You are the new investment manager of Michael and Ariel. You received from the previous investment manager of Michael and Ariel’s partial information regarding their portfolios:
- Both have an optimal portfolio.
- The expected return in Michael’s portfolio is 6%.
- The SD in Ariel’s portfolio is 12%.
You know that the current risk-free interest rate is 5% and the market portfolio has an expected return of 8% and a SD of 10%.
a. What is the proportion of each brother’s investment in a risk-free asset out of their portfolio?

b. Is it possible to rank the brothers’ risk preference? Explain.

c. What is the beta in each brother’s portfolio?

d. Suppose that today Michael and Ariel received an offer to buy a share with an expected return of 6% and beta of 0.3. Will they accept the offer?

Suppose there is a random sample of 200 observations, divided into three groups. The table below summarizes the count of observations that were seen in each group.

We are interested in testing the null hypothesis H0:p1=0.5,p2=0.2,p3=0.3, against the alternative hypothesis HA:Atleastoneproportionisincorrect.

a) What is the value of the test statistic?

Round your response to at least 2 decimal places.

b) What conclusion can be made at the 5% level of significance?

An insurance portfolio consists of two homogeneous groups of clients; N i, (i = 1 , 2) denotes the number of claims occurred in the ith group in a fixed time period. Assume that the r.v.'s N 1, N 2 are independent and have Poisson distributions, with expected values 200 and 300, respectively.

The amount of an individual claim in the first group is a r.v. equal to either 10 or 20 with respective probabilities 0.3 and 0.7, while the amount of an individual claim in the second group equals 20 or 30 with respective probabilities 0.1 and 0.9.

Let N be the total number of claims, and let S be the total aggregate claim.

is a compound Poisson r.v. that can be written as S = ∑ i = 1 N Y i.

T or F

Suppose that

The Elasticity of Imports in the USA in the short Run is 0.5

The Elasticity of Imports in Japan in the short Run is -0.3

The Elasticity of Imports in the USA in the long Run is 1.2

According to the Elasticities approach to the Current Account Balance, if the Exchange Rate goes from Yen=$1/100 to Yen=$1/50 ...

Expected return and standard deviation. Use the following information to answer the​ questions:

a.  What is the expected return of each​ asset?

b.  What is the variance and the standard deviation of each​ asset?

c.  What is the expected return of a portfolio with 8​% in asset​ J, 46​% in asset​ K, and 46​% in asset​ L?

d.  What is the​ portfolio's variance and standard deviation using the same asset weights from part ​(c​)?

The following three games are scheduled to be played at the World Curling Championship one morning. The values in parentheses are the probabilities of each team winning their respective game.
Game 1: Finland (0.2) vs. Canada (0.8)

Game 2: USA (0.3) vs. Switzerland (0.7)

Game 3: Germany (0.4) vs. Japan (0.6)
(a) The outcome of interest is the set of winners for each of the three games. List the complete sample space of outcomes and calculate the probability of each outcome.

(b) Let X be the number of European teams that win their respective games. Find the probability distribution of X.

(c) Find the expected value and variance of X.

(d) If two European teams win their games, what is the probability that Finland is one of them?

4. You are visiting the rainforest, but unfortunately your insect repellent has run out. As a result, at each second, a mosquito lands on your neck with probability 0.5. If one lands, with probability 0.2 it bites you, and with probability 0.8 it never bothers you, independently of other mosquitoes.
a. What is the expected time between successive mosquito bites? What is the variance of the time between successive mosquito bites?
b. In addition, a tick lands on your neck with probability 0.1. If one lands, with probability 0.7 it bites you, and with probability 0.3, it never bothers you, independently of other ticks and mosquitoes. Now, what is expected time between successive bug bites? What is the variance of the time between successive bug bites?

They are all in their currency in billions and I need to make them into US dollar. Like Yen is 84.5 billion yen and also 14.2 billion yen, what are they if their converted to US dollars. Do that for all in the table below. Please show formula

The Neal company wants to estimate next year's (ROE) under different financial leverage ratios. Neal's total capital is $14million, it currently uses only common equity, it has no future plans to use preferred stock in its capital structure and its federal-plus-state tax rate is 40%. The CFO has estimated next years EBIT for three possible states of the world: $4.2 million with a 0.2 probability, $2.8 million with a 0.5 probability, and $700,000 with a 0.3 probability . Calculate Neal's expected ROE, standard deviation, and coefficient of variation for each of the following debt-to-capital ratios; then evaluate the results:

Debt/capital ratio- interest rate

0%- ----------
10- 9%
50- 11
60- 14

Consider an economy with a production function given by Y =K^1/4 (EL)^3/4 . The depreciation rate is = 0.1, the population growth rate is n = 0.02 and the technological growth rate is g = 0.03. The economy's current savings rate is s = 0.3 and the current level of capital per effective worker K₀ = 1. Answer the following questions.

1. What is the consumption per effective worker in the current year (C₀) ?
2. What is the capital per effective worker in the next period (k₁) ?
3. What is the steady state level of output per effective worker (y*) ?
4. Find the golden rule level of output per-effective worker (y_G) ?
5. Compare the economy's savings rate with the golden-rule savings rate. Is the economy saving less ?