1. Consider historical data showing that the average annual rate of return on the S&P 500 portfolio over the past 85 years has averaged roughly 8% more than the Treasury bill return and that the S&P 500 standard deviation has been about 20% per year. Assume these values are representative of investors’ expectations for future performance and that the current T-bill rate is 5%.

1. Calculate the expected return and variance of portfolios invested in T-bills and the S&P 500 index with the following weights.                         [5]

2. Calculate the utility levels of each portfolio of Problem in a) for an investor with A =2. What do you conclude? [5]

3. Repeat Problem b) for an investor with A = 3. What do you conclude? [5]

a. A decrease in the aggregate expenditures schedule causes a decline in real GDP that is greater than the decline in the aggregate expenditures schedule because

• Congress will act to lower real GDP.

• the decrease in the aggregate expenditures schedule is multiplied into a larger change in real GDP.

• consumers will decide to spend less if aggregate expenditures decline.

• people will decide to save more.

b. The magnitude of the drop in real GDP that will occur when aggregate expenditures fall depends on

• how quickly the fall in aggregate expenditures occurs.

• the time of year when aggregate expenditures fall.

• whether or not taxes change.

• the size of the marginal propensity to consume.

c. If the slope of the aggregate expenditures schedule is 0.8, what is the multiplier?

• 0.2.

• 8.

• 5.

• 2.

d. If the slope of the aggregate expenditures schedule is 0.8, and aggregate expenditures decline by $4 billion, real GDP will

• fall by $32 billion.

• rise by $0.2 billion.

• rise by $0.5 billion.

• fall by $20 billion.

How have sports changed since the 1940s? Are some of the issues raised in the film still present?

1. An air conditioner using R134a as the working fluid operates on an ideal vapour compression system between 0.3 and 0.8 MPa. If the specified capacity for air conditioning is 20 kW. What would be its capacity for food freezing for which the evaporator temperature -20^oC. Show the cycle on a PH diagram and explain the effect of the changes to the compressor and condenser respectively.

A) Suppose the probability that a mosquito dies when subjected to a 1 unit of insecticide is 0.7, and the probability that a fly dies when subjected to the same dose of insecticide is 0.5.   Assuming independence, what is the probability that both the fly and mosquito die when subjected to 1 unit of insecticide

B) Suppose A and B are events where the probability that B occurs is 0.3, and the probability that both A and B occur is 0.18. The conditional probability of A, given B, is

C) Suppose A and B are independent events, each occurring with probability 0.3 What is the probability that A does not occur and B does not occur?

D) Suppose A and B are disjoint events where A has probability 0.5 and B has probability 0.4. The probability that A or B occurs is

E) Suppose A and B are events where the conditional probability of A, given B, is 0.9, and the probability of B is 0.3. The probability that A and B both occur is

There are two assets, 1 and 2, with Betas: β₁=0.8, β₂=1.2 and Alphas: ɑ₁=0.001, ɑ₂=0.002. The variance of the respective idiosyncratic components are: σ²_ε1=0.004, σ²_ε2=0.001. The variance of the market excess return is: σ2_m=0.016. You form a portfolio P with shares of 1 and 2 equal to w₁=0.8 and w₂=0.2 respectively.

1. What is the Alpha of the portfolio (ɑ_P)?

2. What is the Beta of the portfolio (β_P)?

3. What is the variance of the portoflio idiosyncratic component (σ²_εP)?

4. What is the variance of the excess return on the portfolio?

When you order a Lyft, the probability that you get a Subaru is 0.4. Further, the probability that you get a white car is 0.3, and that you will get a white Subaru is 0.2. Find the probability that,

1. You will get a non-white, non-Subaru car
2. You will get a white, non-Subaru car

Methanol, CH₃OH, is a nonelectrolyte; ammonia, NH₃, is a weak electrolyte; and calcium hydroxide, Ca(OH)₂, is a strong electrolyte. What are the solute particles present in aqueous solutions of each compound? (Select all that apply.)

If 0.1 mol of each compound is dissolved in solution, which one contains about 0.3 mol of solute particles, which contains 0.1 mol of solute particles, and which contains somewhere between 0.1 and 0.2 mol of solute particles?