FNCE401 assignment 4

Assignment 4

Instructions
Assignment 4 should be submitted after you
have completed Unit 7. This assignment is worth
15 percent of your final grade.
Assignment 4 contains six problems. The
maximum mark for each problem is noted at the beginning of the problem. This
assignment has a total of 100 marks.
Read the requirements for each problem and
plan your responses carefully. Although your responses should be concise,
ensure that you answer each of the required components as completely as
possible. If supporting calculations are required, present them in good form.
When you receive your graded assignment,
carefully review the comments the marker has made. This review component is an
important step in your learning process. If you have any questions or concerns
about the evaluation, please contact the Student Support Centre.

Problem 1 (20 marks)
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 (15 marks)
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 (15 marks)
An investor sold sevencontracts 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 (15 marks)
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 (15 marks)

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 (20 marks)

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?
3.
Using Sharpe Index, determine
which manager is performing better than the market in a risk adjusted basis.