FRM P1定量分析精选习题

Instructor: Brady Topic Weight: 20% Quantitative Analysis Quantitative Analysis 25. A bank uses a continuously-compounded annual interest rate of 5% in one of its risk models. What is the equivalent interest rate the bank should use if it converts to semi-annual compounding in the model? A. 4.94% B. 5.00% C. 5.06% D, 5.12% answer: Canswer: C Quantitative Analysis 26. An analyst is looking to combine two stocks with annual returns that are jointly normally distributed and uncorrelated. Stock A has a mean return of 7% and a standard deviation of returns of 20%; Stock B has a mean return of 12% and a standard deviation of returns of 15%. If the analyst combines the stocks into an equally weighted portfolio, what is the probability that the portfolio return over the next year will be greater than 12%? A. 42.07% B. 44.32% C. 55.67% D. 57.93% Quantitative Analysis answer: Aanswer: A Quantitative Analysis 33. An investor holds a portfolio of stocks A and B. The current value, estimated annual expected return, and estimated annual standard deviation of returns are summarized in the table below: Stock AStock B Current Value(USD) Stock AStock B Current Value(USD)40,00060,00040,00060,000 Expected ReturnExpected Return8%9%8%9% Standard DeviationStandard Deviation16%20%16%20% If the correlation coefficient of the returns on stock A and B is 0.3, then the expected value of the portfolio at the end of this year, within two standard deviations, will be between: A. USD 69,600 and USD 130,400. B. USD 71,800 and USD 145,400. C. USD 78,200 and USD 139,000. D. USD 81,400 and USD 135,800. Quantitative Analysis answer: Canswer: C Quantitative Analysis 34. An economic analyst has calculated the probabilities of three possible states for the economy next year: growth, normal, and recession. A bank analyst has estimated the possible returns on two stocks, A and B, in each of the three scenarios shown in the following table: StateProbabilityReturn of Stock AReturn of Stock B Growth StateProbabilityReturn of Stock AReturn of Stock B Growth0.20 0.30 0.20 normalnormal0.60 0.10 0.10 RecessionRecession0.20 -0.20 -0.10 Quantitative Analysis Given that the standard deviations of the estimated returns on stocks A and B are 16.0% and 9.8%, respectively, what is the covariance of the estimated returns on stocks A and B? A. -0.0187 B. -0.0156 C. 0.0156 D. 0.0178 Quantitative Analysis answer: Canswer: C Quantitative Analysis 36. You are examining a pool of senior secured loans and observe that 10% of the loans are delinquent in their interest payments. The outstanding balance on 60% of the delinquent loans exceeds the Value of the collateral pledged to secure them and the outstanding balance on 30% of the non-delinquent loans exceeds the value of the collateral pledged to secure them. If you randomly select a loan from the pool and observe that its collateral value is less than the outstanding balance, what is the probability that the loan is delinquent? A. 6% B. 9% C. 18% D. 54% Quantitative Analysis answer: answer: C Quantitative Analysis QUESTIONS 43 AND 44 REFER TO THE FOLLOWING INFORMATION QUESTIONS 43 AND 44 REFER TO THE FOLLOWING INFORMATION A bank analyst run an ordinary least squares regression of the daily returns of the stock on the daily returns on the S&P 500 index using the last 750 trading days of data. The regression results are summarized in the following tables: Quantitative Analysis PredictorCoefficient Standard Error t-statisticp-valuePredictorCoefficient Standard Error t-statisticp-value Constant0.05610.0029419.09710.00000 Constant0.05610.0029419.09710.00000 Return on the S&P 500 1.20540.00298404.252250.00000 Return on the S&P 500 1.20540.00298404.252250.00000 2 R=87.86% Analysis of Variance Source Degree of Freedom Sum of Squares Mean Square F-statistic p- value Source Degree of Freedom Sum of Squares Mean Square F-statistic p- value RegressionRegression111.4393911.43939 163419.87 971 0.0000 0 Residual Error Residual Error 7490.054250.00007 TotalTotal7500.44677 Quantitative Analysis 43. The bank analyst wants to test the null hypothesis that the beta of the portfolio is 1.2 at a 5% significance level. According to the regression results, the analyst would: A. Reject the null hypothesis because the t-statistic is greater than 1.64. B. Fail to reject the null hypothesis because the t-statistic is greater than 1.64. C. Reject the null hypothesis because the p-value is greater than 5%. D. Fail to reject the null hypothesis because