This paper is not to be removed from the Examination Halls

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1 ~~FN3023 ZA d0 This paper is not to be removed from the Examination Halls UNIVERSITY OF LONDON FN3023 ZA 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 UL14/0233 Page 1 of 5

2 1. (a) Explain what we mean by exchange traded funds. What benefits do these funds offer to investors? You spread your investment equally in 10 stocks. Each stock has a beta of 1.2, and idiosyncratic risk (the difference between total variance and systematic risk) of 5%. The variance of the market portfolio is 10%. What is the total risk and the idiosyncratic risk of your portfolio? Stocks have a two-factor structure. Two widely diversified portfolios have the following data. Portfolio A has average return 10% and factor betas 1.5 and 0.4, respectively, on the first and second factor. Portfolio B has average return 9% and factor betas 0.2 and 1.3, respectively, on the first and second factor. The risk free return is 2%. What are the risk premia for factor one and factor two? 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 an annual coupon rate of 5% and yield to maturity of 6%. What is the duration of the bond? What is the convexity of the bond in part? 3. (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? UL14/0233 Page 2 of 5

3 4. (a) Explain why asset allocation over longer time horizon can be approached as a myopic problem when relative risk aversion is independent of wealth. Consider the situation where a company has a pension liability next year of 1,000, and that the pension liability is expected to grow at a rate of 1% each year indefinitely. The discount rate for this liability is 5%. You are interested in immunising the value of the liability from changes in the interest rate. To do this you can trade a 20-year zerocoupon bond which has 5% yield-to-maturity. What are the details of your immunisation strategy? You can buy stocks on margin by borrowing from your broker on a margin account with 60% initial and maintenance margin. You utilise your margin account maximally. You buy 1,000 shares of a stock valued at 10 per share in year 0. In year 1 you first receive a dividend of 1 per share, and then you sell 700 of your shares at an ex-dividend price of 11 per share. In year 2 you first receive another dividend of 1 per share, and then you sell the remaining shares at an ex-dividend price of 10 per share. What is the 2- year return on your capital? Assume the cash proceeds are kept in the margin account with zero interest rate. 5. (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 (annually compounded). 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 Jensen s alpha UL14/0233 Page 3 of 5

4 According to the Treynor-Black model, the optimal mix of the A and M portfolios for variance-averse investors is given by the formula: w = α A α A (1 β A ) + (Er M r F ) Var(ε. A) 2 σ M 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 M 2 is the variance of the market portfolio. Work out the optimal weight w and interpret your answer. 6. (a) Explain what we mean by the equity premium puzzle. Based on the subject guide, explain one way to resolve this puzzle. The Black-Scholes call option formula is C = S N(d 1 ) PV(X) N(d 2 ), where S is the current stock price, PV(X) is the present value of the exercise price paid at the maturity of the option, N(.) is the cumulative standard normal distribution function, and d 1 and d 2 are parameters that depend on S, X, the risk free interest rate, the volatility of the stock, and the time to maturity. Suppose S = PV(X) = 100, d 1 = 0.1, d 2 = -0.1, N(d 1 ) = , and N(d 2 ) = Use the call formula to derive the expression of a put option with the same exercise price. What are the call and the put prices? Suppose you buy x call and y put options of the type mentioned in part of this question. What is the ratio x/y such that the delta of the option portfolio is zero (i.e. such that the value of the option portfolio does not change for small changes in the underlying stock price S)? Explain how this portfolio can be used to hedge against changes in the volatility of the stock. 7. (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 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 Sharpe ratio is required to meet your investment objective? UL14/0233 Page 4 of 5

5 8. (a) The information ratio for a portfolio is defined as Jensen s alpha divided by the unsystematic (idiosyncratic) risk of the portfolio. Explain how this ratio works, and discuss its usefulness for investors. In Roll s model described in the subject guide we consider a dealer market for an asset that has the fundamental price at time t of m t, which changes in response to the arrival of new information, m t = m t 1 + u t, where u t represents new information at time t. The transaction price at time t at which trade takes place is p t = m t + q t c, where q t is equal to +1 or -1 and c is a constant. Roll argues that Cov( p t, p t 1 ) = c 2, where Δp t is the price change at time t (= p t p t-1 ). Explain the relationship between the transaction price and the fundamental price of the asset. Derive Rolls covariance term and explain what additional assumptions are needed as you go along. How can we interpret this result? You are given the following information about 1-year put and call prices for an asset that is currently trading at a price of 100. Exercise price 90 Exercise price 100 Exercise price 110 Call Put Are there arbitrage opportunities in this market? If so, demonstrate how they could be exploited. END OF PAPER UL14/0233 Page 5 of 5