Sir
If possible please give PDF of questions in subject wise format
It will be very helpful in preparations
Sir
If possible please give PDF of questions in subject wise format
It will be very helpful in preparations
Answer for 17 March:-
1. a
2. b
3. a
4. c
5. b
6. a
Solutions to Item set for 17-March
1. Correct Answer is A: Asset beta of Mintax Limited = Equity beta/(1+D/E). Cost of equity using CAPM = 6% + equity beta*(10% - 6%) = 12% => Equity beta = 1.5. Asset beta = 1.5/1.667 = 0.9.
2. Correct Answer is B: Equity beta for Brooklyn Inc. = Asset beta of Mintax limited*(1+D/E of Brooklyn Inc.) = 0.9*1.8 = 1.62. Cost of equity = 6% + 1.62*(10% - 6%) = 12.48%
3. Correct Answer is C: Holding period return for Ashish = (18-12.5)/12.5 = 44%.
4. Correct Answer is C: Ashish is incorrect regarding Pastor-Stanbaugh model when he states that the base value for the liquidity factors is one. The actual base value for the liquidity factor is zero.
5. Correct Answer is A: Cost of equity for Yemen Inc. = 7.8% + (-0.3)*2.5% = 7.05%.
6. Correct Answer is B: Time horizon risk arises due to the unanticipated change in the return difference between 20-year government bonds and 30-day Treasury bills. It would get affected the most.
Item set for 18-March (Quantitative Methods):
Vivek Raj Case Scenario
Vivek Raj is a quantitative research analyst in HSMC bank. He is checking whether there is any relationship between the rate of change in price of commodities and the rate of change in the supply of money in the economy. He extracts the monthly data for last 5 years and runs a linear regression between the rate of price change in commodities and the rate of change in supply of money. The rate of change of price in commodities is a dependent variable and the rate of change in supply of money is an independent variable.
The result of ANOVA (analysis of variance) is shown in Exhibit 1.
Exhibit 1
Coefficient Standard error t-statistic p-value Intercept 2.00% 0.54 ? <0.005 Rate of change in money supply 0.82 0.14 ? <0.005
ANOVA df SS MS F Significance F Regression - 235.50 - - <0.005 Error - 85.00 - Total - 320.50 - - - R^2 -
Vivek Raj checks the result at 5% level of significance. He also finds out the confidence interval for regression coefficient. He shows the result to his manager and drafts his findings in a research report.
His manager asks him to calculate the confidence interval of the predicted values so that statistically 95% of the values lie in that confidence interval for 5% increase in supply of money. Vivek calculates the 95% confidence interval for the predicted value of the change in commodities price for a 5% change in supply of money.
His manager asks him about the assumptions taken by him in the linear regression analysis. Vivek explains the assumptions by assuming that the regression equation as:
Y1 = b0 + b1 Xi + ei , i= 1, 2,…,n
Assumption 1: A linear relationship exists between the dependent and the independent variable in the parameters b0 and b1
Assumption 2: The independent variable, X, is not random
Assumption 3: The expected value of the residual term is zero {E (e) = 0}
Assumption 4: The variance of the residual term is constant for all observations {E (ei2) = σe2}, i= 1, 2… n
Assumption 5: The error term, e, is uncorrelated across observations, {E (ei ej) =0, j≠i}
Assumption 6: The error term, e, is normally distributed
1. What is the value of F-statistics in the table given in Exhibit 1?
a) 2.77
b) 20.93
c) 160.91
2. What is the value of test statistics for the hypothesis test checking whether coefficient of rate of change in money supply is greater than 1?
a) -1.28
b) 3.70
c) 5.86
3. What is the standard error of estimate (SEE) for the given regression analysis?
a) 1.19
b) 1.21
c) 1.47
4. Which of the assumptions stated by Vivek ensures that the linear regression produces the correct estimates of b0 and b1?
a) Assumption 1 and 2
b) Assumption 2 and 3
c) Assumption 1,2 and 3
5. What is the correlation coefficient between the dependent variable and the independent variable in the given regression analysis?
a) 0.735
b) 0.797
c) 0.857
6. What is the confidence interval for the predicted value if the standard error of forecast is 1.85% for a 5% increase in the supply of money?
a) 2.39% to 9.80%
b) 2.47% to 9.72%
c) 3.01% to 9.19%
@Konvexity:- Sir, plz explain answer 4 & 6 of 17th March.
Question is tough... Not able to crack it :-(
Ans1. B
Ans.5 C
-Shubhojit.
Answers for 18th March case:
n= 5*12 = 60
k = 1
RSS = Regression Sum of Squares = 235.5
MSR = Mean Sum of Regression Squares = RSS/k = 235.5/1 = 235.5
SSE = Sum of Squared Errors = 85
MSE = Mean Squared Errors = SSE/(n-k-1) = 85/ (60-1-1) = 1.46552
SEE = Standard Error of Estimate = [SSE/(n-k-1)]^1/2 = 1.21059
SST = Total Sum of Squares = RSS + SSE = 235.5 + 85 = 320.5 (GIVEN)
R^2 = Coeffecient of determination = RSS/SST = 235.5/320.5 = .73479
1) c - F stat => MSR/MSE => (235.5/1)/(85/58) = 160.69 ; closest option C (though I cudnt find 160.91 at any level of rounding)
2) a - t stat = (0.84-1)/0.14 = -1.28
3) b - solved above
4) b- (I think) not 100% sure
5) c- r = root square of R^2 = 0.73479^1/2 = 0.85720
6) a- (edited)for 5% supply increase, predicted change in price = 2+.84(5) = 6.1
critical t value at df = n-2 = 58 @ 95% significance => ~2
Predicted interval at 1.85% forecast error = 6.1 - 1.85*5 to 6.1 + 1.85*2
=> 2.4% to 9.8% (closest option a)
huffff huffff
Last edited by rahuldaga89; 19-03-2013 at 06:04 PM. Reason: calculation mistake in 6th part
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You can do anything You set your mind to !!!
