CFA Domain 2: Quantitative Methods (Quiz 1)

A borrower has entered into a fully amortizing, 4%, 30-year fixed mortgage with monthly payments. The principal is GBP 200,000. At the end of 5 years, the borrower wants to change the payments so that the mortgage will be completely paid off in another 15 years. The adjusted monthly payment (in GBP) needed to pay off the mortgage in the borrower's time frame (Years 6–20) is closest to:

An investor receives a research report that analyzes two securities through a simple linear regression. The study discloses the coefficient of determination (R2) and the sum of squares error (SSE). To estimate the accuracy of the model using an absolute measure of the errors, the investor will most likely need to know the:

An analyst determines that a return distribution has the same mean, standard deviation, and skewness as a normal distribution, but has an excess kurtosis of 2.2. If an analyst incorrectly assumes the returns are normally distributed, then in this analysis, extreme values would most likely be:

The expected value of a random variable is most likely a(n):

"After running a simple linear regression, a trader analyzes the resulting residual plot: Based on only the residual plot, this regression model most likely violated which of the following linear regression assumptions?"

A bank offers a certificate of deposit (CD) with a stated annual rate of 7% compounded continuously. The CD's effective annual rate is closest to:

"There is a 0.6 probability that a portfolio manager will add a new asset to an existing portfolio. If the manager adds the asset, then there is a 0.9 probability that the overall portfolio will beat its benchmark. If the manager does not add the asset, then there is a 0.7 probability that the portfolio will beat its benchmark. If the portfolio beats its benchmark at the end of the year, the probability that the manager bought the new asset is closest to:"

"An analyst estimates a joint probability function of two assets' returns during good, average, and poor business conditions: The covariance of returns is closest to:"

Given that continuously compounded returns are normally or approximately normally distributed, asset prices are:

For a given series of returns, the variable that will cause the largest difference between the returns' arithmetic mean and geometric mean is:

"A semiconductor company wants to estimate how many of the computer chips it produces each month will be defective and creates a distribution based on multiple samples of 100 months of past manufacturing data. Based on its analysis of the data, the company believes that: the historical mean monthly defects is a good estimate of the expected number of defects each month going forward; and the variance of the sample distribution would not decrease by changing the sample size. Based on this information, the sample mean is best described as an estimator that is:"

An analyst finds that a sample of 16 returns has a mean of 6.5% and a standard deviation of 12%. The population variance is unknown, and the population distribution is assumed to be nonnormal. If the analyst performs a hypothesis test that the population mean is 6%, then the analyst's most appropriate conclusion is that:

If a cumulative distribution function of a random variable indicates that P(X < a) is equal to P(X ≤ a), then the distribution is most likely:

For a positively skewed distribution, most likely the

A sample containing 49 bonds has a mean maturity of 10 years. If the underlying population is normally distributed with a variance of 4, then a 95% confidence interval for the population mean will have an upper limit closest to:

A trader runs a linear regression model and calculates a prediction interval. The trader reviews the results, then runs a second model based on the same data set and calculates a significantly narrower prediction interval. Based only on this information, the trader most likely:

A retiree will begin taking withdrawals of NOK 50,000 per year from an investment account 15 years from today. The payments will last for 20 years. The retiree also wants to have NOK 100,000 remaining in the account at the end of the withdrawal period. If the discount rate is 7%, the lump sum (in NOK) that must be invested today to satisfy both retirement goals is closest to:

An analyst runs a regression with 30 observations, producing the following regression model: Y = 0.53 + 0.85 X + e. The analyst wants to test, at a 5% significance level, if Y will change by more than 0.50 for each one-unit change of X. Additional data that the analyst needs to perform this test is most likely the:

"An analyst wants to statistically determine whether the mean monthly returns of two large funds are significantly different. The monthly returns from the two funds are assumed to be independent of each other. The population variances are unknown but assumed to be equal. For a hypothesis test at a 0.1 level of significance, the critical value is closest to:"

An analyst performs a hypothesis test on the correlation of monthly returns of Fund A and Fund B. The null hypothesis is that the returns are uncorrelated with each other. Increasing the number of observations used in the test most likely results in an increase in the: