An investor wishes to measure the investment risk presented by an asset which has the following distribution:                   

State   Return   Probability                       

1       10%         0.5                      

2        20%        0.3

3        50%        0.2   

(i) Evaluate any three different measures of investment risk for this asset. Where necessary, you may assume a benchmark return of 25%.     

(ii) State two key properties of Value at Risk (VaR).

Let X denote the amount of space occupied by an article placed in a 1-ft³ packing container. The pdf of X is below.

f(x) =

(a) Graph the pdf.

Obtain the cdf of X.

Graph the cdf of X.

(b) What is P(X ≤ 0.65) [i.e., F(0.65)]? (Round your answer to four decimal places.)


(c) Using the cdf from (a), what is P(0.3 < X ≤ 0.65)? (Round your answer to four decimal places.)


What is P(0.3 ≤ X ≤ 0.65)? (Round your answer to four decimal places.)


(d) What is the 75th percentile of the distribution? (Round your answer to four decimal places.)


(e) Compute E(X) and σ_X. (Round your answers to four decimal places.)

(f) What is the probability that X is more than 1 standard deviation from its mean value? (Round your answer to four decimal places.)

Suppose an economy has three states: boom, normal, and recession. Assume that the probability of a boom state is 0.2, a normal state is 0.5, and a recession state is 0.3. And there are three stocks in this economy, called Alpha, Beta, and Gamma respectively. The return performance of these stocks has been summarized by the following table:

(Please show your intermediate processes, instead of just a final number for your answers. Only round your final answers to two decimal places.)

(a) What is the expected return of Stock Alpha?

(b) What is the variance of Stock Beta?

(c) What is the standard deviation of Stock Gamma?

(d) Suppose you build a portfolio by including these three stocks. The weight of Stock Alpha in your portfolio is 0.2, the weight of Stock Beta is 0.3, and the weight of Stock Gamma is 0.5. What are the expected return, variance, and standard deviation of your portfolio?

(e) Based on what you observe from the calculations and what you learned from the class, could you specify what are the characteristics of portfolios?

Question 01 (Part A)

Define the regression if the raw material used in production of a certain synthetic fiber measurement of the relative humidity the storage location and the moisture content.

1. Plot a graph Y vs. X showing these points or the graph is also called scatter diagram.
2. Calculate ∑ X, ∑ Y, ∑X2, ∑Y2, ∑XY, mean of X and mean of Y.
3. Calculate regression equation Y on X.
4. If ? = 82 find the estimated value of Y.

(PART B)

Give an example a box contain (0.75x5H) Envelops of which (0.5x5H) contain $100 in cash. (0.10x5H) contain $25 in cash rest of the envelops contain $10.

1. Construct a sample space for the different amount of money.
2. Assign the probabilities to the each sample point.
3. Find    the     probability    that     the     first    envelop     purchased     contain    less     than    $100.

The economist for the ABC Truck Manufacturing Corporation has calculated a production function for the manufacture of their medium-size trucks as follows: Q = 1.3L0.75 K 0.3 where Q is number of trucks produced per week, L is number of labor hours per day, and K is the daily usage of capital investment.

a. Does the equation exhibit increasing, constant, or decreasing returns to scale? Why? ( 5 marks)

b. How many trucks will be produced per week with the following amounts of labor and capital?

Labor Capital

100 50

120 60

150 75

200 100

300 150

c. If capital and labor both are increased by 10 percent, what will be the percentage increase in quantity produced?

d. Assume only labor increases by 10 percent. What will be the percentage increase in production? What does this result imply about marginal product?

e. Assume only capital increases by 10 percent. What will be the percentage increase in production?

f. How would your answers change if the production function were Q = 1.3L0.7 K 0.3 instead? What are the implications of this production function? ( 5 marks)

? A. B. C. D. E. 1.The amount of charge on a capacitor in an electric circuit decreases by 30% each second.

   ?    A    B    C    D    E      2. Polluted water is passed through a series of filters. Each filter removes all but 30% of the remaining impurities from the water.

   ?    A    B    C    D    E      3. In 1950, the population of a town was 3000 people. Over the course of the next 50 years, the town grew at a rate of 10% per decade.

   ?    A    B    C    D    E      4. The percent of a lake's surface covered by algae, initially at 35%, was halved each year since the passage of anti-pollution laws.

   ?    A    B    C    D    E      5. In 1950, the population of a town was 3000 people. Over the course of the next 50 years, the town grew at a rate of 250 people per year.

A. ?(?)=?(0.3)?f(x)=B(0.3)x

B. ?(?)=?(2)−?f(x)=A(2)−x

C. ?(?)=?0+??f(x)=P0+rx

D. ?(?)=?(0.7)?f(x)=B(0.7)x

E. ?(?)=?0(1+?)?f(x)=P0(1+r)x

6. In Experiment 13, the class studied the aquation of [Co(NH3)5Cl]2+. Below are sets of absorbance data taken during this study using 1.2 x 10-2 M [Co(NH3)5Cl]2+ in 0.1 and 0.3 M HNO3.

0.1 M HNO3

t (min) A @ 550 nm

15 0.346

30 0.314

40 0.300

60 0.280

75 0.264

0.3 M HNO3

t (min) A @ 550 nm

15 0.492

30 0.446

40 0.420

60 0.393

75 0.372

The first-order rate constants can be determined using the following equation ln(A-A) = -kt + ln(A0-A) where A0 is the initial absorbance at 550 nm before aquation began to occur.

A. (10 POINTS) What is the value of A? (show work)

B. (20 POINTS) Plot ln(A-A) vs. t and give the values of k and A0 for both sets of data above (attach both plots and show all work).

C. (5 POINTS) Based upon the above rate constants, by which mechanism to you believe that the aquation is occurring? Explain.

Corporate governance is the set of rules that control a company’s behavior towards its directors, managers, employees, shareholders, creditors, customers, competitors, and community. It can help control agency problems that managers may act in their own interests at the expense of stockholders

True/False

Nominal rate is the rate stated in contracts, and quoted by banks and brokers. Periodic rate is equal to nominal rate divided by the number of compounding periods per year.

True/False

Term structure of interest rate describes the relationship between interest rate and maturity. A graph of the term structure is called yield curve.

True/False

The present value of a future sum decreases as the discount rate increases or the number of periods per year decreases, other things held constant.

True/False

Two stocks can be combined to form a riskless portfolio if the correlation of -1.0. Risk is not reduced at all if the two stocks have correlation of +1.0. In general, stocks have correlation less than 1.0, so the risk is lowered but not completely eliminated.

True/False

Portfolio provides average return but much lower risk. The key is the negative correlations among individual stocks. As more stocks are added, each new stock has a smaller risk-reducing impact on the portfolio.

True/False

Using a regression to estimate beta, we run a regression with returns on the stock in question plotted on the Y axis and returns on the market portfolio plotted on the X axis. The intercept of the regression line, which measures relative volatility, is defined as the stock’s beta coefficient, or b.

True/False