the p-value is greater than 5%. Quantitative Analysis answer: answer: A Quantitative Analysis 2 R 2 R 44. A colleague of the bank analyst suggested adding the returns on the Dow Jones Industrial Average (DJIA) index as an additional explanatory variable. The new regression results show that the increased and the adjusted decreased. What conclusion can be drawn from these results? A. The increased 2 R gives an inflated estimate of how well the regression fits the data. B. The decreased adjusted 2 R suggests that the coefficient of the returns on the DJIA is not significant. C. The increased 2 Rindicates an improvement in the regression. D. The decreased adjusted 2 R suggests the existence of omitted variable bias in this regression. Quantitative Analysis answer: Banswer: B Quantitative Analysis 46. An operational risk analyst is attempting to analyze a banks loss severity distribution. However, historical data on operational risk losses is limited. Which of the following is the best way to address this issue? A. Generate additional data using Monte Carlo simulation and merge it with the banks operational losses. B. Estimate the parameters of a Poisson distribution to model the loss severity of operational losses. C. Estimate relevant probabilities using expected loss information that is published by credit rating agencies. D. Merge external data from other banks with banks internal data after making appropriate scale adjustments. Quantitative Analysis answer: Danswer: D Quantitative Analysis 48. You are conducting an ordinary least squares regression of the returns Y and X as Y=a+b*Y+ based on the past three years daily adjusted closing price data. Prior to conducting the regression, you calculated the following information from the data: Sample covariance0.000181Sample covariance0.000181 Sample Variance of Stock X0.000308Sample Variance of Stock X0.000308 Sample Variance of Stock Y0.000525Sample Variance of Stock Y0.000525 Sample mean return of stock X-0.03%Sample mean return of stock X-0.03% Sample mean return of stock Y0.03%Sample mean return of stock Y0.03% What is the slope of the resulting regression line? A. 0.35 B. 0.45 C. 0.59 D. 0.77 Quantitative Analysis answer: Canswer: C Quantitative Analysis 49. A risk analyst is estimating the regression = + * + * +, where is the return of stock X, is the return of stock Y, and is the return of stock Z, using 20 years of daily return data. He wants to test the null hypothesis that =0 and =0 with a 95% confidence level by using an F- test. Critical values of the F-statistic at the 95% confidence level are given in the following table: X R Y Y R Z Z R Y R Z R Y Z =3.8415 3.8415 =2.9957 2.9957 =2.60492.6049 1 F 2 F 3 F Quantitative Analysis If the t-statistics for and are 2.34 and 1.64, respectively, and the correlation between the two t-statistics is 0.3. What conclusion can the risk analyst infer from the regression results? A. The risk analyst should reject the null hypothesis since the F-statistic is more than 2.9957 B. The risk analyst should fail to reject the null hypothesis since the F-statistic is less than 2.9957 C. The risk analyst should reject the null hypothesis since the F-statistic is more than 3.8415 D. The risk analyst should fail to reject the null hypothesis since the F-statistic is less than 3.8415 Y R Z R Quantitative Analysis answer: Aanswer: A Quantitative Analysis 60. An analyst is considering an investment in stock DKR and has gathered the following information: Expected return of DKR8.00%Expected return of DKR8.00% Risk-free rate2.50%Risk-free rate2.50% Standard deviation of DKR returns14.75%Standard deviation of DKR returns14.75% Standard deviation of market returns13.50%Standard deviation of market returns13.50% Correlation of DKR return and market returns 0.76Correlation of DKR return and market returns 0.76 The analyst believes DKR is fairly valued according to the CAPM. Based on this information, what is the expected return of the market portfolio? A. 9.12% B. 10.43% C. 12.19% D. 15.12% Quantitative Analysis answer: Aanswer: A Quantitative Analysis 69. A quantitative analyst used a simulation to forecast the S&P 500 index value at the end of the year with an index value of 1,800 at the beginning of the year. He generated 200 scenarios and calculated the average index value at year-end to be 1,980 with a 95% confidence interval of 1,940,2,020. In order to improve the accuracy of the forecast, the quantitative analyst increased the number of scenari