### Portfolio Management and Investment Analysis

**1. Portfolio risk and return. [25 Marks]**

a) Consider the following scenario analysis

– Calculate the expected rate of return and standard deviation for each

investment. [8 Marks]
– Which investment would you prefer? Explain using the concept of utility. [5 Marks]

b) A pension fund manager is considering three mutual funds. The first is a stock fund, the second is a long-term government and corporate fund, and the third is a T-bill money market fund that yields a rate of 5.5%. The data of the risky funds are:

– In forming the portfolio of the two risky assets, what must be the correlation coefficient between their returns if there are to be gains from diversification. [4 Marks] – The correlation between the two fund returns is 0.15. Calculate the investment proportions in the minimum-variance portfolio of the two risky funds, and calculate the expected return and standard deviation of the minimum-variance portfolio.[8 Marks]

**2. Asset pricing models. [25 Marks]**

a) As an equity analyst, you have developed the following return forecasts and risk estimates for two different stock mutual funds (Fund T and Fund U):

– If the risk-free rate is 3.9% and the expected market premium is 6.1%, calculate the expected return for each fund according to the CAPM. [4 Marks] – Based on the estimated expected returns from the previous part, demonstrate whether Fund T and Fund U are currently priced. Explain using the graph of SML. [6 Marks]

b) You have been assigned the task of estimating the expected returns for two stocks: UVW and XYZ. Your preliminary analysis has identified three risk factors: the market risk factor (MKT), and two variables

capturing general macroeconomic exposures (MACRO1 and MACRO2). The factor risk premiums are 𝜆𝑀𝐾𝑇 = 7.5%, 𝜆𝑀𝐴𝐶𝑅𝑂1 = −0.3%, 𝜆𝑀𝐴𝐶𝑅𝑂2 = 0.6%. You have also estimated the following factor betas for two stocks with respect to each risk factor

– Calculate the expected returns for the two stocks using just the MKT factor. Assume the risk-free rate is 4.5% [4 Marks] – Calculate the expected returns for the three stocks using all three risk factors and the same 4.5% risk-free rate [4 Marks] – Discuss the differences between the expected return estimates from the single-factor model and those from the multi-factor model. Which estimates are likely to be more useful in practice? [7 Marks]

**3. Efficient market hypothesis. [25 Marks]**

a) Explain the concept of the efficient market hypothesis (EMH) and each of its three forms – week, semistrong and strong. [15 Marks]

b) Give three examples of empirical evidence or events that raise doubts about market efficiency. Explain [10 Marks]

**4. Security analysis. [25 Marks]**

a) Discuss the factors of the sensitivity of a firm’s earnings to the business cycle. [9 Marks]

b) Given the following earnings and dividends. Starting in year 6, the dividends are growing at a perpetual constant rate, and during this time the firm is expected to pay out 60% of its earnings and return on equity is expected to be 15%. Discount rate is 8.5%. What is the intrinsic value of the stock? [9 Marks]c) Briefly describe the rationale using price multiples to value equity. [7 Marks]

**5. Performance evaluation. [25 Marks]**

a) The following table shows the return and risk measures for Portfolio X and S&P 500 (benchmark). The risk-free rate of return over the period was 2%.

– Calculate the Sharpe ratios for Portfolio X and S&P 500. [4 Marks] – Calculate the M2 for Portfolio X and discuss the advantage of M2 [6 Marks] – Calculate the Jensen’s alpha for Portfolio X. Has Portfolio X outperformed the market? [3 Marks]

b) A global equity manager is assigned to select stocks from a universe of large stocks throughout the world. Results for a given month are contained in the following table:

– Calculate excess return relative to the benchmark portfolio. [4 Marks] – Calculate the contribution of country allocation decisions. [4 Marks] – Calculate the contribution of stock selection ability within countries. [4 Marks]

**6. Alternative Investments. [25 Marks]**

a) Define alternative investments and describe the characteristics of alternative investments. [12 Marks]

b) Describe fee structure (management fee and incentive fee) commonly

used in hedge funds. [8 Marks]

c) Describe the problems of survivorship bias and backfill bias in the performance evaluation of hedge funds. [5 Marks]

END OF EXAMINATION