simply want to bene®t from a spread perceived too wide between S1and S2 . To do so, we ®rst consider the appropriate hedge ratio asbeing given by the current market conditions, but we adopt again a®xed quantity. S1 and S2 trade respectively at $100 and $51; therefore, the appropriate hedge is $100=$51  1:961. Under theseassumptions, we would manage the position as in Table 1-6. Herethe total pro®t of the position is 1  $90 $100 1:961 $45 $51  $1:765, slightly inferior to the previous case becausewe were less short of S2 .TABLE 1-4Date
S1
S2
Jan. 15Jan. 16Jan. 17Jan. 18
$100$105$98$90
$51$52$501/ 2$45
CHAPTER 1 INTRODUCTION
37
TABLE 1-5Date
S1
S2
Deals S1
Deals S2
Pos. 1
Jan. 15Jan. 16Jan. 17Jan. 18
$100 $51$105 $52$98 $501/ 2$90 $45
+1 @ 100ÐÐ1 @ $90
2 @ $51ÐÐ2 @ $45
111Ð
a
h  N2 a
Pos. 2 V  N1222Ð
$2$1$3Ð
h stands for the relevant hedge ratio to compute V . Note that we neglect the time value of moneyin these calculations for simplicity.
Now consider a small variation of the above scheme in which weadopt the beta of the two stocks as the appropriate ratio. If we want$100 exposure on S1 Ðthat is, 1 share, we know that we should take anexposure of 1=2  $100 for S2 . Assuming, for example, 1=2  1:3, weneed $130 of S2 which turns out to be $130/$51  2:549 shares. In thatcase, the position evolves as in Table 1-7. The total pro®t is here evenhigher, at 1  $90 $100 2:549  $45 $51  $5:294, because themove in S1 and S2 from January 15 to 18 was signi®cantly differentfrom the original beta suggested. S2 lost 11.76 percent $45 $51=$51, and consequently, S1 should have lost 15.3 percent 11:76 percent  1:3 because of the beta of 1.3. Because S1 lost only10 percent, we ended up with a signi®cant gain on the long, in comparison to what historical data would have suggested.It is interesting to note in these three examples that V 6 0, and stillwe consider the position hedged adequately. This particular pointshows that hedging a position in number of units, as we do, doesnot imply that it is also hedged in nominal terms, something we mentioned earlier.Finally, assume we want to hedge the position in delta and get ridof excess nominal exposure at the close every day. We start with a ratiosimilar to that of a previous case and trade from there, as in Table 1-8.On January 16, the existing position has a nominal valuation of1  $105 1:961  $52  $3:038, which we have to hedge away, by selling S1 or buying S2 . We decide for example to sell S1 , to reduce theTABLE 1-6Date
S1
S2
Jan. 15Jan. 16Jan. 17Jan. 18
$100$105$98$90
$511 @ $100$52ÐÐ$501/ 2$451 @ $90
Deals S1
Deals S21:961 @ $51ÐÐ+1.961 @ $45
Pos. 1 Pos. 2111Ð
1:9611:9611:961Ð
V  N1
h  N2
Ð$3:039$1:020Ð
38
THEORY AND TOOLS
TABLE 1-7Date
S1
Jan. 15Jan. 16Jan. 17Jan. 18
$100 $51$105 $52$98 $501/ 2$90 $45
S2
Deals S1
Deals S2
Pos. 1 Pos. 2
+1 @ $1002:549 @ $51ÐÐÐÐ1 @ $90 +2 .549 @ $45
111Ð
V  N1
2:5492:5492:549Ð
h  N2
$30.00$27.55$30.73Ð
exposure on each leg, and we have to sell $3:038=$105  0:029 shares.On January 17, the position is unhedged again, and this time we decideto buy back S2 . The total pro®t is more dif®cult to compute because ofthe succession of deals, but it amounts to 0:029  $105 $1000:971  $90 $100 0:076  $501/2 $51 1:884  $45 $51 $1:788.Notice also that V is systematically equal to zero, which is the intendedeffect of the hedging procedure.The point behind these examples is not to demonstrate that oneparticular method is better than the others, but to show that they yielddifferent results, indeed different by a wide margin. Each method is theconsequence of a number of assumptions and expectations about thesecurities in the portfolio or in contrast to their observed historicalbehavior. In any case, the adequate choice depends on the tradingstrategy implemented.Arbitrage and HedgingStatic and dynamic hedging are critically different in terms of riskmanagement. In a context of arbitrage, it can be argued that the verynature of the underlying convergence requires some sort of ®xed-quantity hedging, for two reasons. The ®rst one has been advanced alreadyand consists of a pure risk assessment. Because delta hedging essentially means that no satisfactory hedge can ever be achieved permanently, it is not well equipped to describe situations in which we expectthe hedge to be so perfect that we consider our pro®t to be locked evenbefore the expiry of the position.TABLE 1-8Date
