coefficient of correlation between their returns is 0.4. What is the five day 95% Value at Risk (VaR) for the portfolio (95% confidence level represents 1.65 standard deviations on the left side of a normal distribution)?
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.

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daily volatility is 1%. Use the quadratic change in the portfolio value.