Investments and Portfolio Management- Assignment Problem

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Assignment Questions:

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Q.1 James is considering investing in security A that has offered average annual return of 12% and standard deviation of 18% and security B which has offered average annual returns of 10% and standard deviation of 14% in the recent past.

(a) If the correlation between A and B is 0.35, what is the least risky combination of these two assets?

(b) James does not mind taking excess risk provided he can earn an average return of 10% from the portfolio. The returns on 90-day T-bills are around 2.50% per annum. Assuming that James can borrow and lend at the risk free rate of return, advise how much James should invest in the portfolio (comprising of security A and security B) and the risk free asset so that the combination of risky portfolio and risk free asset provides 10% return. How much would be invested in security A, security B, and the risk free asset and what would be the risk of the new portfolio?

Q.2 Read the enclosed article in the Wall Street Journal and answer (word limit maximum: 500 words) the following questions:

a) Why did Merck's price fall so significantly and which important finance theory the case relates to and why?

b) As CEO of Merck, Raymond Gilmartin made the decision to stop sales of Vioxx. Should he have withheld this information since it would have a clear negative effect on share price and he had an obligation to maximize the value of these shares?

Q.3. What is the price of a 365-day Treasury Bill with a face value of £1,000,000 and which has 59 days to maturity if it trades at a discount rate of 6.75%.

Q.4 You own the following portfolio, which is a significant part of your wealth:

My portfolio

My portfolio

 

 

 

 

 

Security

Face

Market

Term

Coupon

Yield to

 

Value

Value

(years)

paid

maturity

 

 

 

 

Annually

 

US Treasury Bill

$20,000

$19,192

1

0%

 

Corporate Bond

$67,500

$60,359.2

8

10%

12.14%

Rated Aa

 

 

 

 

 

Corporate Bond

$112,500

$89,968.9

10

12%

16.17%

Rated B

 

 

 

 

 

Corporate Bond

$37,500

$39,753.2

5

15%

13.28%

Rated Baa

 

 

 

 

 

Cash

$7,500

 

 

 

 


(a) What is the yield to maturity for the T Bill?

(b) Calculate the Macaulay duration of each of the securities, and the Macaulay duration of the portfolio?

(c) If your friend has an investment horizon of 3 years and wants to sell the portfolio at that time to use the principal + interest, what recommendations would you make regarding the composition of the portfolio?

(d) Using Excel Solver show how much would need to be invested in each instrument to obtain a portfolio Macaulay duration of 3.25 years. There are the following constraints.

1 The total investment should not change.

2 The same amount needs to be held in cash

3 A total of $100,000 market value needs to be invested in the T Bill and $20,000 in the Aa Bond.

4 Yield is maximized.

NB Work on numbers in the above portfolio table.

(e) Is default risk a major concern for this portfolio?

(f) The Baa rated bond has just been re-rated by one of the rating agencies and this has the impact of reducing its yield to maturity by 5 basis points. If at the same time there is a general change in interest rates so that yields fall across the whole of the yield curve by 20 basis points (including the rerated bond), what is the new value of the portfolio?

Reference no: EM132401037

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