Options on the stock of a certain company

Reference no: EM13755003

Problem 1:

The following information is given about options on the stock of a certain company:

S₀ = $20, X =$20, r =5% (c.c.), T = 0.5 year, s= 0.20

No dividends are expected. One option contract is for 100 shares of the stock. All notations are used in the same way as in the Black-Scholes-Merton Model.

Answer the following questions:

1. What is the European call option price and European put option price, according to the Black-Scholes model?

2. What is the cost of buying a protective put?

3. What is the cost of writing a covered call?

4. What will be the payoff and profit of the protective put if the stock price on maturity is $16, $18, $20, $22, or $24?

Problem 2:

A stock currently sells for $50. In six months, it will either rise to $55 or decline to $45. The risk-free interest rate is 6% per year.

1. Find the value of a European call option with an exercise price of $50.

2. Find the value of a European put option with an exercise price of $50, using the binomial approach.

3. Verify the put-call parity using the results of Questions 1 and 2.

Problem 3:

An investor sold seven contracts of June/2012 corn. The price per bushel was $1.64, and each contract was for 5000 bushels. The initial margin deposit is $2000 per contract with the maintenance margin at $1250.

1. How much did the investor have to deposit on the investment?

2. The prices of the futures on the four days following the short sales were 1.60, 1.66, 1.70, and 1.75. Calculate the current balance on each of the next four days.

3. If the investor closed out her position on the fifth day, what was her final gain or loss over the five days in dollars and as a percentage of investment?

4. If the investor kept her position, and the futures price on the sixth day was 1.80, would the investor face a margin call? If yes, how much would she need to put up?

Problem 4:

Suppose the US dollar and Euro interest rate for the next one year are 1.5% and 2%, respectively. Both are annually compounded. The spot price of Euro is $1.3000, and the one-year forward price of Euro is $1.2900. Determine the correct forward price and recommend an arbitrage strategy.

Problem 5:

The following data are available relating to the performance of CSF Equity Fund and the market portfolio:

	Fund A	Fund B	Fund C	Market Portfolio
Average return	18%	12%	30%	15%
Standard deviation	25%	15%	30%	20%
Beta	1.25	0.6	2.5

The risk-free return during the sample period was 5%.

1. Calculate the performance measures of each of the funds (A, B, and C) using Sharpe's, Treynor's, and Jensen's measures. Rank the results for each of the funds.

2. Identify the fund(s) that outperformed the market using the Sharpe's ratio and Treynor's measure, respectively.

3. Are the rankings consistent? Explain any inconsistency.

Problem 6:

The following performance information given to you:

Benchmark Portfolio			Joe's Portfolio			Kim's Portfolio
	Weight	Return		Weight	Return		Weight	Return
Stocks	0.6	-5.00%	Stocks	0.5	-4.00%	Stocks	0.3	-5.00%
Bonds	0.3	3.50%	Bonds	0.2	2.50%	Bonds	0.4	3.50%
T-Bills	0.1	1.00%	Cash	0.3	1.00%	Cash	0.3	1.00%

The risk-free rate is 1% and the standard deviation for the Benchmark portfolio is 3.50%, Joe's portfolio is 5.00% and Kim's portfolio is 3.00%.

1. Compare Joe's and Kim's performance relative to the benchmark in terms of portfolio returns.

2. If they are beating the market, determine the sources of their success in terms of security selection and asset allocation.

(a) Who is superior in security selection?

(b) Who is superior in asset allocation?

Using Sharpe Index, determine which manager is performing better than the market in a risk adjusted basis.

Reference no: EM13755003

Questions Cloud

Accumulated benefits approach and projected benefits : What is the defined pension plan? Is there a difference between accumulated benefits approach and projected benefits approach in determining the amount of future benefits earned by employees under a defined benefit pension plan? Explain

Explain distinction between democrats and the republicans : The fundamental distinction between the Democrats and the Republicans during the late nineteenth century arose from differences

Forming a partnership type of business : Why would a tax payer think of forming a partnership type of business, as compared to a corporation? What do you think about general partnership, limited partnership, LLC, LLP and family partnership?

Federal taxation of wealth transfers : On December 1, 1976, Bart made a gift and claimed a $30,000 specific exemption. When Bart died in 2008, his tax base was $2,000,000. Assuming the maximum unified credit is $780,800, what is the credit available when computing Bart's estate tax is wha..

Options on the stock of a certain company : The following information is given about options on the stock of a certain company:

Discuss the transferor provisions relating to the estate tax : Discuss the transferor provisions relating to the estate tax, and provide three examples of transactions governed by the transferor provisions.

Calculate gross profit : Calculate gross profit for Jonas Co. based on the data given below:

Why did stamp act and the townshend act upset the colonists : Why did the Stamp act and the Townshend act upset the colonists?

Summary of a specific business communication technology : Write an individual 350-word summary of a specific business communication technology from the list of interests and discuss its present and potential future impact on business communication

User Account

All Pages