Solutions to Item set for 18-March
1. Correct Answer is C: The value of F-statistics = MSR/MSE = (RSS/k)/ {SSE/ (n-k-1)} = 235.50/ {85/ (60-1-1)} = 235.50*58/85 = 160.91.
2. Correct Answer is A: t-statistics = (0.82 -1)/0.14 = -1.28.
3. Correct Answer is B: SEE = [SSE/ (n-2)] 0.5 = (85/58)0.5 = 1.21.
4. Correct Answer is B: Assumptions 2 and 3 ensure that the regression produces the correct estimates of b0 and b1.
5. Correct Answer is C: Correlation coefficient in a linear regression equation = Square root of R2 = (RSS/SST) 0.5 = (235.50/320.50)0.5 = 0.857.
6. Correct Answer is A: The regression equation is: Percentage change in price of commodities = 2.00% + 0.82*(Percentage change in money supply). The predicted value for 5% increase in money supply = 2.00% + 0.82*5.00% = 6.10%. The t-critical value for 95% confidence interval and 58 degrees of freedom = ±2.002. Confidence interval of the predicted value = 6.10% ± 2.002*(1.85%) = 2.39% to 9.80%.
Item set for 19-March (Quantitative Methods):
Vinod Jayakumar Case Scenario
Vinod Jayakumar, CFA, is trying to predict the P/E ratio of a company using various fundamental factors associated with the stock. In his model, he has assumed that the predicted P/E would depend upon three independent variables. Those variables are dividend payout ratio, earning growth rate, and beta of a stock.
He runs regression on 50 stocks. The result of ANOVA is shown in Exhibit 1.
Exhibit 1
Coefficient p-value Intercept 5.35 <0.005 Dividend payout -0.32 0.095 Earnings growth rate 12.5 0.12 Beta -0.60 0.15
ANOVA SS Significance F Regression 72.8 <0.005 Error 24.7 Total 97.5 R^2 0.7467 Adjusted R^2 -
Vinod checks the heteroskedasticity, serial correlation and multicollinearity for the given regression analysis. He conducts the Durbin Watson test and Breusch- Pagan test. The results of those tests are given in Exhibit 2.
Exhibit 2
Durbin Watson Test
Durbin Watson Statistics 1.96 d(l) 1.54 d(u) 2.42
Breusch – Pagan Test
R^2 from the regression of residuals 0.032 Critical Chi-square value 3.841
Vineet Saini, who is colleague of Vinod Jayakumar, asks him about the ways to correct the heteroskedasticity, serial correlation, and multicollinearity in a multiple regression analysis.
Vinod: To correct heteroskedasticy, we use White corrected standard error and replace the standard error of independent variable with that error and again conduct a t-test using the original regression coefficient.
Vineet: What about multicollinearity and serial correlation?
Vinod: Serial correlation can be correcting by adjusting the specification of the model by incorporating a seasonal term. For correcting multicollinearity, one or two independent variables can be omitted from the original regression equation and the regression can be conducted again.
Vineet: If the above problems are with the multiple regression equations, then what kind of errors we can expect in out hypothesis testing?
Vinod: Heteroskedasticity and multicollinearity lead to too many Type I errors and serial correlation leads to too many Type II errors.
1. What is the value of adjusted R2 in the table given in Exhibit 1?
a) 0.7009
b) 0.7301
c) 0.7622
2. Which of the following combinations is correct?
a) BP test: Heteroskedasticity, DW test: Serial correlation
b) BP test: Serial correlation, DW test: Heteroskedastcity
c) BP test: Serial correlation, DW test: Multicollinearity
3. Which of the following is most likely to be present in the given multiple regression analysis?
a) Heteroskedasticity
b) Serial Correlation
c) Multicollinearity
4. Which of the correction method specified by Vinod Jayakumar is least accurate?
a) Regarding serial correlation
b) Regarding multicollinearity
c) All are correct
5. What is the predicted P/E value for a stock according to the multiple regression equation obtained from the above analysis? The stock is having dividend payout ratio as 0.60 and earnings growth rate as 0.08. The beta of the stock is 1.2.
a) 5.438
b) 5.822
c) 6.878
6. Is Vinod Jayakumar correct about the types of errors from the problems associated with the multiple regression analysis?
a) Yes
b) No, Heteroskedasticity and serial correlation: Too many Type I errors; Multicollinearity: Too many Type II errors
c) No, Heteroskeadasticity: too many Type I errors; Serial correlation and multicollinearity: Too many Type II errors
Ans to Item set for 19-March:
1. c
2. b
3. c
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