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Asset Pricing, Traded Assets, Different Groups, Utility Function, Consumption, Measures Risk Aversion, Chosen Portfolio, Information Contained, Risky Asset, Sub Innovations are some points from past exam paper of Financial Economics.
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There are three questions on the exam, representing Asset Pricing (236D or 234A), Corporate Finance (234C), and Empirical Finance (239C). Please answer exactly two 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. Asset Pricing Consider an economy with two traded assets, a safe asset with net return zero, and a risky asset that makes a single dividend payment of
X^ T
j=
εj
on a finite future date T. Here εj ∼ N(0, σ^2 ) are i.i.d., and each εj can be decomposed as εj = ε^1 j +ε^2 j +...+εzj for some fixed z > 0 integer, where the εkj (k = 1, ..., z) are i.i.d. normal. This economy has z equal-sized groups of news-watchers, who gradually learn the in- formation contained in the εkj news. Learning about εt+z− 1 starts in period t, when group 1 observes ε^1 t+z− 1 , group 2 observes ε^2 t+z− 1 , and so on, with group z observing εzt+z− 1. In period t + 1, groups “rotate” in learning about εt+z− 1 : now group 1 observes ε^2 t+z− 1 , group 2 observes ε^3 t+z− 1 , and so on, with group z observing ε^1 t+z− 1. Thus all subinnovations of εt+z− 1 are observed by exactly two groups at the end of period t + 1. Learning about εt+z− 1 continues in this fashion over the subsequent periods, and by the end of period t + z − 1, εt+z− 1 becomes publicly known. This procedure implies that at the end of some date t, any given agent knows εt completely, knows z − 1 of the z sub-innovations in εt+1 (i.e., a “share” (z − 1) /z of εt+1), knows a share (z − 2) /z of εt+2, and so on, and knows a share 1/z of εt+z− 1. Thus, while agents in different groups have different information, on any given date they have the same “amount” of information. (Throughout this problem, you can assume that t is much smaller than T , so t + z − 1 does not “bump” into T ). (a) Suppose that news-watchers have utility function
U = E [− exp{−a · cT }]
where cT is consumption in period T and a measures risk aversion. News-watchers choose their portfolios on every date t. Each time, however, they assume (incorrectly) that they will have to hold their chosen portfolio until T , i.e., that they will not be able to rebalance before T. Show that, under these assumptions, the number of shares of the risky asset demanded by a news-watcher in group i on date t is
xit =
Eit [DT ] − Pt a · varit [DT ]
where Pt is the asset price, and Eit and varit are the conditional mean and variance. Explain the comparative statics of xit with respect to Eit [DT ], varit [DT ] and a. (b) Assuming that news-watchers only use information contained in the news they observe when computing Eit [DT ] and varit [DT ], (i.e., that they ignore the information content of the asset price), prove
1 z
X^ z
i=
Eit [DT ] = Dt +
z
[(z − 1) εt+1 + (z − 2) εt+2 + ... + 2εt+z− 2 + εt+z− 1 ]
where Dt = D 0 +
Pt j=0 εj^. (c) Denote the supply of the risky asset by Q and assume that there is a unit mass of news-watchers (so each group has a mass of 1/z people). Write down the market clearing
Question #2. Corporate Finance Consider a company A that announces the acquisition of another company T. The acquisition is fully stock-financed: A has s shares outstanding and issues additional s^0 shares to target shareholders. The stand-alone values one day prior to the merger announcement are V (^) −A 1 and V (^) −T 1 and one day after the merger announcement V (^) +1A and V (^) +1T. Let’s assume that the merger is completed at the end of the day after the merger announcement (lawyers and investment bankers have become incredibly fast and efficient ...), and denote the value of the joint company on that day by V (^) +1A∪ T.
(a) Provide the formula for the ‘announcement effect’, separately for A and T , to measure the abnormal returns from the merger for the shareholders of acquiring company and for the target company. Provide also the formula for overall abnormal returns, measuring the net announcement effect, denoting the market return from day −1 to day +1 by Rm − 1 ,+1.
(b) Suppose that you find that the abnormal acquiror returns are negative, but you believe that the negative returns do not indicate that the merger is (jointly) value-destroying across the two companies. Rather you suspect that A ‘overpaid’ so that A-shareholders are worse off. How can we use the abnormal returns calculated above to test this hypothesis? Calculate the threshold value for the number of newly issued shares, s^0 , so A overpays iff s > s^0. Provide an interpretation of the formula.
(c) Calculate the minimum number of shares, s^0 , for which T -shareholders are willing accept the tender offer. Provide an interpretation of the formula. Explain why A may need to pay more than the minimum, i.e., why s > s^0 , due to ‘free-riding’ as pointed out by Grossman and Hart (1980). Assume that A needs to acquire at least 50% of T -shares for the merger to be completed.
(d) Suppose that the additional test from (b) indicates that the negative abnormal re- turns to A are not (only) due to overpayment, but you are still not convinced that the merger is value-destroying. List two more alternative interpretations of the negative abnormal ac- quiror returns, which allow for the merger to be value-creating, with a brief explanation.
(e) At the morning of the second day after the merger, before the markets open, the Department of Justice decides not allow the merger for anti-trust reasons. (Inspired by our fast lawyers and ibankers, the DOJ has become incredibly fast, too ...) Explain how one can use this policy experiment to distinguish between value destruction and the alternative interpretations you listed under (c). Be specific about the returns you calculate to test different explanations.
(f) Suppose that your calculations from (d) indicate that your initial prior was right: Despite the negative abnormal announcement effect, you can use the policy experiment to prove that the merger was value-creating (or, rather, would have been value-creating, had it gone through.) Explain why one should not generalize the inference from this — why might the abnormal returns to this policy experiment not representative of the average merger in a broad cross- section of mergers?
(g) Let’s now assume that the initial negative abnormal returns of the acquiror were due to overvaluation, as pointed out by Shleifer and Vishny (2003), even though the merger was value-creating (or, rather, even though the merger would have been value-creating had it gone through). What will be the stock price reaction of A to the announcement of the merger break-up? Specify both the sign of the returns and whether A will reach its pre-merger level V A^ again (adjusted for daily expected returns).
(h) The table below is from a recent working paper (Savor, 2006), in which the author undertakes a similar exercise as the policy experiment discussed above. (He uses a broad sample of ‘failed bids’ including all failed bids other than those failed “due to mispricing of the acquiror. See the notes for a definition of the other subsamples.) Discuss the results in the table. In particular, discuss what the first and fifth column (+/-1 day returns) imply, given your calculations and derivations above. Then discuss the additional insights from columns 2-4 and 6-8. How do you interpret the differences between stock-financed and cash-financed bids?
