Assignment 1 for Ch 1 to Ch 4

Assignment 1 (for Ch 1 to Ch 4)

Question 1

Suppose that one investment has a mean return of 8% and a standard deviation of returns of 14%. Another investment has a mean return of 12% and a standard deviation of returns of 20%. The correlation between the investments is 0.3. Produce a chart similar to Figure 1.2, showing alternative return-risk portfolios from the two investments.

Question 2

A fund manager has maintained an actively managed portfolio with a beta of 0.2. During the last year, the risk-free rate was 5% and major equity indices performed very badly, providing returns of about ?30%. The manager produced a return of ?10% and claims that in the circumstances it was good. Discuss this claim.

Question 3

Regulators calculate that DLC bank (see Section 2.2) will report a profit that is normally distributed with a mean of $0.6 million and a standard deviation of $2.0 million. How much equity capital in addition to that in Table 2.2 should regulators require for there to be a 99.9% chance of the capital not being wiped out by losses?

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Question 4

An investment bank has been asked to underwrite an issue of 10 million shares by a company. It is trying to decide between a best-efforts deal where it charges a fee of $0.2 for each share sold and a firm-commitment deal where it buys the shares for $10 per share. For the latter deal, the bank considers that the selling price per share is either $10.8 or $9.8. What are the break-even probabilities of selling prices so that the bank is indifferent to the two deals (assume that all 10 million shares are sold out)?

Question 5

Use Table 3.1 to calculate the minimum premium an insurance company should charge for a $5 million three-year term life insurance contract issued to a man aged 60. Assume that the premium is paid at the beginning of each year and death always takes place halfway through a year. The risk-free interest rate is 6% per annum (with semi-annual compounding).

Question 6

Suppose that in a certain defined benefit pension plan

(1) Employees work for 45 years earning salaries that increase at the real rate 實 質 利 率 of 2% per year (= the nominal rate 名 義 利 率 ? the inflation rate 通 脹 率 ).

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(2) The pension fund’s income is invested in bonds, which earn the real rate of 1.5% per year.

(3) They retire with an annuity equal to 70% of their final salaries. This annuity decreases at the real rate of 1% per year.

(4) The annuities are received for 18 years.

Calculate (using a software, say Excel) the percentage R of an employee’s salary that must be contributed to the pension plan if it is to remain solvent.

Assume that the initial salary is $100,000 per year. Note that the salary of the employee makes no difference to the answer. This is because it has the effect of scaling all numbers up or down.

Do all calculations in real rather than nominal dollars. Each team is required to hand in a spreadsheet only. (Given that the required contribution rate R = 25.02%.)

Question 7

An investor buys 100 shares in a mutual fund on 1 January 2015, for $50 each. The fund earns dividends of $2 and $3 per share during 2015 and 2016. These are reinvested in the fund. The fund’s realized capital gains in 2015 and 2016 are $5 per share and $3 per share, respectively. The investor sells the shares in the fund during 2017 for $59 per share. Explain how the investor is taxed.

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Question 8

Good years are followed by equally bad years for a mutual fund. It earns +8%, –8%, +12%, –12% in successive years.

(a) What is the investor’s overall return for the four years? (b) What is the investor’s average return each year?

Form a team having 4 or 5 students (who register with the same Monday's or Friday's classes) to complete this assignment.

Please hand in a hard copy of your team work during the classes held on 29 February 2016 (Monday's classes) / 4 March 2016 (Friday's classes).

Note that this assignment carries only 5 marks out of 15 marks (the total of continuous assessment).

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