Asset Pricing and Macro-Finance
Assignment 1-Spring 2025
Instructions
(1) Deadline: 20 February, noon. This is an individual assessment and counts towards 25% of the overall course grade.
(II) Answer all questions. Clearly separate and number answers to each of the questions in the submitted document.
(III) Submission to be made electronically via the course Moodle page. This includes the written answers including analytical steps taken, numerical answers when required (hand written or typed are equally acceptable).
(IV) The word count and grade are indicated in each part—While the overall report is expected to be around 4 pages, there is no penalty for exceeding this limit.
Question 1
Consider a risk-averse investor with the power preferences (where y denotes the risk aversion magnitude) and an initial fund value of Wi at date t. The investment environment offers two alternatives to the investors including: (i) a safe asset with a fixed risk-free rate Rp = 1 + r per invested unit between dates t and t + 1; and (ii) common equity share of a private company that pays dividend Dt+1 per share. The equity return (Re) involves risk depending on the future company's performance. Consider that the company's dividend per share value summarises the performance and follows a Normal distribution with D+i~N(μ,o2) for any future date i>1.
1.1. Assume that the investor intends to invest all of their fund value where the fraction w is allocated to the risky investment and the remaining 1-w is allocated to the riskfree investment such that Rw=(1-w).Rp+w.Rg. Derive the pricing expression for the common equity (price per share Pi) according to the first fundamental asset pricing equation. Denote all additional terms you used and define the stochastic discount factor in this context. (Mark: 10%, 0.5 page)
1.2. Suppose the investor considers a scenario where w is pre-determined: the equity share is priced based on the stochastic discount factor obtained in the previous part when w 0.50. Under this scenario, compute the present value of the equity share (from the perspective of date t). Suppose that r = 4.75%, μ=£0.50, o= £0.15 and y3. (Mark: 20%, include brief derivations and final numerical answers: 0.5-1 page)
1.3. How much will the price change, when o increases to £0.20 and y = 0? Provide an asset pricing argument to explain the difference between valuations in this part comparing to the previous part. (Mark: 30%, 2-3 lines)
Question 2
Consider the asset pricing framework from the course, with a particular emphasis on the first fundamental asset pricing equation. According to Kremens and Martin (2019), the expected currency appreciation (ECA) is summarised by the interest rate differential (IRD) + the quanto-implied risk premium (QRP). Equivalently, the currency risk premium anticipated by such an investor (assume logarithmic preferences) is revealed by QRP What is the overall relationship between the IRD and QRP (negative, unrelated, postive)? Explain why. Provided answer needs to refer to a combination of analytical foundations, equations and financial interpretation of the technical expressions. Ensure to define all terms used and clarify the units of variables and any other notations. (Mark: 40%, max: 2 pages, 500-800 words)
References
Lukas Kremens and Ian Martin. The quanto theory of exchange rates. American Economic Review, 109(3):810-843, 2019.