#### Capital Market Analysis

Answer any THREE questions.

Only silent, self-contained calculators with a Single-line Display or Dual-line Display are permitted in this examination. Dictionaries are not allowed with one exception. Those whose first language is not English may use a dictionary to translate between that language and English provided that neither language is the subject of this examination. Subject specific translation dictionaries are not permitted.

**Question 1**

(a) A classic study by Jensen (1968) has proved pivotal in suggesting a method for conducting tests of the performance of fund managers. Explain, with the use of empirical models, the tests of the performance of mutual funds. [30 marks]

(b) Based on the study by Jensen (1968), the following table shows some summary statistics of a sample of annual returns on the portfolio of 115 mutual funds from 1945 to 1964. Evaluate the results in the context of the funds’ performance.[20 marks]

(c) The following figure represents the results from Jensen (1968) by plotting the number of mutual funds in each t-ratio category for the alpha coefficient, gross and net of transactions costs. Evaluate the results.

(d) Are the best portfolio managers able to repeat their high performance? Propose an empirical

model to examine whether it is possible to pick groups of funds that earn positive abnormal

returns in the future. [30 marks]

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**Question 2**

(a) Discuss the weaknesses of asset allocation using modern portfolio theory. [30 marks]

(b) Three equivalent formulations normally used in portfolio optimisation process include: (1) the minimum variance formulation; (2) the expected return maximisation formulation; and (3) the risk aversion formulation. Explain these formulations using a mathematical approach. [30 marks]

(c) An optimal risky portfolio is available with the following information.

i. Calculate the expected returns, standard deviations, and utility levels for various positions in risky assets (0, 0.2, 0.4, 0.6, 0.8 and 1.0) for an investor with risk aversion A = 4. The risk-free rate is 7%. Determine the optimal complete portfolio. [15 marks]

ii. Use the utility maximising formula to find the optimal complete portfolio. Calculate the expected return, standard deviation, and the reward-to-variability for the complete portfolio. Verify that the reward-to variability of the complete portfolio is equivalent to that of optimal portfolio. [15 marks]

iii. Plot the indifference curve and capital allocation line. Locate the optimal complete portfolio on the same graph. [10 marks]

**Question 3**

(a) In modern portfolio theory, an estimate of the covariance matrix for asset returns is required for portfolio optimisation. However, for large numbers of assets the number of terms in the covariance matrix becomes extremely large, making the sample covariance matrix a computationally expensive estimate. Demonstrate the efficiency of a single-factor model in the covariance matrix estimation. [40 marks]

(b) The data below describe a three-stock financial market that satisfies the single-index model.

The single factor in this economy is perfectly correlated with the value-weighted index of the stock market. The standard deviation of the market index portfolio is 25%.

i. Compute the mean excess return of the index portfolio. [10 marks]

ii. Compute the covariance between each stock and the index. [10 marks]

iii. Break down the variance of each stock into its systematic and firm-specific components. Show all your calculations. [10 marks]

iv. Which of the individual beta is categorised as aggressive stock? Defensive stock? Explain. Which stock is desirable in a rising market? [10 marks]

v. How many stocks would an investor have to hold in order to totally eliminate firm-specific risk? Provide three examples of systematic and unsystematic factors that cause the returns on holding common stocks to vary over time. [10 marks]

vi. You expect stock market to rise in the next year or so. Could you beat the market portfolio by holding, say, five securities with the highest betas? Explain. [10 marks]

**Capital Market Analysis ****Question 4**

(a) Studies by DeBondt and Thaler (1985, 1987) showed that stocks experiencing a poor performance over a three to five-year period subsequently tend to outperform stocks that had previously performed relatively well. What does this imply in the context of efficient market hypothesis? With reference to relevant literature, provide two explanations to justify the phenomenon. [50 marks]

(b) High-beta and high-volatility stocks have long underperformed low-beta and low-volatility stocks. This anomaly runs counter to the basic finance principles that higher risk is compensated with higher expected return. With reference to relevant literature, evaluate the reasons for the low-volatility anomaly. [50 marks]

**Question 5**

(a) With reference to relevant literature, critically discuss the issue of data-snooping in the context of factor models. [40 marks]

(b) What do experimental markets teach us about the likelihood of bubbles in the real world according to Ackert et al. (2006)? [Ackert, L.F., N. Charupat, B.K. Church, and R. Deaves, 2006, “Margin, short selling, and lotteries in experimental asset markets,” Southern Economic Journal 73(2), 419-436] In what sense does this research have its limitations? Evaluate. [40 marks]

(c) Treynor and Mazuy’s model that is used to explain the market timing of fund managers is represented below:

In this model, how is the c coefficient interpreted? [20 marks]

**Capital Market Analysis ****Question 6**

(a) The following table shows the long-run linkages between the gross domestic return and uncovered gross foreign return. Spot exchange rates are used and expressed in direct quotation (i.e. domestic currency per unit of USD). The gross domestic return and the expected uncovered gross foreign return are computed separately in nominal terms.

i. It is often said that interest rate parity is satisfied when the differential between the interest rates denominated in two currencies equals the spot changes between the two currencies. Explain why this is an imprecise statement, as argued by Tang (2011). [20 marks]

ii. If uncovered interest parity (UIP) is valid in its precise form, what would be the value of the long-run coefficient? Explain. [10 marks]

iii. Based on the estimated slope coefficients (FMOLS and DOLS estimators), is there a violation of the UIP for each country? Explain. [20 marks]

(b) The dividends of LSS Inc. are expected to grow at a constant rate. The expected earning for next year is $6 per share. The return on equity is 12% and the plowback rate is 2/3.

i. Given the business risk of LSS, the investors require an average rate of return on the stock of 10%. What would be the fair value of this share? The current market price of the share is $85. As a speculator should you buy or sell this share? What are the risks involved in your strategy? Show all your calculations and explain your answer. [20 marks]

ii. What is the amount of present value of growth opportunities (PVGO) for this share? What does it imply? Explain your answer. [10 marks]

iii. In real world we know that a dividend cut is almost always accompanied by steep drops in stock price, does this contradict with our analysis in parts (i) and (ii)? Evaluate. [20 marks]

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