1. Frane Ltd has available two investment opportunities with the following risk return
characteristics

Frane Ltd plans to invest 65% of its available funds in Security A, and 35% in B.
The directors believe that the correlation coefficient between the returns of the
securities is +0.2.

(i) Calculate the expected return of the portfolio and the risk of the portfolio.

E(RP)=15.45%

σp= 4.18%

This one I have calculated, thank you.

(ii) Suppose the correlation coefficient between A and B was -1.0. How should Frane
Ltd invest its funds in order to obtain a zero risk portfolio?

by using ( a – b )² = a²-2ab+b²

I have tried, but also don't know how to do. Thank you.

σp² = (xσA)² + [(1-x) σB]² + 2x(1-x) ρAB σAσB

= (0.65 x 0.04)² + (0.35 x 0.08)² + 2(0.65)(0.35)(-0.1)(0.04)(0.08)?

(iii) According to CAPM, “The only risk that matters to an investor is
non-diversifiable risk.” Do you agree with the comment?

2. “Both trade-off theory and pecking order theory explain why companies may differ
in their levels of gearing.” Discuss this statement.

1. Frane Ltd has available two investment opportunities with the following risk return
characteristics

Frane Ltd plans to invest 65% of its available funds in Security A, and 35% in B.
The directors believe that the correlation coefficient between the returns of the
securities is +0.2.

(i) Calculate the expected return of the portfolio and the risk of the portfolio.

E(RP)=15.45%

σp= 4.18%

This one I have calculated, thank you.

(ii) Suppose the correlation coefficient between A and B was -1.0. How should Frane
Ltd invest its funds in order to obtain a zero risk portfolio?

by using ( a – b )² = a²-2ab+b²

I have tried, but also don't know how to do. Thank you.

σp² = (xσA)² + [(1-x) σB]² + 2x(1-x) ρAB σAσB

= (0.65 x 0.04)² + (0.35 x 0.08)² + 2(0.65)(0.35)(-0.1)(0.04)(0.08)?

(iii) According to CAPM, “The only risk that matters to an investor is
non-diversifiable risk.” Do you agree with the comment?

2. “Both trade-off theory and pecking order theory explain why companies may differ
in their levels of gearing.” Discuss this statement.

Suppose you and most other investors expect the inflation rate to be 7% next year, to fall to 5% during the following year, and then to remain at a rate of 3% thereafter. Assume that the real risk-free rate, r , will remain at 2% and that maturity risk premiums on Treasury securities rise from zero on very short-term securities (those that mature in a few days) to a level of 0.2 percentage points for 1-year securities. Furthermore, maturity risk premiums increase 0.2 percentage points for each year to maturity, up to a limit of 1.0 percentage point on 5-year or longer-term T-notes and T-bonds.

a. Calculate the interest rate on 1-, 2-, 3-, 4-, 5-, 10-, and 20-year Treasury securities, and plot the yield curve.

b. Now suppose ExxonMobil’s bonds, rated AAA, have the same maturities as the Treasury bonds. As an approximation, plot an ExxonMobil yield curve on the same graph with the Treasury bond yield curve. (Hint: Think about the default risk premium on ExxonMobil’s long-term versus short-term bonds.)

c. Now plot the approximate yield curve of Long Island Lighting Company, a risky nuclear utility.

A patient is admitted to the ICU with severe necrotizing pancreatitis. A few hours after admission, he developed increasing oxygen requirements and was intubated for hypoxemic respiratory failure. Initially, his oxygen saturation improved to the mid-90% range on an FiO₂ of 0.5 (50%), but in the past 2 hours, the nurse has had to increase the FiO₂ back to 0.7 (70%) and his SaO₂ is still in the lower 90% range. The patient remains on a PEEP of 5 cmH₂O. The respiratory therapist drew an ABG which shows pH 7.35, PCO₂ 38, PO₂ 60, HCO₃ - 22 on an FiO₂ of 0.8 (80%). The patient's repeat chest x-ray is shown a "ground glass appearance". An echocardiogram performed earlier in the day revealed normal left ventricular function.

How do you explain his worsening oxygenation status?

What can you do to improve his oxygenation?

What other changes should you consider making in the ventilator settings?

If his oxygen saturation fails to improve despite being on high levels of support (i.e., FiO₂ of 1.0 and 20 cm H₂O of PEEP), what other options do you have for improving his oxygenation?

Use the data below from an electron impact mass spectrum of a pure compound to deduce its structure. Draw your structure in the drawing window.

The table below contains distance and recessional velocity data for ten galaxies.

1. a) Plot the ‘Hubble Diagram’ for these galaxies. This is simply a plot of the observed velocity on the y-axis and the distance on the x-axis.

