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Financial Innovation, Future Outcomes, Risk Neutral Intermediary, Initial Wealth, Probability of State, Signal Distribution, Realized and Distributed, Financial Claims, Reservation Price, Conditional Expectations are some points from past exam paper of Financial Economics.
Typology: Exams
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There are two questions on the exam, representing Macroeconomic Finance (234A) and Corporate Finance (234C). Please answer both questions to the best of your ability. Do not spend too much time on any one part of any problem (especially if it is not crucial to answering the rest of that problem), and don’t stress too much if you do not get all parts of all problems.
Good luck!
Question #1. Macroeconomic Finance (Economics 234A) This question is about the price and welfare effects of financial innovation when not all future outcomes are equally salient to investors. Consider an economy over three dates t = 0, 1 , 2 with two assets B and A, which pay off at t = 2. B pays R > 1 for sure, while A pays yi with probability πi where i indexes the three possible states of the world at t = 2, which are: g (growth), d (downturn), r (recession). Assume that yg > 1 > yd > yr and that πg > πd > πr. At t = 0 both assets, which are in unit supply, are owned by a patient risk-neutral intermediary with preferences
max E [C 0 + C 1 + C 2 ].
The economy also has an infinitely risk-averse investor with initial wealth w and preferences
max E [C 0 + C 1 + θ min (C 2 g, C 2 d, C 2 r)]
where θ > 1. At t = 0 financial claims are traded and prices set. At t = 1 a signal s ∈ {sL, sH } observed, claims are re-traded and new prices set. Here sH is a “good signal” which raises the probability of state g and reduces that of r, while sL is a “bad signal” which raises the probability of r and reduces that of d. The exact signal distribution will not be important for answering the questions. At t = 2 returns are realized and distributed. Assume that both actors are price-takers and that asset prices are determined to equate demand and supply.
Part A Assume that both actors are rational, and that the financial claims traded, which we label the bond and the share, coincide with the basic assets B and A. (a) Show that at t = 0 the investor’s reservation price is θR for the bond and θyr for the share. What is the intermediary’s reservation price for these two financial claims? From now on, assume that θyr < E 1 [y|sL]. Argue that this condition implies that there is no trade in shares. (E 1 [.|.] denotes conditional expectations at t = 1.) (b) To solve for the equilibrium in the bond market at t = 0, plot the demand curve of the investor and the supply curve of the intermediary in a diagram where the vertical axis is the bond price and the horizontal axis is the bond quantity. Recalling that the investor may be constrained by her total wealth, show that demand is first horizontal then decreasing, and compute the point at which is starts to decrease. Explain why supply is a step function. Assuming that w is large enough, what is the equilibrium bond price pB, 0? Indicate the area in the diagram which measures the gains from trade. (c) What is the bond price at t = 1 after the signal is realized? Why?
Part B Now we introduce financial innovation. Both actors are still rational, but now the inter- mediary can repackage some of the payoffs of A to obtain a new synthetic safe bond which promises to pay R with certainty at t = 2. The synthetic bond is a perfect substitute for the true bond and can be sold to the investor, while the intermediary keeps the residual risky claim. (d) What is the maximum amount of synthetic bonds that the intermediary can create from the unit supply of A?
Question #2. Corporate Finance (234C - Financial Decision-Making in Firms)
Applying Differences in Beliefs to Investment and Capital Structure Policies (maximum of 64 points)
In class, we considered the implications of differences between managerial and market beliefs about the profitability of a firm’s investment project for internal investment, external investment (mergers), and for capital structure decisions. Capital structure decisions include the decision to payout dividends, which we did not draw out explicitly in the models and empirical analyses considered class. In this exam, we will again investigate investment and financing decisions, but also undertake a simply attempt to model out the dividend decision. Moreover, we will consider a new model of differences in beliefs.
