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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.
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- 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).In 1973, Fischer Black and Myron Scholes developed the Black-Scholes option pricing model (OPM). (1) What assumptions underlie the OPM? (2) Write out the three equations that constitute the model. (3) According to the OPM, what is the value of a call option with the following characteristics? Stock price = 27.00 Strike price = 25.00 Time to expiration = 6 months = 0.5 years Risk-free rate = 6.0% Stock return standard deviation = 0.49Ms. B has $1000 to invest. She is considering investing in the common stock of company M. In addition, Ms. B will either borrow or lend at the risk-free rate. Ms. B decide to invest $350 in common stock of company M and $650 placed in the risk- free asset. The relevant parameters are 1) What is the expected return? 2) What is the variance of the portfolio? 3) What is the standard deviation of the portfolio?
- As an option trader, you are constantly looking for opportunities to make an arbitrage transaction (that is, a trade in which you do not need to commit your own capital or take any risk but can still make a profit). Suppose you observe the following prices for options on DRKC Co. stock: $3.18 for a call with an exercise price of $60, and $3.38 for a put with an exercise price of $60. Both options expire in exactly six months, and the price of a six-month T-bill is $97.00 (for face value of $100). a. Using the put-call-spot parity condition, demonstrate graphically how you could synthetically re-create the payoff structure of a share of DRKC stock in six months, using a combination of puts, calls, and T-bills transacted today. b. Given the current market prices for the two options and the T-bill, calculate the no-arbitrage price of a share of DRKC stock. c. If the actual market price of DRKC stock is $60, demonstrate the arbitrage transaction you could create to…Explain how a financial market operates? Which of the investment constraints is expected to have the most impact on your decision process? You plan to buy common stock and hold it for one year. You expect to receive both ₱150 and ₱260 from the sale of the stock at the end of the year. How much will you pay for the stock, if you want to a. Have a return of 8% b. A return of 20% c. A return of 15%Consider a two-state outcome for the following problem: Winterhold Publishing House Current Stock Price $25.00 Exercise Price $27.00 Risk-free Rate 0.05 Share Price, High $30.00 Share Price, Low $20.00 Required: Using the data above, please find the hedge ratio. You currently own several shares of this company. The purchase puts according to the Hedge ratio to construct a non-random portfolio. Show the payoff for both outcomes, then solve for present value and the price of the put.
- Assume that you are using the Capital Asset Pricing Model (CAPM) to find the expected return for a share of common stock. Your research shows the following: Beta = βi = 1.54 Risk free rate = Rf = 2.5% per year Market return = E(RM) = 6.5% per year Based on this information, answer the following: A. Based on the beta, how does the stock's risk compare to the market overall? On what do you base your answer? B. Based on the beta, how would you expect the stock's returns to react to a decrease in returns in the market overall? Why? C. According to the CAPM and the information given above, what is the expected return E(Ri) for this stock? D. If the required rate of return on this stock were 7% per year, would you invest? Why or why not?Suppose the 1-year futures price on a stock-index portfolio is 1,914, the stock index currently is 1,900, the 1-year risk-free interest rate is 3%, and the year-end dividend that will be paid on a $1,900 investment in the market index portfolio is $40.a. By how much is the contract mispriced?b. Formulate a zero-net-investment arbitrage portfolio and show that you can lock in riskless profits equal to the futures mispricing.c. Now assume (as is true for small investors) that if you short sell the stocks in the market index, the proceeds of the short sale are kept with the broker, and you do not receive any interest income on the funds. Is there still an arbitrage opportunity (assuming that you don’t already own the shares in the index)? Explain.d. Given the short-sale rules, what is the no-arbitrage band for the stock-futures price relation-ship? That is, given a stock index of 1,900, how high and how low can the futures price be without giving rise to arbitrage opportunities?You are considering an investment in Justus Corporation's stock, which is expected to pay a dividend of $2.00 a share at the end of the year (D1 = $2.00) and has a beta of 0.9. The risk-free rate is 3.1%, and the market risk premium is 4.0%. Justus currently sells for $31.00 a share, and its dividend is expected to grow at some constant rate, g. Assuming the market is in equilibrium, what does the market believe will be the stock price at the end of 3 years? Do not round intermediate calculations. Round your answer to the nearest cent.
- You are considering an investment in Justus Corporation's stock, which is expected to pay a dividend of $2.00 a share at the end of the year (D1 = $2.00) and has a beta of 0.9. The risk-free rate is 5.9%, and the market risk premium is 4.0%. Justus currently sells for $45.00 a share, and its dividend is expected to grow at some constant rate, g. Assuming the market is in equilibrium, what does the market believe will be the stock price at the end of 3 years? (That is, what is ?) Round your answer to two decimal places. Do not round your intermediate calculations.You are considering an investment in Justus Corporation's stock, which is expected to pay a dividend of $3.00 a share at the end of the year (D1 = $3.00) and has a beta of 0.9. The risk-free rate is 5.0%, and the market risk premium is 5.5%. Justus currently sells for $47.00 a share, and its dividend is expected to grow at some constant rate, g. Assuming the market is in equilibrium, what does the market believe will be the stock price at the end of 3 years? (That is, what is ?) Do not round intermediate calculations. Round your answer to the nearest cent. $ Holtzman Clothiers's stock currently sells for $25.00 a share. It just paid a dividend of $3.25 a share (i.e., D0 = $3.25). The dividend is expected to grow at a constant rate of 9% a year. What stock price is expected 1 year from now? Round your answer to two decimal places.$ What is the required rate of return? Do not round intermediate calculations. Round your answer to two decimal places. %You are considering an investment in Justus Corporation's stock, which is expected to pay a dividend of $3.00 a share at the end of the year (D1 = $3.00) and has a beta of 0.9. The risk-free rate is 5.0%, and the market risk premium is 5.5%. Justus currently sells for $47.00 a share, and its dividend is expected to grow at some constant rate, g. Assuming the market is in equilibrium, what does the market believe will be the stock price at the end of 3 years? (That is, what is ?) Do not round intermediate calculations. Round your answer to the nearest cent. $ Holtzman Clothiers's stock currently sells for $25.00 a share. It just paid a dividend of $3.25 a share (i.e., D0 = $3.25). The dividend is expected to grow at a constant rate of 9% a year. What stock price is expected 1 year from now? Round your answer to two decimal places.$
