Examen 2. Etapa 2 Quantitative Methods

A fund reports the following eight annual returns: 3.0%, 6.1%, 4.8%, 2.0%, 5.5%, 1.2%, 7.0%, and 3.5%. Using a target return of 5.0%, the sample target semideviation is closest to:

An analyst gathers five annual returns for a stock: 8.1%, 10.4%, 5.2%, 6.9%, and 2.8%. Given a coefficient of variation of 0.431, the variance of the returns is closest to:

An analyst computes a correlation coefficient of zero between the returns of two assets. Based only on this result, the analyst can most accurately conclude that the two assets:

In a typical year, 6% of division heads are dismissed for underperformance. Dismissal decisions track unit results, and 55% of units post above-average results (a ‘strong’ rating). Historically, 35% of dismissed division heads had a ‘strong’ rating. Using Bayes’ formula, the probability that a division head is dismissed given a ‘strong’ rating is closest to:

Fifty-five percent of exam candidates passed. Of those who passed, 80% studied more than 320 hours; of those who failed, 25% studied more than 320 hours. The probability that a candidate who studied more than 320 hours passed the exam is closest to:

An analyst models recovery on $100,000 of defaulted principal under two scenarios. Scenario 1 (probability 35%): recover $55,000 with probability 60% or $35,000 with probability 40%. Scenario 2 (probability 65%): recover $85,000 with probability 85% or $65,000 with probability 15%. The expected recovery is closest to:

The expected return on a random variable given that a related event has occurred is best described as a(n):

An estimator is described as unbiased if:

An analyst wants to determine whether the mean monthly return on a mid-cap equity fund is greater than 0.9%. Which of the following pairs of hypotheses is stated correctly for this test?

A researcher tests whether the mean daily trading volume of a stock exceeds 4.0 million shares. A random sample of 36 days yields a mean of 4.8 million and a sample standard deviation of 2.4 million shares. Using a 5% significance level (one-tailed critical value 1.690 for 35 degrees of freedom), the test statistic and conclusion are closest to:

An analyst compares mean returns of two equally sized portfolios and assumes equal but unknown population variances. Portfolio X: mean 12.4%, s = 3.2%, n = 25. Portfolio Y: mean 10.9%, s = 3.6%, n = 25. Testing for any difference at the 5% level (two-tailed critical value 2.011 for 48 df), the conclusion is closest to:

A risk manager tests whether the variance of a fund’s returns exceeds 25 (standard deviation of 5%). A sample of 30 observations produces a sample variance of 36. At the 5% significance level, the upper-tail chi-square critical value with 29 degrees of freedom is 42.557. The test statistic and conclusion are closest to:

An analyst rejects a true null hypothesis that a portfolio manager adds no value. This outcome is best described as:

If the probability of a Type II error for a hypothesis test is 0.16, the power of the test is:

For a two-tailed test the computed z-statistic is 2.10, giving a p-value of approximately 0.036. At which of the following significance levels would the analyst reject the null hypothesis?

A backtest of a trading strategy produces a statistically significant mean excess return of 4 basis points per year (p-value = 0.02). Which statement is most accurate?

An analyst tests whether a fund’s mean return differs from 100 (index level basis). A sample of 100 observations gives a mean of 105 and a sample standard deviation of 15. At the 1% significance level (two-tailed critical value 2.626 for 99 df), the test statistic and conclusion are closest to:

A portfolio manager tests whether the variance of tracking error is less than 6.25 (standard deviation of 2.5%). A sample of 25 observations gives a sample variance of 4.0. The 2.5% lower-tail chi-square critical value with 24 degrees of freedom is 12.401. The test statistic and conclusion are closest to:

An analyst estimates a sample correlation of 0.42 between two asset returns using 28 paired observations and tests whether the population correlation differs from zero. At the 5% significance level (two-tailed critical value 2.056 for 26 df), the test statistic and conclusion are closest to:

A researcher builds a contingency table with 3 rows and 2 columns to test whether investment style and region are independent. The number of degrees of freedom for the chi-square test of independence is: