EXAMINATION FOR

125.701 Quantitative Methods for Accounting and Finance

Semester One 2018

SECTION A

Each question is worth 2 marks.

Q1. Analysts issue recommendations on stocks as strong buy, buy, hold, sell and strong sell. Which of the following scales can be used to best measure analyst recommendation?

A.  Nominal

B.  Ordinal

C.  Interval

D.  Ratio

E.  None of the above

Q2. Assume you invest in a portfolio consisting 5 stocks, stock returns are 3.25%,   2.96%, -1.58%, 4.88% and -1.50% respectively. Stocks are equally weighted in the portfolio. The weighted average return of the portfolio is:

A.  2.834%

B.  1.602%

C. 9.612%

D. -1.54%

E.  None of the above

Q3. An analyst intends to rank order 5 best performing stocks out of 8 stocks selected. How many different rankings are possible?

A.  56

B.  40

C. 6720

D.  120

E.  None of the above

Q4. Suppose the prospects for recovering principal for a default bond issue depend on which of the two economic scenarios prevails. Scenario 1 has probability of 0.65 and will result in recovering principal of $50,000 with probability of 0.4, or in recovering principal of $30,000 with probability of 0.6. Scenario 2 has probability 0.35 and will result in recovering principal of $80,000 with probability of 0.8, or in recovering principal of $60,000 with probability of 0.2. What is the amount of expected recovery?

A.  $51,300

B.  $38,000

C. $76,000

D. $55,000

E.  None of the above

Q5. Assume returns of portfolios are normally distributed, if the shortfall level is equal to the risk-free rate of return, the optimal portfolio should have:

A.  The highest safety-first ratio and lowest Sharpe ratio

B.  The lowest safety-first ratio and lowest Sharpe ratio

C. The lowest safety-first ratio and highest Sharpe ratio

D. The highest safety-first ratio and highest Sharpe ratio

E.  None of the above

Q6. Over the past 4 years, the company’s quarterly earnings increased 10 times and decreased 6 times. You decide to model the number of earnings increases as a binomial random variable. Which of the following statements is correct:

A.  The estimated probability of success is 0.625

B.  The expected number of quarterly earnings increases during the next 2 years is 1.25

C. The variance of the number of quarterly earnings increases during the next 2 years is 0.4688

D. The assumptions of binomial distribution are valid in this example.

E.  None of the above

Q7. As degrees of freedom increase, the t-distribution will:

A.  less closely resemble a normal distribution

B.  become less peaked

C.  have less fat tails

D. All of the above

E.  None of the above

Q8. Assume that monthly returns for a portfolio are normally distributed with a mean of 0.2 and a sample standard deviation of 0.25. The population standard deviation is unknown. If the sample size is 15, the 90% confidence interval of the population mean of monthly returns is closest to:

A.  (0.1132, 0.2868)

B.  (0.1868, 0.3232)

C.  (0.0863, 0.3137)

D.  (0.1174, 0.2826)

E.  None of the above

The following information related to Questions 9- 11.

ABC Ltd is a car manufacturer. During the most recent industry cycle, its net income averaged $20 million per year with a standard deviation of $5 million (n=5 observations). Management claims that ABC’s performance during the most recent cycle results from new technology introduced in manufacturing process and the company can dismiss the profitability expectations based on its average net income of $15 million per year in prior cycles.

Q9. With µ as the population value of mean annual net income, which of the following hypotheses is the most accurate?

A. Ho : µ > $15 million; Ha ≤ $15 million

B. Ho : µ ≤ $15 million; Ha   > $15 million

C. Ho : µ = $15 million; Ha   ≠ $15 million

D. Ho : µ ≠ $15 million; Ha   = $15 million

E.  None of the above

Q10. Assume that ABC’s net income is normally distributed, which of the following test statistics is the most appropriate?

A. z-statistic

B. t-statistic

C. chi-square

D. F-statistic

E.  None of the above

Q11. Identify the rejection point or points at the 0.05 level of significance for the hypothesis stated in Q9 and determine whether or not to reject the null hypothesis at the 0.05 significance level:

A.  Rejection point is 2.132, reject the null hypothesis

B.  Rejection point is 2.132, do not reject the null hypothesis

C.  Rejection point is 1.96, reject the null hypothesis

D.  Rejection point is 1.96, do not reject the null hypothesis

E.  None of the above

Q12. In a regression analysis, if you delete some observations with small residual values, then:

A.  R-squared will decrease, standard error will have no change

B.  R-squared will have no change, standard error will increase

C.  R-squared will increase, standard error will decrease

D.  R-squared will decrease, standard error will increase

E.  None of the above

Q13. XYZ Ltd sells dairy product to five European countries. XYZ’s sales are very sensitive to exchange rates. You have estimated a linear regression with exchange rate as the independent variable and sales as the dependent variable. The regression equation is yi   = 81.6 − 152.64xi . What would be the impact on sales if exchange rate decreases by 1%?

A.  Sales will remain unchanged

B.  Sales will increase by 152.64

C.  Sales will decrease by 71.04

D.  Sales will increase by 234.24

E.  None of the above

Q14. Assuming a regression with one independent variable, which of the following best describes F-statistic in the ANOVA:

A. F-statistic measures how well the regression equation explains the variation in the dependent variable.

B. F-statistic depends on 1 and n-2 degrees of freedom.

C. F-statistic is the ratio of the average regression sum of squares to the average sum of the squared errors.

D. All of the above

E.  None of the above

Q15. Which of the following statements is correct about conditional heteroscedasticity?

A.  Conditional heteroscedasticity results in consistent parameter estimates

B.  Conditional heteroscedasticity results in biased standard errors

C.  Conditional heteroscedasticity results in biased t-statistics and F-statistics

D. All of the above

E.  None of the above

Q16. Which of the following is used to determine the significance of regression model as a whole?

A. t-statistics

B. F-statistics

C. R-squared

D. All the above

E.  None of the above

Q17. Suppose you hypothesize that firm size (measured by market value of equity) and book-to-market ratio (B/M) are useful for explaining the cross-sectional variation in asset returns. You have formulated the following regression model:

Ri  = b0  + b1sizei    + b2 (B/M)i  + εi

The table below shows the results of the regression

Which of the following is correct?

A.  Firm size is significantly different from 0 at the 0.10 significance level.

B.  Market-to-book is significantly different from 0 at the 0.10 significance level.

C.  Firm size is significantly different from 0 at the 0.05 significance level.

D.  Market-to-book is significantly different from 0 at the 0.05 significance level.

E.  None of the above

Q18. Which of the following is correct about autoregressive model?

A.  Autoregressive model can be estimated using ordinary least squares if the times series is covariance stationary and the errors are uncorrelated.

B.  The Durbin-Watson statistic cannot be used for a regression that has a lagged value of the dependent variable as one of the explanatory variables.

C. We examine the autocorrelations to test for serial correlation.

D. All of the above

E.  None of the above

The following information related to Questions 19-20.

Suppose changes in unemployment rate can be modelled as:

∆UERt  = −0.023 − 0.3565∆UERt−1

The current change (first difference) in the unemployment rate is 0.02.

Q19. What is the best prediction of the next change?

A.  -0.023

B.  -0.3565

C. -0.0301

D. -0.0159

E.  None of the above

Q20. What is the prediction of the change following the next change?

A.  -0.023

B.  -0.3563

C. -0.0123

D. -0.0173

E.  None of the above

SECTION B

Each question is worth 5 marks

Q21. For firm XYZ, the prior probabilities of earning performance are as follows

P(Earning exceeded analysts’ consensus) = 0.50

P(Earning met analysts’ consensus) = 0.30

P(Earning fell short of analysts’ consensus) = 0.20

The conditional probabilities of firm’s expansion are as follows

P(Expansion | Earning exceeded analysts’ consensus) = 0.70

P(Expansion | Earning met analysts’ consensus) = 0.20

P(Expansion | Earning fell short of analysts’ consensus) = 0.10

Firm XYZ recently announced an expansion, what is the probability that unreleased earning exceeds consensus? Show all calculations in details. (5 marks)

Q22. The cross-sectional mean and standard deviation of all 500 fund returns are 10 and 15 percent. Assume that the returns are independent across managers.

Q22.1 Compute a 95 percent confidence interval for the mean return. The critical value is 1.96. (2 marks)

Q22.2 For a fund with a mean return of 12%, does it statistically outperform the average fund given 95 percent confidence interval? (3 marks)

Q23. Answer the questions below:

Q23.1 To test the hypothesis that on average female CEOs earn less than male CEOs, explain under what conditions we would commit a Type I error and under what conditions we would commit a Type II error. (3 marks)

Q23.2. All else equals,what is the impact of increasing sample size on Type I and Type II errors (2 marks)

Q24. The multiple regression model between stock XYZ’s return and the three factors (F1, F2, F3) using 240 monthly observations are as follows.

XYZ return = b0 + b1*F1 + b2*F2 + b3*F3 + e

Q24.1 Which factor can explain the time variation in stock XYZ’s return given 95 percent confidence level (The critical value is 1.96)? (2 marks)

Q24.2 Test whether this three factors model is better than the random walk model in explaining the stock XYZ’s return given 95 percent confidence level (The critical value is 2.60). (3 marks)

Q25. The time-series regression between unemployment rate and one-month lagged of 3-month treasury bill yield is as follows:

Unemployment rate = b0 + b1*one-month lagged of 3-month T-bill yield + e

The model has the R-square of 0.77. The critical value for the 95 percent confidence level is 1.96. The first-order autocorrelations of unemployment rate and 3-month T-bill are 0.85 and 0.78 and both are statistically significant.

Q25.1 Can we use the regression model to produce meaningful predictions of an unemployment rate? What could be a concern with this regression? (2 marks).

Q25.2 What should be done to have a model that is meaningful to predict unemployment rate? (3 marks).