**Investment Analysis and Portfolio Management** Lecture 11 Gareth Myles

**Introduction** • This revision lecture will talk about the 2010 exam paper • The important points about the questions will be discussed • The usual mistakes will be noted

**Question 1** (i) Describe what the Capital Asset Pricing Model (CAPM) is intended to explain. [8 marks] (ii) What assumptions does the CAPM make? Which of these assumptions are not made by the Markovitz model of portfolio choice? What is the consequence of the additional assumptions? [8 marks] (iii) What is the security market line? If the CAPM is true, will all securities have observed returns that are on the security market line? Explain your answer. [10 marks] (iv) How can you use CAPM to value a new issue of stock? [7 marks]

**Question 1** (i) Describe what the Capital Asset Pricing Model (CAPM) is intended to explain. [8 marks] This part of the question is usually treated too briefly. There should be two or three coherent paragraphs of explanation. What should this say? The CAPM is intended to explain how the returns on assets are related to the risks. The CAPM is intended to explain the equilibrium pattern of returns in a financial market.

**Question 1** The CAPM is intended to explain the equilibrium prices of assets in a financial market. The CAPM is intended to explain the nature of equilibrium in a financial market. It can also be claimed to explain how individual choices lead to an equilibrium.

**Question 1** (ii) What assumptions does the CAPM make? Which of these assumptions are not made by the Markovitz model of portfolio choice? What is the consequence of the additional assumptions? [8 marks] The assumption should be listed. It is necessary to explain what the Markovitz model is: a model of individual portfolio choice. What assumptions does it make? You can refer back to the CAPM assumptions. What are the additional assumptions of CAPM? That all investors have the same expectations.

**Question 1** This additional assumption has strong implications: it ensures all investors face the same efficient frontier. From this they face the same tangency portfolio, and this must be the market portfolio.

**Question 1** (iii) What is the security market line? If the CAPM is true, will all securities have observed returns that are on the security market line? Explain your answer. [10 marks] It is necessary to explain that the security market line is an equilibrium relationship between the expected return on an asset and the covariance between the return on the asset and the return on the market portfolio. Then the equation for the security market line can be derived from the diagram relating expected return and covariance.

**Question 1** The important step in the construction is the definition of beta. The final part – are observed returns on the SML – is the one that causes mistakes. It is expected return that appears in the SML. The meaning of expected return needs to be carefully distinguished from observed return.

**Question 1** (iv) How can you use CAPM to value a new issue of stock? [7 marks] This question should be answered by reference to the pricing formula. But then it must be observed that there are two unknowns in this formula: the beta and the expected future price. Some comments should be offered on how beta might be estimated.

**Question 2** (i) What is the single index model? [3 marks] (ii) Assume that asset returns are generated by a model for which the market is the single index. The details of the model for three stocks are: The expected return on the market is 12% with a standard deviation of 25%. The risk free rate is 5%. Plot the portfolio frontier for stocks A and B. Plot the portfolio frontier for stock B and C.

**Question 2** How would you construct the portfolio frontier for all three stocks? [15 marks] (iii) An investor you are advising has decided to short sell stock A to finance the purchase of stock B. Would you advise for or against this investment? Explain your reasoning. [5 marks] (iv) Are the data in the table consistent with the predictions of the Capital Asset Pricing Model? If not, would this imply rejection of the CAPM or the single index model? [10 marks]

**Question 2** • The answer should describe the single index as a statistical model of returns. The equation should also be given with an explanation of alpha, beta, and the error term. The answer should also say something about the choice of index. • The calculations for parts (a) and (b) should use the usual table giving return and standard deviation for portfolios with different proportions of the two assets in each part. 11 points should be adequate. The term “plot” means draw two axes on the answer sheet, mark the axes, and plot the points. It does not have to be excessively accurate.

**Question 2** The answer for part (c) should observe that the portfolio frontier for 3 assets is found be calculating return and variance for all combinations of the assets. It should also observe that it is the outer envelope. (iii) The answer should relate back to the plot. Where on the frontier is shortselling of stock A? It is either on the efficient part or the inefficient part. Its location determines the advice. (iv) Use the Security Market Line to calculate returns implied by CAPM. Compare to what the single index model applies. CAPM in this case.

**Question 4** (i) What is an option? Describe the major features of call and put options, and distinguish between European and American options. [6 marks] This is very straightforward. It helps to say it is a derivative security whose value is derived from that of an underlying asset.

**Question 4** (ii) Explain the put-call parity relationship. A stock is currently trading at £10. A European call option on that stock which expires in 3 months and has an exercise price of £11 is currently trading at £1. If the (annual) risk-free rate of return is 6%, what is the price of a put option on the stock with the same exercise price and expiry date? [6 marks] Explain here means provide a description of it as a relationship between the values of puts and calls. Observe that it derives from an arbitrage argument using a risk-free portfolio. State the equation.

**Question 4** The remainder is the application of put-call parity. It is an annual rate of interest so the discrete discounting formula should be applied. (iii) Compute the equilibrium price of a European put option with 6 months until the exercise date if the exercise price is £5.10, the current stock price £5.00, and the stock price at the exercise date may be £5.25 or £4.80. Assume that the annual risk free rate of return is 5%. [7 marks] Observe that it is a put. It has 6 months until exercise but the interest rate is for 1 year.

**Question 4** It is always a good idea to draw the binomial tree. Even if the calculations are wrong this can be marked. (iv) Note that this now switches to an expiry of 9 months. So the interest rate will need adjusting to take account of this. Which answer is “best”? The argument has to be that more sub-periods is always better since the analysis then become closer to approximating the actual behaviour of a stock price. (v) We didn’t do American this year.