EFN515: Financial and Economic Modelling

Assignment 1 Semester 2, 2020

Question One: Time series regression. Datasets includes Monthly returns for the Dow-

Jones 30 Industrials and the S&P 500 for July 1997–July 2007.

a. Calculate the continuous monthly returns for D-J30 and S&P 500. Construct and comment

on the return time series. (4 marks)

b. Use the functions match () and offset () to compare the distributions of returns on the S&P

500 for three periods: the second half of 1999, the second half of 2003, and the second

half of 2006. For the same periods calculate descriptive statistics (mean, standard

deviation, min, max, skewness). Comment on the results. (3 marks)

c. The test of CAPM is based on the time series regressions introduced by Black et al (1972).

Regress the monthly returns of each of the stocks on the S&P 500 using the following

equation:

, = + , + ,

Compute the slope, intercept, R2, and t-statistics for the slope and intercept.

Comment on the results. (4 marks)

d. Conduct a second-pass regression: Regress the expected return of each stock on its beta and

test the validity of CAPM, using the following equation:

= 0 + 1 +

Comment on your result and provide your own thought on the validity of the TEST.

(4 marks)

e. CAPM hypothesis holds true when the returns and betas are linearly related with each

other, which means that the slope 2 should be equal to zero. Extend part c by running a

test of non-linearity between the stock returns and their individual betas using the following

equation:

= 0 + 1 + 2

2 +

Comment on your results. (3 marks)

Total Marks for Question 1 is 18. Each question has the number of marks identified

Question Two: Simulation

The Company A. would like to restart production and sale of a specific new product from

Jan. next year. It makes the following assumptions about the project.

• The product’s price is constant and equal to $750 per unit.

• The number of units sold per month follows a normal distribution with μ=1,500 and

σ=700.

• 20-50 percent of the payments will come in the same month as the sale. The rest will

come the next month.

• Material cost per unit in a given month will be $320 if sales are less than 800 units

that month, $290 if the sales are between 800 and 1,200 units. $270 if the sales are

between 1,200 and 1,600 units, $250 if the sales are between 1,600 and 2,000 units,

and $235 if the sales are more than 2,000 units.

• Variable cost that comes in addition to material costs is 12 percent of the monthly

sales.

• Fixed cost per month is $200,000 if the sales are less than 1,700 units. Otherwise

fixed cost per month is $250,000.

• Wage cost is $300,000 per month. From May the wage cost will increase by

1,2,3,4,5,6 or 7 percent. The probabilities for these outcomes are defined by a

binomial distribution with p=0.55.

• Taxes are paid with $75,000 in Jun. and $85,000 in December.

Use simulation to address the following questions.

a. Simulate a yearly cash budget for Company A. 2000 times and calculated the

probability of a liquidity surplus after one year. (3 marks)

b. Assume that the Company A. required rate of return is 10 percent p.a. Calculate

the probability of accepting the project using an appropriate NPV analysis and

draw a probability distribution for the NPV based on your simulation.

(3 marks)

c. Suppose that the product price is nonconstant and it is driven by the market

condition, where a low, median and high level of demand with their corresponding

probabilities of 20 percent, 30 percent and 50 percent. The product price given

these individual market condition probabilities is estimated as:

1,000*exp(-p)

Re-evaluate the probability of accepting the project using the expected price.

(4 marks)

Total Marks for Question 2 is 10. Each question has the number of marks identified

Question Three: Investment strategy. Datasets includes Monthly returns for Company A, B, C,

D and E for January 2009–September 2019.

It is the beginning of 2020. You are debating between passive and active portfolio

investment strategies.

• Passive investment strategy: you buy and hold 5 stocks equally weighted to

form your market portfolio till the end of the year, replicating the performance

of the market index.

• Active investment strategy: you trade actively and rebalance your stock weights

in your portfolio frequently given individual stock performance.

The return of Market Index is normally distributed with a mean return of 20% and standard

deviation of 30%. Historical data for each of the five stocks that are heavily weighted in

the Market Index are given. Assume that there are no transaction costs. The value of the

initial investment is $100 million. No dividend paid throughout the year.

Part A. If you are after the passive investment strategy, use the market index to answer

the following questions.

a. What is the distribution of the end-of-year portfolio value? (2 marks)

b. What is the probability of a loss of more than $20 million by the end of year?

(2 marks)

c. With 1 percent probability what is the maximum loss at the end of year? (The VaR

at 1 percent) (2 marks)

Part B. Compare the passive investment strategy to active investment strategy.

Addressing the following problems using simulations.

a. Suppose that in accordance with the active investment strategy, you rebalance your

portfolio every month by sorting out the individual stock’s performance and choose

the top three to form your portfolio (3 stocks are equally weighted in this case). Set

up 2000 simulations to evaluate the performance of both investment strategies in

terms of expected return and standard deviation. (Excel built in function: Rank (),

offset () and match () may be helpful). (3 marks)

b. Calculate the probability that the active investment strategy outperforms the passive

investment strategy. (3 marks)

Total Marks for Question 3 is 12. Each question has the number of marks identified