Which probability model would be appropriate for modeling the price of Microsoft stock?

A. Lognormal distribution

B. Continuous uniform distribution

C. Bernoulli trial

D. Standard normal distribution

Suppose we use a binomial tree to represent the dynamics of the daily changes in the S&P 500, and the daily probability of an upward movement is p=0.5. If the daily price movements are independent, what is the probability that the S&P 500 increases three days in a row?

A. 0.500

B. 0.250

C. 0.875

D. 0.125

Suppose you manage an investment portfolio, and the distribution of the portfolio value is represented by a normal distribution. The minimum acceptable value of the portfolio is one standard deviation below the mean value. What is the shortfall risk?

A. 16%

B. 32%

C. 68%

D. 34%

Suppose you and three other finance professionals form a new wealth management firm. Each partner has a different last name (A, B, C, and D) and an equal share in the new firm. How many different ways are there to name the new firm if you use each partner's name like A, B, C, and D Associates or B, A, C, and D Associates?

A. 256

B. 12 names

C. 24 names

D. 10 names

Let A be a random variable that represents the daily outcome for the US equities market, and B is a random variable that represents the daily outcome for the European equities markets. Both random variables have three possible outcomes: up, down, or unchanged. Suppose the joint probability that both markets are up in a given day is 0.12 and the probability that the European market is up equaling 0.4. What is the probability that the US market is up given that the European market was up earlier in the same day?

A. 0.03

B. 0.30

C. 0.048

D. 0.036

Let's use the same information about the US and European equities markets from Question 5. Also, suppose the probability that the US market is up on a given day is 0.35. What is the probability that the US market or the European market is up on a given day?

A. 0.12

B. 0.63

C. 0.40

D. 0.30