~~FN3023 ZB d0 This paper is not to be removed from the Examination Halls UNIVERSITY OF LONDON FN3023 ZB BSc degrees and Diplomas for Graduates in Economics, Management, Finance and the Social Sciences, the Diplomas in Economics and Social Sciences and Access Route Investment Management Monday, 19 May 2014 : 14:30 to 17:30 Candidates should answer FOUR of the following EIGHT questions. All questions carry equal marks. A calculator may be used when answering questions on this paper and it must comply in all respects with the specification given with your Admission Notice. The make and type of machine must be clearly stated on the front cover of the answer book. PLEASE TURN OVER UL14/0234 Page 1 of 5
1. (a) Explain the difference between exchange trading and over-the-counter (OTC) trading of securities. Discuss the relative benefits for investors of the two forms of trading. Suppose a competitive risk neutral market maker clears the market by offering bid and ask quotes at which she is willing to trade one share of a stock. Traders are either uninformed noise traders who are as willing to buy a share as sell a share of the stock, or informed traders who know exactly the value of stock and who consequently buy when the value is high and sell if the value is low. The ratio of informed to uninformed traders is 1 to 5. The value of the stock is 110 if it is high and 90 if it is low, and both are seen as equally likely by the market maker. Work out the market maker s bid and ask quotes in the first round of trading. You seek to implement a return based trading strategy to exploit potential momentum effects in the stock market. The following table shows the most recent 3-month returns on 5 stocks in which you seek to trade. Stock A B C D E 3-month return 5% 3% -1% -2% 8% Based on these data, work out a set of weights for your portfolio such that you commit no capital to your position. 2. (a) Explain what we mean by floating-rate debt. Discuss ways in which these instruments are helpful to borrowers. A 5-year bond has annual coupon rate of 5% and yield to maturity 6%. What is the duration of the bond? What is the convexity of the bond in part? 3. (a) Explain the difference between hedging using put-option protection and Value-at-Risk (VaR). Discuss the relative advantages and disadvantages of the two hedge-strategies. A portfolio has a value V that follows a geometric Brownian motion with drift parameter (instantaneous return) m=0.10 and diffusion parameter (volatility) σ=0.2, which implies that the log return of the portfolio value from time t to time T, ln V T ln V t, is normally distributed with mean (m σ 2 /2)(T-t) and variance σ 2 (T-t). What is the 1%, 20-day VaR of the portfolio? Hint: If X is a normally distributed random variable with mean M and variance S 2, then Z = (X-M)/S is a standard normally distributed random variable with mean 0 and variance 1 with probability Prob(Z -2.33) = N(-2.33) = 0.01. Consider the portfolio in part, and assume that the risk free rate (continuously compounded) is 2%. The costs of a 20-day European call and put options on the portfolio with exercise price 1,000 are, respectively, 17.766 and 16.671 per 1,000 capital invested at time t (i.e. assuming V t = 1,000). Create a put-protected portfolio which over a 20-day period will not end up at a value below its current levels V t. UL14/0234 Page 2 of 5
4. (a) Explain the Treynor-Black model outlined in the subject guide. A competitive risk neutral market maker clears the market for trading in an asset. There are two traders, an uninformed noise trader and an informed trader who has perfect information about the true value of the asset, which is 110 or 90. The market maker thinks the two prices are equally likely. The uninformed trader buys one unit or sells one unit of the asset with equal probability. The market maker observes the aggregate orders from the two traders and clears the market. Work out the optimal trading strategy and the expected profits for the informed trader. You find that the auto-covariance in price-changes (measured transaction by transaction) is -0.02. What do you expect is the spread between the bid and ask prices in this market (measured in dollars and not in percentages)? 5. (a) Hedge transactions involving the trading of derivatives have zero net present value, so will never increase the value of the corporation. Discuss this statement, and explain why hedging of corporate risk nonetheless can add value to corporations. A portfolio has a beta of 0.5, and idiosyncratic risk with variance 3%. The variance of the market portfolio is 10%, and the return on the market portfolio is 8% on average. The risk free return is 2%. What is the required return on the portfolio in order that it matches the market portfolio in terms of the Sharpe ratio? Define absolute and relative risk aversion. In asset allocation situations where the investors split their investments into a safe and a risky asset, how do investors with constant absolute risk aversion optimally choose their portfolios as their wealth changes? What about investors with constant relative risk aversion? UL14/0234 Page 3 of 5
6. (a) Explain what we mean by the term structure of interest rates. Name three different types of hypotheses explaining the shape of the term structure of interest rates. The price of a bond is P, and the yield to maturity is r. You estimate that the current ratio of the change in the bond price, ΔP, over the change in the yield to maturity, Δr, is -4.5 times the price of the bond P. You also recognise that the ratio ΔP/Δr above is not constant for varying levels of r and you are trying to work out the numbers for the current yield to maturity of 5%. If the price of the bond is P=100, what is the (Macaulay) duration of the bond? Explain how we can make use of bond duration in practice. You are given the following information about a portfolio, denoted A, the market portfolio, denoted M, and the risk free asset, denoted R. Portfolio A Market portfolio M Risk free asset R Expected return 7.3% 8% 2% Variance 10% 9% 0 Beta 0.88 1 0 Jensen s alpha 0.04 0 0 According to the Treynor-Black model, the optimal mix of the A and M portfolios for variance-averse investors is given by the formula In this formula, w is the weight on portfolio A, α A is Jensen s alpha of portfolio A, β A is the beta of portfolio A, Er M is the expected return on the market portfolio, r F is the risk free return, Var(ε A ) is the idiosyncratic risk of portfolio A, and σ 2 M is the variance of the market portfolio. Work out the optimal weight w. UL14/0234 Page 4 of 5
7. (a) Explain what we mean by collateralised debt/loan obligations. It has been claimed that these instruments played a role in undermining banks lending operations in the period leading up to the financial crisis in 2007 explain the argument behind this assertion. An investor has mean-variance preferences which can be expressed as the function U(µ,σ2) = µ - (ρ/2)σ 2, where µ is the expected return on the investor s portfolios, σ 2 is the variance of the investor s portfolio, and ρ > 0 is a parameter describing the investor s variance aversion. Derive the optimal portfolio for the investor when all investors have mean-variance preferences and there exists a risk free asset. Also derive the critical value of ρ which determines the cut-off point between investors who are net lenders and net borrowers of the risk free asset. In the subject guide there is a discussion about the difficulties of measuring the performance of hedge funds. The following table is an extract from this material, and shows the actual performance data on a hedge fund against the S&P 500 index. S&P 500 Hedge Fund Monthly mean return 1.4% 3.6% Monthly standard deviation 3.6% 5.8% Annual Sharpe ratio 1.39 2.15 Explain what the numbers in the table mean. Explain how the hedge fund achieved these numbers, and why the real performance of the hedge fund may not be as high as the numbers indicate. 8. (a) Explain how you can use the single index model to estimate the variance-covariance matrix of stocks. Why is this method useful in practice? A bond is quoted with a price of 100.20 per 100 face value. The coupon of 3.2% of face value is paid once a year, and it is 45 days since the last coupon payment. If you were to trade this bond, what price do you expect to pay for the bond? The expected return on the market index is 8%, with standard deviation 0.3, and the risk free return is 2%. You consider holding a portfolio that has at most standard deviation 0.2, subject to the constraint that the portfolio earns an M 2 measure of 2%. What expected return is required to meet your investment objective if the portfolio has maximum risk? END OF PAPER UL14/0234 Page 5 of 5