Question 1
Each year stocks are sorted into quintiles based on market capitalization. For each quintile portfolio value weighted monthly log excess returns are computed. Small (Large) caps contains the returns to the quintile of stocks with the smallest (largest) market capitalization at the end of the previous fiscal year. Independent variables are the Fama-French three factors. T-statistics are in parenthesis. Sample period: 1963-2010 at the monthly frequency.
REQUIRED
a. Assume annual risk premia of E[Rm-rf]=6%, E[SMB]=1% and E[HML]=3%. Using these together with the estimates in the table, compute the expected excess return of Small caps based on the CAPM and also based on the Fama-French three factor model. Briefly discuss what contributes to the difference, if any, between the two results. (20 marks)
b. Compare your results in part a. with the average past performance of Small caps reported in the above table. Discuss potential reasons for any differences. (25 marks)
c. What do the coefficients on SMB and HML reveal about the characteristics of stocks that are sorted into Small caps and Large caps? (30 marks)
d. Compute the CAPM alpha of a long-short strategy that buys the Small cap portfolio and short sells the Large cap portfolio. Comment on the risk profile of such a strategy. (25 marks) Total 100 marks
Question 2
The Jupiter India Fund is an actively managed fund investing in companies that operate in India. Its stated benchmark is the MSCI India index.
REQUIRED
a. Compute the annualized Sharpe ratio of the Jupiter India Fund (use the standard deviation of the fund’s return for the denominator of the Sharpe ratio). (20 marks)
b. Discuss the disadvantages of using the Sharpe ratio as a performance measure in this case. (15 marks)
c. Interpret the estimated coefficients. (25 marks)
d. Test the null hypothesis that the estimated beta for Jupiter is equal to 1 against the 2- sided alternative (state the null and alternative hypotheses, state the used significance level, compute the t-statistic, compare t-statistic to critical value and decide whether to reject the null or not reject). (20 marks)
e. Discuss the possible advantages and disadvantages of using the MSCI India index as benchmark in this case. (20 marks) Total 100 marks
Question 3
You are interested in forecasting the average transaction price of semidetached houses in the region of South West England.
REQUIRED
a. Discuss why a time series of average house prices are likely to violate the conditions of weak stationarity. (20 marks)
The following table gives the results of two OLS regressions. “lsemidetached” is the log of the monthly average transaction price of semidetached houses. “trend” is a deterministic trend increasing by one unit each month, i.e., it takes values 1,2,3,4 and so on. “L.” is the lag operator. Sample period: 1995m1-2021m10.
b. Interpret the coefficient on the “trend” variable in (1). (10 marks)
c. Based on the regression output, is there any concern that “lsemidetached” contains a unit root? Describe how the Dickey-Fuller test would help to decide whether “lsemidetached” contains a unit root. (25 marks)
d. Suppose that in both September and October 2021 the prices of semidetached houses increased by 5%. Based on the estimated model above, what is the expected price change for November and December 2021? (25 marks)
e. You would like to take advantage of an error correction model in providing improved forecasts for semidetached houses in the South West of England. Describe your strategy. (20 marks) Total 100 marks
Question 4
a. Joanne and Paul are interested in investigating the effect of firms’ profitability on leverage. They have concluded that both positive and negative impacts can theoretically be justified. Required:
i.Explain why both predictions, although contradicting each other, may be correct. In your response, carefully discuss the justifications for each prediction in light of economic arguments/theories. (20 marks)
ii.They have conducted an analysis using a large panel of firms: leverage ratio is regressed on profitability and other known determinants. The result shows that the coefficient on profitability is negative and significant. They interpret this result as evidence in favor of the Pecking Order prediction. Provide reasons why this empirical result may not be used as the supporting evidence for the Pecking Order hypothesis. (20 marks)
b. AEye, a developer of AI-assisted farming vehicles, is considering a large expansion of its production capacity. This significant investment will change its fixed capital to asset ratio from 0.10 to 0.40. The firm expects other accounting ratios to remain unchanged postexpansion. However, in line with the investment, AEye is looking to determine a new target level of leverage suitable for the firm post-expansion. To aid the decision, CFO Amy has conducted an analysis using a large sample of industrial firms.
Required:
AEye has maintained the leverage ratio around 0.12, which is close to its current target taking into account other factors. Based on the regression result, find a new target level of leverage that the CFO can propose for the firm following the expansion (calculation details and discussion must be presented to justify your answer). (30 marks)
c. A group of researchers is investigating the impact of creditor protection laws (CPLs) on corporations’ leverage around the world, controlling for common determinants of corporate leverage. To conduct the analysis, they have collected the data on firms’ leverage in fiscal year 2020, along with various determinants, for a large sample of firms.
Required:
Explain
(i) why their empirical method and the data collection may be problematic and
(ii) propose a better way to carry out this investigation. (30 marks) Total 100 marks
Comments