When answering each question, state any additional assumptions you may need to make. Show all working/calculations.

(a) Stock A has a beta of 0.8 and an expected return of 0.084. Stock B has a beta of 1.5 and an expected return of 0.14. (i) Assuming that the CAPM holds, what is the risk-free rate and expected return of the market? [3 marks]

(ii) If Stock C has a beta of 2 and expected return of 0.2, does CAPM still hold? Would an investor want to be long or short Stock C? Explain. [2 marks]

(b) An investor is considering two investments. The first investment is a perpetuity that pays 500 at the end of each odd year and 750 at the end of each even year. The second investment is a growing annuity that pays 400 at the end of the year, has an annual growth rate of 2% and has a final payment in 50 years. The term structure is flat at 5% per year. Which investment should the investor choose? Explain. [5 marks]

(c) You are a bond trader and observe that the current one-year spot rate is 2% and the current two-year spot rate is 4%. If the term structure stays the same for a year, what is the oneyear return on a default-free two-year 15% annual coupon bond with a par value of 1000? [5 marks]

(d) When there is an increase in the short-term interest rate, does it have a greater effect on longer-term government bond prices or on shorter-term government bond prices, holding everything else constant? Explain. [5 marks]

(e) There are N securities in the market. All securities have a variance of 0.1, and the correlation between every pair of securities is 0.5. An investor wants to construct an equally weighted portfolio which has a variance of 0.052. How many securities does the investor need to include in their portfolio to fulfil this requirement? [5 marks] Question 2 [25 marks] When answering each question, state any additional assumptions you may need to make. Show all working/calculations.

(a) Consider the following two strategies: Strategy 1: Go long one call option with strike price K + 2C, go long one call option with strike price K 2C, and go short 2 call options with strike price K. Strategy 2: Go short two put options with strike price K, go long one put option with strike price K 2C, and go long one put option with strike price K + 2C. Both strategies are based on the same underlying non-dividend paying stock and all options are European and have the same maturity date, T. Both K and C are positive constants, K 2C > 0 and the stock price today is equal to K. Which strategy has the higher cost to implement today? You must use a payoff table at maturity to comprehensively justify your answer, stating any assumptions. Why would a trader use these strategies? [10 marks] (b) Consider a three-period binomial model (t = {0, 1, 2, 3}), with a risky non-dividend paying stock, Prudential, which is currently trading for 1,350. In each period the stock can go up by 30% or down by 20%. The risk-free rate is 2% in the first period, 3% in the second period, and 1% in the third period. Using the risk-neutral pricing method, what is the no-arbitrage value today of an at-themoney European put option on Prudential stock with maturity date t = 3? Would the value of the option change if it was American? Explain. [5 marks]

(c) You work as a commodities trader and are trying to calculate the no-arbitrage price of a forward contract on gold. The current spot price of gold is 1,325 per kg and the annual risk-free rate is 3% per year, constant over time. The storage cost of gold is 50 per year per kg, and is paid at the beginning of each year the gold is stored. Assume the convenience yield for gold is zero. What is the 10-year forward price if the forward contract specifies 250kg of gold? [5 marks] (d) Explain intuitively how volatility in the underlying stock price affects the prices of both call and put options written on the underlying stock. [5 marks] Section B: Answer all questions from this section and all questions from Section A Question 3

[25 marks]

As a new analyst at an investment firm that specialises in alternative investments, your first assignment is to advise the investment committee on a potential investment in Digital Collective (DC), a new gallery that is planning to specialise in digital art, and is looking to raise 15M. The gallery does not have any pre-existing debt obligations. The committee has warned you that the digital art scene is new and therefore fraught with information asymmetries about the quality of galleries, alongside uncertainty about the chances of disrupting the art world. A gallery can either disrupt the market and generate a one-off cash flow of 150M, or fail to disrupt the art market, and produce a one-off cash flow of 10M. There are broadly two types of galleries, innovative and stale, and there is an equal number of each type in the market. Each type differs in their probability of disrupting the art world. Innovative galleries have a 4/5 probability of disrupting the market, whereas stale galleries have a lower probability of disruption equal to 1/10. The owner of Digital Collective knows whether their gallery is innovative or stale, everyone is risk neutral, there is no discounting, there are no taxes, markets are competitive, and there are no costs of financial distress. When answering each question, state any additional assumptions you may need to make. Show all working/calculations.

(a) Suppose that you know DCs true type, i.e. whether it is innovative or stale. If you are considering an equity investment in DC, would DC face the same financing terms regardless of its type? Why/why not? How large an equity stake would you advise the investment committee to ask for? [5 marks] (b) Suppose now that you do not know DCs type. How large an equity stake in DC would you advise the investment committee to ask for? [4 marks]

(c) Repeat parts (a) and (b), but now assume that you are considering a debt investment in DC. That is, determine what face value(s) of debt you would advise the investment committee to ask for. [6 marks] (d) Suppose you dont know the gallerys type, and you offer the owner of DC a choice between the debt and equity financing contracts you found above. Which contract will the owner choose if DC is an innovative gallery? Explain. [5 marks]

(e) Suppose now that costs of financial distress C > 0 exist, such that firm value decreases by C if the gallery goes into default. Suppose too that you cannot distinguish DCs type. For what values of C would the owner of DC prefer equity financing over debt financing? Explain.