Assume that the leather market is a perfectly competitive market. The market demand curve for leather is?
A market that satisfies the assumptions of the Capital Asset Pricing Model (CAPM) comprises n assets. Let the random return on asset i be denoted by R,, the expected return by y , and the corresponding returns for the market portfolio by R,, and ry- Let x, be the proportion of asset i in the market portfolio. (1) (a) Define B, algebraically in this market. (b) Write down the relationship between these expected returns in this market, including a definition of any additional notation that you use. (c) Show that Ex, B, = 1. [6] Consider a market where n = 4, that is, there are four assets in the market with the following attributes: Asset 2 4 Risk-free Asset Expected return (per annum) 14% I'3 3% Market capitalisation C4m [2m (2m The variance-covariance matrix (in %%) of annual returns on the four assets is as follows: Asset x2 for some x2 > 0. The variance of the return on the market portfolio is %%. (ii) (a) Calculate the proportions of each asset in the market portfolio. (b) Calculate B, B2. B, and B4-You are an actuary working for a small, general insurance company that specialises only in long-tailed insurance risks in its local insurance market. The company has a moderate level of free assets. The Board, who require a risk averse investment strategy, has asked for a review of the investment guidelines given to the company's investment managers. It is assumed that there are no regulatory investment restrictions. (i) Outline the instructions that would be given to the investment managers in respect of the assets that they may or may not hold, including any relevant limits. [6] At a recent Board meeting, one of the members suggested that, given the long-tailed nature of the risks insured and the current low historic level of the stock market, the equity proportion of the investment portfolio should be increased to benefit from future stock market increases. (ii) Explain the advantages and disadvantages of his suggestion for the company. [6] Another Board member has suggested increasing the proportion invested in index- linked Government bonds. (11i) Explain the advantages and disadvantages of this suggestion compared with that given to the previous Board member. [4](i) Describe how the Merton model can be used to value the debt issued by a company. [5] A company has a value of 6100m. Its total equity is currently worth 650m, and it has (80m nominal of debt maturing in ten years. The risk-free force of interest is 4% per annum. (ii) Calculate the implied volatility of the value of the company to the nearest 1% using the Merton model. 141 (iii) Calculate the value of vega for the value of the company's debt under the Merton model. [1] (iv) Explain why a low value of vega might be desirable when using the Merton
