Quantitative Methods - Basics of Probability

A mutual fund has the return frequency distribution shown in the following table. Which of the following statements is correct?

• The relative frequency of the interval “–1.0 to +2.0” is 20%.

• The relative frequency of the interval “+2.0 to +5.0” is 23%.

• The cumulative relative frequency of the interval “+5.0 to +8.0” is 91.7%.

When analyzing investment returns, which of the following statements is correct?

• The geometric mean will exceed the arithmetic mean for a series with non-zero variance.

• The geometric mean measures an investment’s compound rate of growth over multiple periods.

• The arithmetic mean accurately estimates an investment’s terminal value over multiple periods.

Published ratings on stocks ranging from 1 (strong sell) to 5 (strong buy) are examples of which measurement scale?

• Ordinal

• Interval

• Nominal

For a distribution of 2,000 observations with finite variance, sample mean of 10.0%, and standard deviation of 4.0%, what is the minimum number of observations that will lie within 8.0% around the mean according to Chebyshev's Inequality?

• 720.

• 1,500.

• 1,680.

The following is a frequency polygon of monthly exchange rate changes in the US dollar/Japanese yen spot exchange rate for a four-year period. A positive change represents yen appreciation (the yen buys more dollars), and a negative change represents yen depreciation (the yen buys fewer dollars).

Based on the chart, yen appreciation:

• occurred more than 50% of the time.

• was less frequent than yen depreciation.

• in the 0.0 to 2.0 interval occurred 20% of the time.

The following table shows the annual returns for Fund Y.

The geometric mean for Fund Y is closest to:

• 14.9%

• 15.6%

• 19.5%

The following table shows various statistics for Portfolios 1, 2, and 3.

Compared with a normal distribution, the distribution of returns for Portfolio 3 most likely:

• has less weight in the tails.

• has a greater number of extreme returns.

• has fewer small deviations from its mean.

A distribution with excess kurtosis less than zero is termed:

• mesokurtic.

• leptokurtic.

• platykurtic.

An analyst develops the following covariance matrix of returns.

The correlation of returns between the hedge fund and the market index is closest to:

• 0.005.

• 0.073.

• 0.764.

An analyst produces the following joint probability function for a foreign index (FI) and a domestic index (DI).

The covariance of returns on the foreign index and the returns on the domestic index is closest to:

• 26.39.

• 26.56.

• 28.12.