Reference no: EM13900266
1. Within the APT (Arbitrage Pricing Theory) model of equilibrium returns, you are considering an investment in two equities: Company A operating in country 1 (home country) and Company B operating in country 2 (foreign country), with both companies operating in the same sector of the economy in a single country (home country). Both countries share common currency but have differential inflation rates.
Assume that a two-factor APT model holds and the factors are as follows:
• Factor 1: General News Component: Inflation
• Factor 2: Idiosyncratic factor: Company A strategy differential from Company B. Specifically, assume that Company A is operating a high profit margin strategy, while Company B is operating a low margin strategy.
a. How would you model explicitly these two factors' impact on equities A and B? What assumptions will be required to assure general applicability of the standard APT framework to this model?
b. Define the risk premium (or the market price of risk) under APT in the above model setting for both companies.
c. Now, suppose that Company B diversifies its markets to exports into the home country 1. This puts it into direct competition with Company A. How will the APT model change in this case? Explain your answer.
2. Distortionary taxation refers to tax rates that have a direct impact on investment decisions of the agents by altering risk premium paid to investors in the risky assets. Conversely, non-distortionary taxation implies that once the tax is levied on an investor, it has only the effect of reducing her rates of return, without altering her preferences or the degree of risk aversion. Assume both taxes apply to all investors in the market.
a. Graphically, define market portfolio allocations within the CAPM framework in the presence of a non-distortionary tax.
b. Briefly compare and contrast the two market portfolios and investors' portfolio allocations before and after tax for more and less risk-averse investors.
3. Consider the CAPM model of equity returns.
a. In a general CAPM setting, define the market price of risk relationship in the presence of inflation. How will the risk premium evolve over time if inflation is persistent and rising?
b. Now, suppose that in addition to inflation, you are also facing the market with two types of agents. Assume each agent has a distinct information set. Denoting by R, the rate of return on investment in risky asset i, one type has expectations given by E(1)(R1) = E(1)(R1 |I1,t), where I1,t is the information set available at time t to agent 1.
The other investor has E(2)(R1) = E(2)(Ri) |I2,t) where I2., is the information set available at time t to agent 2. Suppose II,, is contained within I2,, so that at any point in time, Agent 1 has less information than Agent 2. What do you expect to happen to the efficiency frontier for the market and for each agent? Explain your answer and all assumptions that form the basis for your answer.
c. What will be the optimal portfolia for Agents 1 and 2? What will be the new market portfolio and how will it relate to Agents 1 and 2 information sets? Please, discuss your answers and state all required assumptions you make.