1. Chloe plans to invest some of her savings into two blue-chip stocks, namely Stock A and Stock B. Suppose that the mean and standard deviation of the annual return of Stock A are 5% and 5%, respectively, and the mean and standard deviation for the annual return of Stock B are 10% and 10%, respectively. In this investment portfolio, Chloe will put 50% of her money into Stock A and 50% of her money into Stock B.

   1. (i) [3 marks] If the correlation coefficient of the two stock returns is -0.2, do you think that this investment portfolio can achieve diversification? (for this one, i think corr is the indicator of diversification, in this question, Corr=-0.2<0, which means achieve diversification. But the answer gives: "V[R]=26.25, cannot achieve portfolio diversification". please help, thx!

   2. (ii) [1 bonus mark] In order to achieve portfolio diversification, what advice will you give Chloe?

The Bogard Corporation produces three types of bookcases, which it sells to large office supply companies. The production of each bookcase requires two machine operations, trimming and shaping, followed by assembly, which includes inspection and packaging. Each type requires 0.4 hours of assembly time, but the machining operations have different processing times, as shown in the table below (in hours per unit). Each machine is available for 150 hours per month, and the current size of the assembly department provides capacity of 200 hours. Each bookcase produced yields a unit profit contribution as shown below.

Standard Narrow Wide

Trimmer 0.2 0.4 0.6

Shaper 0.6 0.2 0.5

Profit $8 $6 $10

Write a linear optimization model (i.e., identify decision variables, objective function and constraints)

Assume that the real risk-free rate of return, r*, is 1%, and it will remain at that level far into the future. Also assume that maturity risk premium on Treasury bonds increase from zero for bonds that mature in one year or less to a maximum of 2%, and MRP increases by 0.2% for each year to maturity that is greater than one year – that is, MRP equals 0.2% for two-year bond, 0.4% for a three-year bond, and so forth. Following are the expected inflation rates for the next five years:

Compute the interest rate for 1, 2, 3, and 4-year bond.

If inflation is expected to equal 3% every year after 2021, what should the interest rate be for 5- through 20-year bond?

Draw a graph of the yield curve.

Table below shows monthly beer sales at Gordon’s Liquor Store in 2017.

The sales manager had predicted that January 2017 beer sales would be 950.

• Forecast beer sales needed for January 2018 using the moving average with 3 periods.

• Forecast beer sales needed for January 2018 using an exponential smoothing method with α = 0.2 and α = 0.9

• What is the best method to forecast the beer sales according to MSE. (moving average with 3 periods, exponential smoothing method with α = 0.2, or exponential smoothing method with α = 0.9)

Northwood Company manufactures basketballs. The company has a ball that sells for $32. At present, the ball is manufactured in a small plant that relies heavily on direct labor workers. Thus, variable expenses are high, totaling $22 per ball, of which 69% is direct labor cost. Last year, the company sold 30,000 of these balls, with the following results: Sales (30,000 balls) $ 960,000

Variable expenses 660,500

Contribution margin 300,000

Fixed expenses 210,000

Net operating income $ 90,000

Required: 5. Refer to the original data. The company is discussing the construction of a new, automated manufacturing plant. The new plant would slash variable expenses per ball by 31.25%, but it would cause fixed expenses per year to DOUBLE. If the new plant is built, what would be the company’s new break-even point in balls? (Do not round intermediate calculations.) 6. Refer to the data in (5) above. a. If the new plant is built, how many balls will have to be sold next year to earn the same net operating income, $90,000, as last year? (Do not round intermediate calculations.) b-1. Assume the new plant is built and that next year the company manufactures and sells 30,000 balls (the same number as sold last year). Prepare a contribution format income statement (Do not round your intermediate calculations.) b-2. Compute the degree of operating leverage. (Do not round intermediate calculations and round your final answer to 2 decimal places.)

Suppose a batch of metal shafts produced in a manufacturing company have a variance of 6.25 and a mean diameter of 206 inches.

If 90 shafts are sampled at random from the batch, what is the probability that the mean diameter of the sample shafts would differ from the population mean by more than 0.3 inches? Round your answer to four decimal places.

Let the number of tropical cyclones per year in the Atlantic Basin (?) have a discrete uniform between 5 to 15; i.e. ? ∈ {5, 6, … , 15} with ?_X(?) = 1 /11. If each cyclone can turn into a major hurricane with probability 0.3; find the expected number of major hurricanes per year (?). Hint: Use the Law of Interated Expectation; ?[?] = ?[?[?|?]].

The average number of mosquitos in a stagnant pond is 80 per square meter with astandard deviation of 12. If 36 square meters are chosen at random for a mosquitocount, find the probability that the average of those counts is more than 81.6 mosquitosper square meter. Assume that the variable is normally distributed.

A)0.3%B)21.2%C)78.8%D)28.8%

Estimate the heat loss rate from a person who can be approximated as a cylinder of diameter 0.3 m and height 1.8 m. The (clothing) surface temperature is 23 °C and the cross wind flow velocity is 15 m/s. The ambient temperature is –23 °C. Neglect end effects from the cylinder. Assume steady state.