Suppose a fund has a portfolio with two risky assets; stock and bond. Annual expected return of stock is 0.15 and standard deviation of 0.10 and expected return of bond is 0.08 and standard deviation of 0.07. The correlation-coefficient between stock and bond is 0.2. while t-bill has annual return of 0.03

Draw the opportunity set with 25% increment in bond fund. Also indicate the variance minimizing weight for bond and stock

Draw the optimal CAL line and calculate the sharp ratio

If the investor requires the complete portfolio standard deviation of 5%, how much of his fund to be invested in the risky portfolio (in terms of proportion, how big is y?)

1. Kiwi traders have invested in two securities traded at the Nairobi Stock Exchange (NSE). The security A Possible returns are estimated as 4%, 4.5%, 6%, 8%, 11%, 13%, 15%, 16%, 16.5% and 18%, with probabilities: 0.09, 0.07, 0.1, 0.2, 0.04, 0.03, 0.01, 0.02, 0.21 and 0. 23 respectively. Those of Security Y are estimated as 16%, 14%, 12%, 10%, 8%, 6%, 4%, 4%, 3%, and 2%, with probabilities: 0.08, 0.1, 0.07, 0.25, 0.09, 0.12, 0.03, 0.11, 0.1 and 0.05 respectively.

Required

If Kiwi trader’s portfolio formation is Ksh 300,000, committing equal amounts in each asset, determine the Portfolio risk

Consider a Solow economy with the following production function

F(K,N) = zK^(1/3)N^(2/3)

and parameters d = 0.05, s = 0.2, N0 = 100 and z = 1.0. Suppose K = 300 in period 0 and the

unit period is one year. In contrast to the standard Solow model, we assume that the population

growth rate n is no longer exogenous but rather endogenous and determined by

(1 + n) = N’/N = g(C/N) = (C/N)^3 as it is the case in the Malthusian model.

Question: Find k* the steady state per-capita capital stock, consumption per capita (c*) and output

per capita (y*).

Hooper Chemical Company, a major chemical firm that uses such raw materials as carbon and petroleum as part of its production process, is examining a plastics firm to add to its operations. Before the acquisition, the normal expected outcomes for the firm were as follows:
  

Compute the expected value, standard deviation, and coefficient of variation prior to the acquisition. (Do not round intermediate calculations. Enter your dollar answers in millions rounded to 2 decimal places (e.g., $12,300,000 should be entered as "12.30"). Round the coefficient of variation to 3 decimal places.)

Please show the calculation process in Excel, thank you

7. With the gasoline time series data from Table 8.1, show the exponential smoothing forecasts using α=0.1.

   1. Applying the MSE measure of forecast accuracy, would you prefer a smoothing

      constant of α=0.1 or α=0.2 for the gasoline sales time series?

   2. Are the results the same if you apply MAE as the measure of accuracy?

   3. What are the results if MAPE is used?

   4. Week	Sales (1000s of gallons)
      1	17
      2	21
      3	19
      4	23
      5	18
      6	16
      7	20
      8	18
      9	22
      10	20
      11	15
      12	22

Question 5.
A nailing gun produces a short, loud sound as the tool drives in a nail. The sound has an intensity
level of 136 dB at the ear of the user (0.2 m from the tool), for a duration of 0.1 s.
(a) What is the corresponding sound intensity? (1.5 marks)
(b) The tool is a good approximation to a point source of sound. What is the rate at which it
produces sound energy? (1.5 marks)
(c) How much energy would be transported to the user’s eardrum (of area 6.0 x 10-5 m2) as the
tool drives in a nail? (1.5 marks)
(d) Explain why earplugs or earmuffs are recommended to be worn when using the tool.
(0.5 mark)

The following are the data regarding quarterly sales:

1. Find the forecast value of the sales for each quarter starting with Quarter 6, by using a 4-quarter moving average.

                  Evaluate this forecasting method using MAD.

                  Evaluate this forecasting method using MSE.

                  Evaluate this forecasting method using MAPE.

                  Evaluate this forecasting method using MPE.

2. Use exponential smoothing with a smoothing constant of 0.2 and an initial value of 500 to forecast the sales for Quarter 1.

Suppose that we have a red coin and a blue coin. The red coin has probability pR = 0.1 of landing heads, and the blue coin has probability pB = 0.2 of landing heads.

(a) Write R code to generate a sequence of coin tosses, starting with the red coin, and switching coins every time a coin lands heads.

(b) Generate 1000 such sequences, each consisting of 1000 coin tosses, and use them to construct a plot of the 2.5%, 50% and 97.5% quantiles of the proportion of red coins tossed as the number of tosses increases. (c) What is the stationary distribution of colours for this process? Comment on how this experiment relates to Birkhoff’s ergodic theorem

A manufacturer of colored candies states that 13​% of the candies in a bag should be​ brown, 14​% ​yellow, 13​% ​red, 24​% ​blue, 20​% ​orange, and 16​% green. A student randomly selected a bag of colored candies. He counted the number of candies of each color and obtained the results shown in the table. Test whether the bag of colored candies follows the distribution stated above at the a=0.05 level of significance.

What is the P-value of the test? (round to three decimal places as needed)

Assume Nike is exposed to a currency portfolio weighted 50 percent in Canadian dollars and 50 percent in Mexican pesos. Nike estimates the standard deviation of quarterly percentage changes to be 4 percent for the Canadian dollar and 6 percent for the Mexican peso. Also assume that Nike estimates a correlation coefficient of 0.2 between these two currencies.
a) Calculate the portfolio’s standard deviation.
b) Assuming i) normal distribution of the quarterly percentage changes of each currency (and so the same of the portfolio as well), and ii) an expected percentage change of -1 percent for the currency portfolio, calculate the maximum one-quarter loss of the currency portfolio based on a 95 percent confidence level.