Consider an all-equity firm with a CEO who acts in the interests of all shareholders. The number of shares is normalized to one, and all investors are risk neutral. The risk-free interest rate is 0. Time Structure. There are three dates. At date 0, the CEO and the market observe signals about a project available to the firm. At date 1, the CEO pays a dividend and/or raises external financing, and also invests capital in the project. At date 2, the cash flows from the project are realized. The cash flows are used to pay off creditors who provided external financing at date 1. Any remaining funds go to shareholders as the final dividend. Investment. An investment I ≥ 0 in the project at date 1 yields cash flows of Y · f(I) at date 2, where Y is the project quality, modelled as a random variable, normally distributed with mean μy and precision ηy (standard deviation 1/ηy) and the function f is increasing and concave with f(0) = 0. Prior to the investment decision, at date 0, the CEO observes a signal s about the project available to the firm, where s is normally distributed with mean equal to the project quality Y and precision ηs. The expected value of the project quality conditional on the signal s, y(s) ≡ E[Y |s] is calculated using Bayes rule. The initial beliefs about the project follow the condition: μyf 0 (0) ≤ 1. Financing. At date 0, the firm starts out with cash C 0 > 0. At date 1, the CEO declares a dividend D and raises external financing F. We model external financing as costly (relative to internal financing) and capture this capital-market friction in a simplified manner: for a given amount F of external financing, the net cash received by the firm is only (1 − β)F , where the cost of external financing β is allowed to be 0 (benchmark of no friction) but assumed to be strictly smaller than one: 0 ≤ β < 1. The amount of dividend paid at t = 1 is limited by the total cash available at t = 1. Any cash remaining after dividend payout is invested in the project.
Question 1. As mentioned above, the initial beliefs about the project follow the condi- tion: μyf 0 (0) ≤ 1. Explain what this condition implies for the ex-ante NPV of the project (i.e., the NPV prior to receiving any signal) and hence for the role of the signal in inducing the CEO to invest. (2 points)
Question 2. Calculate the CEO’s posterior mean of the project quality y(s) ≡ E[Y |s] using Bayes rule and provide an intuitive interpretation (i.e., describe the expression). ( 2 points)
Question 3. Express the level of investment I chosen by the CEO at time 1 as a function of the total amount cash available and the dividend payment. (1 point)
Question 4. Formulate the CEO’s maximization problem. Hint: The CEO chooses a policy (I, D, F ) to simultaneously determine the levels of investment, dividend, and external financing based on the signal s. Provide an intuitive interpretation of the objective function and the constraints. (8 points)
Question 5. In this model, we will not be considering the option of share repurchases. However, in terms of total value created, dividends and share repurchases would be perfect substitutes in this model. Under which assumptions is the CEO indifferent between them? (1 point)
In this model, it is easy to show that the investment, dividend, and financing policies depend on the signal s in the following manner: (a) for lowest signal values, s ≤s, there is no investment, no external capital is raised, and the initial cash C 0 is paid out as a dividend, (b) for higher signal values, s< s < ˆs, investment is positive but less than C 0 and is an increasing function of s, dividend is positive and a decreasing function of s, and external capital is not raised, (c) for even higher signal values, ˆs ≤ s < s, investment equals C 0 , dividend is not declared at time 1, and external capital is not raised, and (d) for highest signal values, s ≤ s, investment exceeds C 0 and is an increasing function of s, dividend is not declared at time 1, and the amount of external financing is an increasing function of s.
Question 6. To gain an intuition for the above results, characterize the CEO’s posterior beliefs about the returns to investment in each of the four regions (a) to (d) — both in terms of sign (positive, negative) and compared to the costs of financing. (You do not need to derive the above results (a) to (d) formally!) (6 points)
We now allow for differences in beliefs: The CEO believes that the signal s has precision Cηs. Thus, C = 1 indicates a rational CEO, C > 1 indicates an overconfident CEO who believes that his signal is more informative than it really is; and C < 1 indicates a “diffident” CEO. This difference in the interpretation of the signal influences, in turn, an overconfident CEO’s investment, dividend, and external financing decisions. In this modified model, the following can be shown: (a) Investment is weakly increasing in CEO overconfidence. (b) Dividends are weakly de- creasing in CEO overconfidence. (c) The amount of capital raised through external financing is weakly increasing in CEO overconfidence.
Question 7. Calculate the CEO’s posterior mean of the project quality, now allowing for bias C. That is, calculate y(s, C) ≡ E[Y |s, C] using Bayes rule and provide an intuitive interpretation for the case of overconfidence (C > 1) compared to the rational case. ( 3 points)
Question 8. Provide an intuition for results (a) and (b) above, i.e., for the result that the more overconfident a CEO is, the more he will invest and the less he will pay out
Figure 1:
