Quantitative Methods - Distributions and Hypothesis Testing

In a discrete uniform distribution with 20 potential outcomes of integers 1 to 20, the probability that X is greater than or equal to 3 but less than 6, P(3 ≤ X < 6), is:

• 0.10.

• 0.15.

• 0.20.

A client holding a £2,000,000 portfolio wants to withdraw £90,000 in one year without invading the principal. According to Roy’s safety-first criterion, which of the following portfolio allocations is optimal?

• Allocation A.

• Allocation B.

• Allocation C.

A portfolio manager annually outperforms her benchmark 60% of the time. Assuming independent annual trials, what is the probability that she will outperform her benchmark four or more times over the next five years?

• 0.26.

• 0.34.

• 0.48.

Which of the following is characteristic of the normal distribution?

• Asymmetry

• Kurtosis of 3

• Definitive limits or boundaries

Which of the following assets most likely requires the use of a multivariate distribution for modeling returns?

• A call option on a bond

• A portfolio of technology stocks

• A stock in a market index

A portfolio has an expected mean return of 8 percent and standard deviation of 14 percent. The probability that its return falls between 8 and 11 percent is closest to:

• 8.3%

• 14.8%

• 58.3%

X is a discrete random variable with possible outcomes X = {1,2,3,4}. Three functions f(x), g(x), and h(x) are proposed to describe the probabilities of the outcomes in X.

The conditions for a probability function are satisfied by:

• f(x).

• g(x).

• h(x).

A stock is priced at $100.00 and follows a one-period binomial process with an up move that equals 1.05 and a down move that equals 0.97. If 1 million Bernoulli trials are conducted, and the average terminal stock price is $102.00, the probability of an up move (p) is closest to:

• 0.375

• 0.500

• 0.625

The lognormal distribution is a more accurate model for the distribution of stock prices than the normal distribution because stock prices are:

• symmetrical.

• unbounded.

• non-negative.

Which of the following statements about hypothesis testing is correct?

• The null hypothesis is the condition a researcher hopes to support.

• The alternative hypothesis is the proposition considered true without conclusive evidence to the contrary.

• The alternative hypothesis exhausts all potential parameter values not accounted for by the null hypothesis.