2. Two-step Binomial Tree St=100 Step: n=0 Su=105 Sd=95.23 n=1 Suu=110.25 Sud=Sdu=100 Sdd-90.70 n=2 Consider the above two-step binomial tree, with each step being three months, At-0.25. The stock price is shown on the tree. The annual risk-free rate is 5%. u= Su/St=1.05, d=1/u. There is no dividend from the stock. 1) Consider an at-the-money European call option (S-K) with six-month maturity a) What is the payoff to this call option at the expiration date at each possible stock price? b) Calculate the call option fair value today. 2) Consider a European put option with six-month maturity and a strike price of $90. a) What is the payoff to this put option at the expiration date at each possible stock price? b) Calculate the put option fair value today.

2. Two-step Binomial Tree St=100 Step: n=0 Su=105 Sd=95.23 n=1 Suu=110.25 Sud=Sdu=100 Sdd-90.70 n=2 Consider the above two-step binomial tree, with each step being three months, At-0.25. The stock price is shown on the tree. The annual risk-free rate is 5%. u= Su/St=1.05, d=1/u. There is no dividend from the stock. 1) Consider an at-the-money European call option (S-K) with six-month maturity a) What is the payoff to this call option at the expiration date at each possible stock price? b) Calculate the call option fair value today. 2) Consider a European put option with six-month maturity and a strike price of $90. a) What is the payoff to this put option at the expiration date at each possible stock price? b) Calculate the put option fair value today.

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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6. Suppose that the simple annual returns on an investment over a 3-year period are: 8%, 2%, and 12%. What is the closest to the annualised holding period return? (a) 22.0% (b) 7.25% (c) 7.33% (d) 23.4% 7. A stock is currently trading at 20. Assume that at the end of one month it will either be 23 or 17. The risk-free interest rate is 5% per annum. The value of an ATM put option with a maturity of 1 month is closest to (a) 0.55 (b) 0.95 (c) 1.45 (d) 3.00
Stock X has a 10.0% expected return, a beta coefficient of 0.9, and a 30% standard deviation of expected returns. Stock Y has a 12.5% expected return, a beta coefficient of 1.2, and a 25% standard deviation. The risk-free rate is 6%, and the market risk premium is 5%. a. Calculate each stock's coefficient of variation. Do not round intermediate calculations. Round your answers to two decimal places. CVx= CVy= 2
I. Consider the following information about K oll and Nell for one-time period: Suppose that the correlation coefficient between the returns for Koll and Nell is -0.40'. If you invest 30% in Koll and 70% in Nell, what are the expected return and standard deviation of the portfolio? Interpret your results. II. The investor achieved the following annual rate of returns over the last four-year period: 25% in Y1, 15% in Y2, 20% in Y3, 10% in Y4. (a) Calculate the geometric average rate of return for the whole 4 year period. (b) Calculate the logarithmic average rate of return for the whole 4 year period. III. Suppose you have a portfolio of IBM and Dell with a beta of 0.4 and 1.1, respectively. If you put 40% of your money in IBM, 55% in Dell and 5% in the risk-free asset, calculate and interpret the beta of your portfolio. IV. Suppose that the beta value for Kei is 1.5, and the risk-free rate of interest is 4%. The investor wishes to (i) have a shareholding in only one company, Kei, and…
Suppose you are attempting to value a 1-year expiration option on a stock with volatility (i.e., annualized standard deviation) of σ = 0.34. What would be the appropriate values for u and d if your binomial model is set up using: 1 period of 1 year. 4 subperiods, each 3 months. 12 subperiods, each 1 month.
Consider the following information on a particular stock:Stock price = $88Exercise price = $84Risk-free rate = 5% per year, compounded continuouslyMaturity = 11 monthsStandard deviation =53% per year. What What is the delta of a call option?
Paycheck, Inc. has a beta of 1.33. If the market return is expected to be 12.70 percent and the risk-free rate is 7.70 percent, what is Paycheck's risk premium? (Round your answer to 2 decimal places.) Paycheck's risk premium %
1. HEJO company has the current stock price of $20 today. Use a 1 step binomial tree to estimate the price of a oneyear call on thisstock. Assume the price can increase or decrease by 10% in in the next year with equal likelihood. Risk free rate is 2%, the strike is $21. A. Find the hedge ratio(H), (make sure have the correct sign, this will be written out as a decimal B) Find the call's value or price today Note: Show the calculation without using excel.
(Computing rates of return) From the following price data, compute the annual rates of return for Asman and Salinas. Time 1 2 3 12 4 14 (Click on the icon in order to copy its contents into a spreadsheet.) How would you interpret the meaning of the annual rates of return? Asman $9 11 Salinas $30 27 32 36 The rate of return you would have earned on Asman stock from time 1 to time 2 is %. (Round to two decimal places.)
6. You are given the following information: Return on three month T - bills - 6% Expected return on S&P 500 = 9% Draw the security - market line. Calculate the expected rate of return on a stock with a beta equal to 1.5.
The risk-free rate is 3.7% and you believe that the S&P 500's excess return will be 11% over the next year. If you invest in a stock with a beta of 1 (and a standard deviation of 30%), what is your best guess as to its expected excess return over the next year? Question content area bottom Part 1 The expected excess return over the next year is enter your response here %. (Round to two decimal places.)
You are given the following partial covariance and correlation tables from historical data: Securities J K Market Securities J K Market 1.24 1.11 1.17 1.03 Covariance Matrix K 0.90 J 0.0020480 0.0021600 Also, you have estimated that the market's standard deviation is 4.3 percent. For the coming year, the expected return on the market is 14.0 percent and the risk-free rate is expected to be 4.0 percent. Given this information, determine the beta for Security K for the coming year, assuming CAPM is the correct model for required returns. Correlation Matrix K 0.60 1.00 0.90 1.00 0.60 0.80 Market 0.0020480 0.0021600 Market 0.80 0.90 1.00 Ston sharing Hidel lines We
6. Create a spreadsheet modeling trajectories of geometric Brownian motion starting at 50 with growth Rate 5 percent (it is also risk-free rate) and volatility 25 percent. Make a spreadsheet that calculates European calls maturing in 1 year with strikes 50 and 51 on non-dividend paying stock using Monte- Carlo method and using 20,000 trajectories with 250 steps in each trajectory. Compare Monte-Carlo price with 20,000 trajectories to theoretical model price.

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