Reading 8: Probability Concepts - LOS b ～ Q1-5

答案和详解如下：

1、Mital Tiene’s investment portfolio currently consists of stocks in two companies, 40 percent in Drysdahl Banking and the remaining amount in Clampett Oil. Performance measurement information for these two stocks is given in the table below:

The covariance between the two stocks is 0.001. Tiene is considering adding a third stock, Hilbilee Investors. Hilbilee Investor’s correlation coefficient with the current portfolio is 0.38.

Which of the following statements is FALSE?

A)   With Hilbilee added to the portfolio, the variance could be 0.026.

B)   As Tiene diversifies, he will reduce the portfolio's unsystematic risk.

C)   The standard deviation of returns for the current portfolio is 15.5%.

D)   The expected return of Tiene's current portfolio is approximately 14.1%.

The correct answer was A)

Since Hilbilee’s correlation coefficient with the existing portfolio is less than 1, there are benefits to diversification, and adding it to the existing portfolio would reduce the variance below the current level of 0.024. (See calculations below).

The other choices are correct.

ER_Portfolio = (w_Drysdahl * ER_Drysdahl) + (w_Clampett * ER_Clampett) = (0.40 * 10.5%) + (0.60 * 16.55%) = 14.13%.

The equation for the standard deviation = σ_1,2 = [(w₁²)(σ₁²) + (w₂²)(σ₂²) + 2w₁w₂σ₁σ₂ρ_1,2]^1/2,

Here stock 1 = Drysdahl and stock 2 = Clampett, and r_1,2 = cov_1,2 / (σ₁ * σ₂) = 0.001 / (0.085 * 0.25) = 0.047

σ_Portfolio = [(0.40² * 0.085²) + (0.60² * 0.25²) + (2 * 0.40 * 0.60 * 0.085 * 0.25 * 0.047)]^1/2 = 0.024^1/2, or 0.155 = 15.5%. (The variance is 0.024)

2、Each lottery ticket discloses the odds of winning. These odds are based on:

A)   past lottery history.

B)   a priori probability.

C)   the best estimate of the Department of Gaming.

D)   marketing principles.

The correct answer was B)

An a priori probability is based on formal reasoning rather than on historical results or subjective opinion.

3、Which of the following is an a priori probability?

A)   On a random draw, the probability of choosing a stock of a particular industry from the S& 500.

B)   A politician's opinion concerning a recession prior to an election.

C)   For a stock, based on prior patterns of up and down days, the probability of the stock having a down day tomorrow.

D)   The probability the Fed will lower interest rates prior to the end of the year.

The correct answer was A)

A priori probability is based on formal reasoning and inspection. Given the number of stocks in the airline industry in the S&500 for example, the a priori probability of selecting an airline stock would be that number divided by 500.

4、Which of the following is an empirical probability?

A)   On a random draw, the probability of choosing a stock of a particular industry from the S& 500 based on the number of firms.

B)   A politician's opinion concerning a recession prior to an election.

C)   The probability the Fed will lower interest rates prior to the end of the year.

D)   For a stock, based on prior patterns of up and down days, the probability of the stock having a down day tomorrow.

The correct answer was D)

There are three types of probabilities: a priori, empirical, and subjective. An empirical probability is calculated by analyzing past data.

5、The probabilities of earning a specified return from a portfolio are shown below:

What are the odds of earning at least 20 percent?

A)   Two to three.

B)   Three to two.

C)   Three to five.

D)   Five to three.

The correct answer was B)    

Odds are the number of successful possibilities to the number of unsuccessful possibilities:
P(E)/[1 – P(E)] or 0.6/0.4 or 3/2