By looking at the sensivities of your portfolio to ds = -$2 and 80 = -1%, you decide to hedge delta, gamma and Vega risk of your portfolio with the underlying stock and two different options on the same asset with below data. Calculate the units of stock you need to trade to hedge away all delta, gamma and Vega risks of your portfolio.(Note that here you have to calculate the units of stock, Option A and Option B, but you will only submit the units of stock.) Variable Delta (A) Gamma (T) Vega (v) Option A Option B -0.5 0.2 0.2 0.1 7 8

By looking at the sensivities of your portfolio to ds = -$2 and 80 = -1%, you decide to hedge delta, gamma and Vega risk of your portfolio with the underlying stock and two different options on the same asset with below data. Calculate the units of stock you need to trade to hedge away all delta, gamma and Vega risks of your portfolio.(Note that here you have to calculate the units of stock, Option A and Option B, but you will only submit the units of stock.) Variable Delta (A) Gamma (T) Vega (v) Option A Option B -0.5 0.2 0.2 0.1 7 8

Essentials Of Investments

11th Edition

ISBN:9781260013924

Author:Bodie, Zvi, Kane, Alex, MARCUS, Alan J.

Publisher:Bodie, Zvi, Kane, Alex, MARCUS, Alan J.

Chapter1: Investments: Background And Issues

Section: Chapter Questions

Problem 1PS

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Two call options, A and B, are on the same stock. Their hedge ratios are 0.4 and 0.7, respectively. If a riskfree portfolio of the two calls contains one Call A, then the portfolio needs to contain Call Bs (use negative numbers to mean short positions. Keep 2 decimal places.)
Consider the following portfolio choice problem. The investor has initial wealth w andutility u(x) = (x^n) /n. There is a safe asset (such as a US government bond) that has netreal return of zero. There is also a risky asset with a random net return that has onlytwo possible returns, R1 with probability 1 − q and R0 with probability q. We assumeR1 < 0, R0 > 0. Let A be the amount invested in the risky asset, so that w − A isinvested in the safe asset.i) What are risk preferences of this investor, are they risk-averse, riskneutral or risk-loving?ii) Find A as a function of w.
After learning the course, you divide your portfolio into three equal parts (i.e., equal market value weights), with one part in Treasury bills, one part in a market index, and one part in a mutual fund with beta of 0.72. What is the beta of your overall portfolio? 고
Carl plans to add one of two alternative stocks to his portfolio. Stock A has a correlation of 0.70 with his portfolio and Stock B has a correlation of 0.10. Both stocks have the same standard deviation of returns. Based on this information, relative to Stock A, Stock B will result in: a. less total risk and more active risk for the portfolio b. less total risk and less active risk for the portfolio С. more total risk and less active risk for the portfolio d. more total risk and more active risk for the portfolio
You are facing three stock investment alternatives, Stock A, Stock B and Stock C. Given the following information, please indicate which stock is (are) overvalued, which stock is (are) undervalued, and which stock is (are) correctly priced based on the required returns calculation using the Capital Asset Pricing Model (CAPM or Security Market Line=SML). The risk free rate is 3% and the risk premium for the market index return is 5%. Please Show Work Expected Stocks Returns BETA A 14% 1.2 B 8% 0.67 C 20% 2.5
The following figures show the optimal portfolio choice for two investors with different levels of risk-aversion graphically. Which statement is correct? E[R] 0.3 0.25 0.2 0.15 0.1 0.05 0 0 0.05 0.1 0.15 Figure 1 0.2 0.25 0.3 0.35 o(R) 0.4 0.45 [H]Z 0.3 0.25 0.2 0.15 0.1 0.05 0 0 0.05 0.1 Figure (2) shows an investor that borrows in risk-free rate and invests in the risky asset. Figure (1) shows an investor with a conservative investment behavior. In the optimal point of both figures, the highest indifference curve is tangent to the efficient frontier. In Figure (1), more aggressive investment decision led to a higher Sharpe ratio. 0.15 Figure 2 0.2 0.25 o (R) 0.3 0.35 0.4 0.45
You own a portfolio equally invested in a risk-free asset and two stocks. If one of the stocks has a beta of 1.23 and the total portfolio is equally as risky as the market, what must the beta be for the other stock in your portfolio? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.) Stock beta
Suppose you have the following information concerning a particular options.Stock price, S = RM 21Exercise price, K = RM 20Interest rate, r = 0.08Maturity, T = 180 days = 0.5Standard deviation,= 0.5 a. What is correct of the call options using Black-Scholes model? * Look for N(d1) and N(d2) from the cumulative standard normal distribution table:
Find the weights of the two pure factor portfolios constructed from the following three securities: r1 = .06 + 2F¡ + 2F, r2 = .05 + 3F, + IF, r3 = .04 + 3F, + OF, Then write out the factor equations for the two pure factor portfolios, and determine their risk premiums. Assume a risk-free rate that is implied by the factor equations and no arbitrage.
You hold 5% of your equity in stock A, 20% of your equity in stock B, and 75% of your equity in Stock C. You rebalance and tilt your portfolio towards stock A with a tilt size of 0.04. (A) What are the weights of the tilted portfolio? (B) Delever the tilted portfolio to create a position with zero risk-free weight that has the same Sharpe ratio as the tilted portfolio. Specify the portfolio weights of the delevered portfolio.
(Portfolio VaR) 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.
ou own a portfolio equally invested in a risk-free asset and two stocks (If one of the stocks has a beta of 1.41 and the total portfolio is equally as risky as the market, what must the beta be for the other stock in your portfolio? ( Hint: Remember that the market has a Beta = 1; also remember that equally invested means that each asset has the same weight - since there are 3 assets, each asset's weight is 1/3 or 0.3333. Use 0.333333, and not only 0.33, sorry, calculation is sensitive to it). Enter the answer with 4 decimals (e.g. 1.1234)

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