2. b) Fit a line to the data that goes through the origin of the plot (that is, where the dis- tanceandvelocityarebothzero). TheslopeofthislineistheHubbleconstant.What is the Hubble constant for these data? NOTE: The value is not the same as the Hubble constant we are adopting in the text.

3. c) Calculate the redshift, ? = ∆?/?& for each galaxy. HINT: Go back to the definition of the Doppler effect in Destination 6 to recall what = ∆?/?& is equal to (or just look at question 1c above). You will see that have the information you need in the table above to calculate the redshift (though, strictly speaking, only for redshifts that are significantly smaller than 1.0).

4. d) Notice that galaxies 2-5 in the table are all at about the same distance, but their ve- locities differ rather significantly. Explain what is likely happening to account for this behavior.

Your friend has decided to make some money during the next State Fair by inventing a game of skill. In the game, as she has developed it so far, the customer shoots a rifle at a 5.0 cm diameter target falling straight down. Anyone who hits the target in the center wins a stuffed animal. Each shot would cost 50 cents. The rifle would be mounted on a pivot 1.0 meter above the ground so that it can point in any direction at any angle. When shooting, the customer stands 100 meters from where the target would hit the ground if the bullet misses. At the instant that the bullet is fired (with a velocity of 1200 ft/sec according to the manual), the target is released from its holder 7.0 meters above the ground. (You see, the trigger is electronically connected to the release mechanism.) Your friend asks you to try out the game which she has set up on a farm outside of town. Before you fire the gun you calculate where you should aim. You may, as usual, neglect any effects of air resistance. Your conclusion? At what angle from the vertical should you aim?

Superior Technologies Inc. sells a product at the unit price of $2,000. Its credit sales in the 2019 financial year were reported at 500 units. The variable cost per unit is $1,350. The firm is now considering a tightening of credit standards that is expected to result in the following: (1) a 10% decrease in unit sales; (2) a decrease in bad-debts expense from 2.0% to 1.0% of sales; (3) a decrease of $2,000 in collection expenses and (4) a decrease in the accounts receivable period from 60 days to 30 days. TTL’s required rate of return is 15% p.a.

Fill in the blanks A-F below to weigh up the financial costs and benefits of such decision and to determine whether the company should tighten its credit standards or not.

Do not use comma (,) or a dollar sign ($) in your answers. If the change is a positive value (benefit) enter it with a plus sign (+) and if it is a negative value (loss) enter it with a minus sign (-) WITHOUT any space between the number and the minus/plus sign. Example: if the answer is a loss of $10000, enter your answer as -10000.

Additional Profit/loss from ΔSales: $

Benefit/loss from ΔBad_Debts: $

Benefit/loss from ΔCollection_Expenses: +2000

Benefit/loss from ΔA/R: $

Δ Net Profit: $

1. What are the main data types in Python? Which data types are sequences?

2. What are some general guidelines for naming a ‘variable’ in Python? Give at least three examples of variable names that follow these guidelines

3. Provide an example of the Python syntax to create a variable to hold the age of a building (for example,40 years old).

a. Provide the Python syntax to test whether the variable created above is more than 35, and print the test result

4. What are some of the key similarities and differences between lists and tuples in Python? Give an example, using geospatial information, of when a list would be more appropriate to use and when a tuple would be a more appropriate data type?

6. Name three methods of string objects in Python, and provide an example of each one's use.

7. Given the code below: leftovers = [‘cake’,’ice cream’] t_list = [[2.5, 1.0], ‘32’, ‘alabi’, ‘Alaska’, ‘Ohio’, ‘Armenia’, 29.05, leftovers]

a. What is the ‘data type’ of the first element in t_list?

b. What is the ‘data type’ of the second t_list element?

c. What is returned by the following code snippet? print(t_list[1])

d. What is returned by the following code snippet? print(t_list[-2])

Design and construct a computer program in one of the approved languages (C, C++, C#, Java, Pascal, Python, etc.) that will illustrate the use of a fourth-order
explicit Runge-Kutta method of your own design. In other words, you will first have to solve the Runge-Kutta equations of condition for the coefficients
of a fourth-order Runge-Kutta method.

Then, you will use these coefficients in a computer program to solve the ordinary differential equation below.
Be sure to follow the documentation and programming style policies of the Computer Science Department.

The initial value problem to be solved is the following:

                          x'(t) = 3 x² cos(5 t)

subject to the initial condition:  x(0) = 1.0   

Obtain a numerical solution to this problem over the range from t=0.0 to t=2.0

for seven different values of the stepsize,

h=0.1, 0.05 , 0.025 , 0.0125 , 0.00625 , 0.003125 , and 0.0015625 .

In other words, make seven runs with 20, 40, 80, 160, 320, 640, and 1280 steps, respectively.
For each run, print out the value of h, then a table of t and x, and then the error at t=2. You may use the following
very precise value for your "true answer" in order to compute the error at t=2:   0.753913186469598763502963347.