You are managing a pension fund with a value of $590 million and a beta of 1.20. You are concerned about a market decline and wish to hedge the portfolio. You have decided to use SPX calls. How many contracts do you need if the delta of the call option is 0.64 and the S&P Index is currently at 1250? (Do not round intermediate calculations. A negative value should be indicated by a minus sign. Round your answer to the nearest whole number.)

You are managing a pension fund with a value of $590 million and a beta of 1.20. You are concerned about a market decline and wish to hedge the portfolio. You have decided to use SPX calls. How many contracts do you need if the delta of the call option is 0.64 and the S&P Index is currently at 1250? (Do not round intermediate calculations. A negative value should be indicated by a minus sign. Round your answer to the nearest whole number.)

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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Suppose you are a seller . At time t = 0 you get £C from the buyer where C is the risk-neutral price of the option. You then have to design a hedging strategy which would allow you to meet your financial obligation in one year’s time. Your portfolio should consist of two investments: you are allowed to buy the underlying shares and to deposit money in the bank. The price of the share evolves according to a geometric Brownian motion. State the formulae you will need to compute the number of shares in the portfolio and the capital deposited in the bank at any time t, 0 ≤ t ≤ 1.
You are managing a pension fund with a value of $300 million and a beta of 1.07. You are concerned about a market decline and wish to hedge the portfolio. You have decided to use SPX calls. How many contracts do you need if the delta of the call option is .62 and the S&P index is currently at 2,030?
You want to use S&P 500 index options to hedge your portfolio. • Portfolio has a beta of -1.0. • It is currently worth $500,000 and index stands at 1000. • The risk-free rate is 0% per annum. • There is no dividend yield on both the portfolio and the index. 1) What option contracts would you consider? 2) How many option contracts should be purchased? 3) What strike price should we consider for insurance against the portfolio value falling below $450,000 in three months? 4) What happens if index level turns out to be 1200 after three months?
You want to create a portfolio equally as risky as the market, and you have $1,000,000 to invest. Given this information, fill in the rest of the following table: (Do not round intermediate calculations. Round the final answers to the nearest whole number. Do not leave any empty spaces; input a O wherever it is required. Omit $ sign in your response.) Asset Stock A Stock B Stock C Risk-free asset Investment $197,000 $308,000 +A $ +A $ Beta 0.80 1.13 1.29
You want to create a portfolio equally as risky as the market, and you have $1,200,000 to invest. Consider the following information: Asset Investment Beta Stock A $300,000 0.70 Stock B $360,000 1.25 Stock C 1.55 Risk-free asset Required: (a) What is the investment in Stock C? (Do not round your intermediate calculations.) (b) What is the investment in risk-free asset? (Do not round your intermediate calculations.)
You want to create a portfolio equally as risky as the market, and you have $ 1,000,000 to invest. Given this information, fill in the rest of the following table: (Do not round intermediate calculations. Round the final answers to the nearest whole number. Do not leave any empty spaces; input a 0 wherever it is required. Omit $ sign in your response.) Asset Investment Beta Stock A $200,000 0.80 Stock B $ 305,000 1.13 Stock C $ 1.29 Risk - free asset Ś
You want to create a portfolio equally as risky as the market, and you have $500,000 to invest. Information about the possible investments is given below: Asset Investment Beta Stock A $ 147,000 .92 Stock B $ 133,000 1.37 Stock C 1.52 Risk - free asset How much will you invest in Stock C? How much will you invest in the risk - free asset? Note: Do not round intermediate calculations and round your answers to 2 decimal places, e.g., 32.16.
a) The cost of a portfolio consisting of a long position in a call option with strike price 50 and a short position in a call option with strike price 80 is zero (both call options are on the same stock and have the same maturity date). True or false? Explain. b) Carefully draw the payoff diagram of a portfolio consisting of a long position in two call options with exercise price ?, a short position in five call options with exercise price 2? and a long position in four call options with exercise price 3?. All options have the same maturity date and the same underlying stock. What reasons could a speculator have for holding such a portfolio (explain in detail)?
Assume that you manage a $10.00 million mutual fund that has a beta of 1.25 and a 9.50% required return. The risk-free rate is 2.20%. You now receive another $15.00 million, which you invest in stocks with an average beta of 0.80. What is the required rate of return on the new portfolio? (Hint: You must first find the market risk premium, then find the new portfolio beta.) Do not round your intermediate calculations. a. 9.17% b. 8.71% c. 7.92% d. 7.45% e. 9.65%
Consider a put option on a stock that curretly sclls for £100, but may rise to £120 or fall to £80 after 1 year. The risk free rate of return is 10%, and the exercise price is £90. (a) Calculate the value of the put option using the risk-neutral valuation relationship (RNVR). Explain the reasoning behind your calculations. (b) Calculate the value of the put option by using first principles (No Arbitrage prin- ciples). Explain the reasoning behind your calculations. (c) What is the price of a call option on the same stock with the same exercise price and the same expiration date? Explain the reasoning behind your calculations.
An investor must decide between two alternative investments—stocks and bonds. The return for each investment, given two future economic conditions, is shown in the following payoff table: Economic Conditions Investment Good Bad Stocks $10,000 $- 4,000 Bonds 7,000 2,000 What probability for each economic condition would make the investor indifferent to the choice between stocks and bonds?
The hedge ratio of an at-the-money call option on IBM is 0.36. The hedge ratio of an at-the-money put option is -0.64. What is the hedge ratio of an at-the-money straddle position on IBM? (Negative answer should be indicated by a minus sign. Round your answe to 2 decimal places.) Hedge ratio

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