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- 9) The measure of risk in a Markowitz efficient frontier is A) specific risk. B) standard deviation of returns. C) reinvestment risk. D) beta. Provide explanation for the accurate answer.a)define market risk. b)define delta-hedged position and describe delta hedging. c)describe gamma hedging and vega hedging. d)define and explain value at risk (VAR). e)describe the analytical (variance-covariance) method of calculating VAR, and discuss its advantages and disadvantages.Suppose the utility function is U = E(r) - 0.5Ao2. Draw the indifference curve corresponding to a utility level of 0.2 for an investor with a risk aversion coefficient of 3. Please note the vertical line indicates expected return, and plot standard deviation on the horizontal line.
- Consider two assets. Suppose that the return on asset 1 has expected value 0.05 and standard deviation 0.1 and suppose that the return on asset 2 has expected value 0.02 and standard deviation 0.05. Suppose that the asset returns have correlation 0.4.Consider a portfolio placing weight w on asset 1 and weight 1-w on asset 2; let Rp denote the return on the portfolio. Find the mean and variance of Rp as a function of w.A plot/graph of the positive relation between systematic risk and expected return is called: O security market line standard deviation and width of the normal distribution O covariance graph O capital asset pricing modelin a Statistical sense, the Single Index Model is best characterized by: the Capital Market Line The Security Market Liner Regression of any asset as a linear function of the Market, plus mean-zero random error A regression of the Market, as a linear function of any given asset, plus mean-zero random error I
- Question 1 Are the following statements true or false? Provide a short justification for your answer. (You are evaluated on your justification.) Remember that a statement is false if any part of the statement is false. A single correct counterexample is sufficient to show that a statement is false. a) assets A, B, C, with expected returns and standard deviations: Suppose you are a mean-variance optimizer. The risk-free rate is 3%. There are three risky E [řa] = 10%, SD [FA] = 5% E [řB] = 15%, SD [řB] = 7% E [řc] = 12%, SD [řc] = 9% You cannot invest in all three risky assets. Instead, you have to choose whether to invest in only assets (A, B), or only assets (A, C). Asset B mean-variance dominates asset C, since it has higher return and lower standard deviation than asset C. Thus, as long as you are risk-averse, you would always prefer the set of assets (A, B) to the set assets (A, C). b) the same market B's. The covariance matrix between A, B, C is: Suppose the CAPM holds. Consider…Which of the following is a justification framework for the mean-variance approach? a)if trading is continuous and asset prices follow a multi-dimensional geometric Brownian motion with drift.b)If the investors’ state-specific utility is an exponential function of the assets variance. c)If investors’ preferences for risk are inter-dependent and serially correlated with asset returns.d)If the returns of all assets follow the Mandelbrot distribution.a) Discuss the difference between a price-weighted index and a value-weighted index. Give one example for the price-weighted index and one example for the value-weighted index and discuss any problems/advantages associated with the specific indices. b) We assume that investors use mean-variance utility: U = E(r) – 0.5 × Ao², where E(r) is the expected return, A is the risk aversion coefficient and o? is the variance of returns. Given that the optimal proportion of the risky asset in the complete port- folio is given by the equation y* = E , where r; is the risk-free rate, E(rp) is the expected returm of the risky portfolio, o, is variance of returns, and A is the risk aversion coefficient. For each of the variables on the right side of the equation, discuss the impact of the variable's effect on y* and why the nature of the relationship makes sense intuitively. Assume the investor is risk averse. Ao
- Under the stop-loss reinsurance model, suppose the total claim follows exponential distribution with mean 1/λ. For given premium P, (a) Derive the retention level M; (b) Calculate the sum of shared variances Var(X*) + Var.XBeta is which of the following: A) standard deviation. B) total risk. C) Beta is the relationship which is between an investment's return, and the market return. D) unsystematic risk.I can use the regression beta as my estimate of beta in a valuation. True or false