The dividend yield of a portfolio of shares with current price of £673,000 is 2.8% pa payable continuously. Calculate the forward price of a one-year forward contract, based on the portfolio, if we assume dividends are received continuously and the risk - free rate of interest is 4.6028% pa effective.

The dividend yield of a portfolio of shares with current price of £673,000 is 2.8% pa payable continuously. Calculate the forward price of a one-year forward contract, based on the portfolio, if we assume dividends are received continuously and the risk - free rate of interest is 4.6028% pa effective.

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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A one-year long forward contract on a dividend-paying stock is entered into, when the stock price is $40 and the risk-free rate of interest is 10% per annum with continuous compounding. The dividend yield on the index is 2% per annum with continuous compounding. What are the forward price and the initial value of the forward contract?
A stock has a current price of 50. The continuously compounded risk - free interest rate is 8%. The stock is going to pay a dividend of 0.5 one month from now and another dividend of 1 five months from now. Suppose that the market prepaid forward price of a prepaid forward contract that delivers one share after 6 months is 49. Construct an arbitrage portfolio and give the arbitrage profit.
The market price of a security is $50. Its expected rate of return is 14%. The risk-free rate is 6%, and the market risk premium is 8.5%. What will be the market price of the security if its correlation coefficient with the market portfolio doubles (and all other variables remain unchanged)? Assume that the stock is expected to pay a constant dividend in perpetuity.
You observe that the settlement price of a one-year futures contract for 1 share of a dividend paying stock is currently at $52. The current stock price is $50 and the risk-free interest rate is 10% p.a. (compounded annually). It is also known that the dividend yield on the stock is 4% p.a. (compounded annually). Set up a strategy to realize an arbitrage profit today and show the initial and terminal cash flows from each position taken in the strategy. Assume that investors can short-sell or buy the stock on margin and that they can borrow and lend at the risk-free rate. Thank you!
The S&P portfolio pays a dividend yield of 1% annually. Its current value is 2,000. The T-bill rate is 4%. Suppose the S&P futures price for delivery in 1 year is 2,050. Construct an arbitrage strategy to exploit the mispricing and show that your profits 1 year hence will equal the mispricing in the futures market.
The current price of a non- dividend paying stock is $38.52. Use a two-step tree to value a European call option on the stock with a strike price $32.3 that expires in 12 months. The risk free rate is 9.9% per annum, and the volatility is 28.1 % . What is the option price?
Suppose XYZ stock pays no dividends and has a current price of $50. The forward price for delivery in 1 year is $55. Suppose the 1-year eective annual interest rate is 10%. (a) Graph the payo and prot diagrams for a forward contract on XYZ stock with a forward price of $55. (b) Is there any advantage to investing in the stock or the forward contract? Why? (c) Suppose XYZ paid a dividend of $2 per year and everything else stayed the same. Now is there any advantage to investing in the stock or the forward contract? Why?
The current stock price is $20, the risk - free interest rate is 5% per annum (consecutive compounding), and the volatility is 15% per annum. Calculate the price of a European call option with a maturity of 3 months and an exercise price of $21. However, this stock is assumed to be non - dividend.
Suppose that the risk-free interest rate is 6% per annum with continuous compounding and that the dividend yield on a stock index is 4% per annum. The index is standing at 400, and the futures price for a contract deliverable in four months is 405. What arbitrage opportunities does this create?
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?
The market price of a security is $27. Its expected rate of return is 13.1%. The risk-free rate is 5%, and the market risk premium is 9.1%. What will be the market price of the security if its correlation coefficient with the market portfolio doubles (and all other variables remain unchanged)? Assume that the stock is expected to pay a constant dividend in perpetuity (round answer to 2 decimal places).
A stock has a current price of $67. An option on this stock that expires in six months has an exercise price of $65. The stock will pay a dividend of $5 in three months. Assume an annualized volatility of 30% and a continuously compounded risk - free rate of 5% per annum. Use the Black - Sholes - Merton model to price this option. 1) Suppose the option is a European put. Calculate the value of the put. 2) Suppose this option is an American call. Use Black's approximation to calculate the value of this call.

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