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Smeal College of Business Taxation and Management Decisions: ACCTG 550Pennsylvania State University Professor HuddartTiming options1In the United States, the taxation of capital gains and losses depends onthe length of time the asset has been held. Short term capital gains arise onthe sale of capital assets held less than one year. Long term capital gains andlosses arise on the sale of assets held more than one year. Currently, shortterm capital gains and losses are taxed at a top rate of 35% while long termgains are taxed at rates of more than 20%, even for taxpayers in the topbracket. The asymmetric treatment of capital gains and losses introducessome interesting “tax timing options” into portfolio trading strategies. Thisproblem set illustrates some aspects of those options.Suppose the long term capital gains tax rate is 30% while the shortterm tax rate is 40%. In working on these problems, assume you have otherincome with which to offset any losses you trigger. Also, you should ignoreany limitations on the deductibility of losses.A graduate of this class has constructed two synthetic securities, A andB, that are taxed as capital assets. These assets are peculiar in that theymay only be traded every 364 days. On each trading date, the asset isworth either half or double the value it had on the previous trading date,independent of the payoff on the other asset. For simplicity, suppose theseoutcomes are equally likely. Then the expected before tax payoff at theend of 364 days from a $1.00 investment in either asset is $1.25, since1/2$2.00 +1/2$0.50=$1.25.(1) What is the after tax expected payoff from holding asset A for one period(i.e., 364 days) and then selling it?(2) What is the after tax expected payoff from holding asset A for one period(i.e., 364 days), then selling it to buy asset B, then selling asset B atthe end of two periods?2(3) What is the after tax expected payoff from holding asset A for twoperiods (i.e., 2 × 364 days) and then selling it? Explain the difference,1See Robert M. Dammon and Chester S. Spatt, “The Optimal Trading and Pricingof Securities with Asymmetric Capital Gains Taxes and Transaction Costs” Review ofFinancial Studies (Fall 1996) 9:3 921–952.2Wash sales rules would deny recognition of a loss on the sale of asset A if it wereimmediately repurchased. But if a different asset is purchased, the wash sale restrictiondoes not apply.cSteven Huddart, 1995–2005. All rights reserved. www.smeal.psu.edu/faculty/huddartACCTG 550 Timing options3if any, between the expected payoff computed here and in the previouscase.(4) Suppose your investment horizon is exactly two periods (i.e., 2 × 364days) long. Your objective is to maximize expected after tax returns.Youwant to stay fully invested over that time in either asset A or B.What is the optimal dynamic investment and trading strategy? (Hint:The problem is dynamic because what you decide to do at the end of thefirst 364 day period can depend on the asset values at that date. Seenthis way, there are four possible strategies. It is instructive to calculatethe expected payoff from each strategy.)(5) How does the net-of-tax payoff from investing in these assets depend onthe trading strategy you adopt?(6) What is the effect of increasing the variance of asset returns on thestrategies described above?(7) Is it possible for the after tax return to exceed the pretax return whenlong and short term capital gains are taxed differently? If so, give anexample. (Hint: Play with the parameters—especially the tax rates—laid out above.)(8) Suppose securities A and B are unavailable. How might you use theintuition developed here in practice?Page


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