S1
S2
Jan. 15Jan. 16Jan. 17Jan. 18
$100$105$98$90
$51$52$501/ 2$45
Deals S1
Deals S2
+1@$1001:961@$510:029@$105ÐÐ+0.076@$501/ 20:971@$90 +1.884@$45
Pos. 1 Pos. 210.9710.971Ð
1:9611:9611:884Ð
V  N1ÐÐÐÐ
h  N2
CHAPTER 1 INTRODUCTION
39
A second set of issues has to deal with information and time consistency. The informational content of an arbitrage position is very highbecause by postulating a convergence, we actively project what shouldhappen. It is also stable over time because usually the convergence is ascertain today as it was yesterday. By contrast, delta hedging is a purelyreactive approach, in which the position is managed as a consequenceof market behavior. And it is not stable, in the sense that it is asrandomly distributed as the underlying market prices. Therefore, weare now in possession of one more test of arbitrage-ness, the hedgeratio. Furthermore, we know why we cannot expect options in generalto be ideal candidates to implement arbitrage strategies.42
Carry
The law of one price requires instruments with similar payoffs to haveequal prices today, and more generally everyday until the convergenceis ``consumed''Ðthat is, one of the legs expires or we decide to exit.Because the relationship supporting the convergence is by nature continuous, the arbitrage once set up should take care of itself, and notrequire any more intervention. This implies in turn that the hedgeratio be constant and known with relative certainty.Therefore we can fairly safely make the conclusion that the ®rstorder market risk disappears, but there may be other risks we haveto take into consideration. In the case of index arbitrage, for example, ®nancing, or an uncertainty about expected dividends, is particularly important. Even though we can argue that these other risksare indeed of second-order magnitude, there are cases in which theycan be serious and even become critical, for example, in the case of asqueeze on the short side of a risk arbitrage position.43 If suddenlyshares of the acquirer company cannot be borrowed anymore, andshares already borrowed get recalled, arbitrageurs may have tounwind their position at a loss. In markets where borrowing secu42
This may again be perceived as a somewhat excessive generalization. For example, aviolation of the put-call parity on listed options is certainly an arbitrage, yet itinvolves options. There are clearly examples of pure arbitrage situations developingwith options, but to be really risk free they must consistently exhibit a delta as close tozero as possible. This is the case with a position derived from a violation of the putcall parity.43A squeeze indicates a situation which a scarce resource becomes even scarcer to thepoint where it cannot be borrowed anymore. This phenomenon may happen withsecurities that cannot be borrowed anymore, or with cash liquidity that becomessuddenly extremely expensive to borrow. More on this last point in Part 2.
40
THEORY AND TOOLS
rities is easy and cheap, this risk tends to be small. In the UnitedStates, for example, a signi®cant portion of the market capitalizationis held by institutional investors with a long-term investment horizonÐpension funds typicallyÐand their holdings usually constitutestable sources of shares for this type of situation. In Japan, by contrast, the market for borrowing securities is far less mature, andcosts and liquidity are primary concerns.Therefore, if it is always true that the carry of an arbitrage positionshould induce only moderate trading, it is not always absolutely riskfree. Because we continuously have a short leg, if this leg is not aderivative, we know that we are exposed to a possible squeeze onthe securities we borrow. Furthermore, even if the magnitude of asqueeze is highly unpredictable, its consequences are not:Arbitrageurs have to liquidate their full position quite rapidly and atthe same time, with the inevitable consequence that all of them realizea signi®cant loss.Is that the only risk we should care about? Unfortunately theanswer is no. Consider again the case of index arbitrage, where supposedly we do not have anything to do after execution until expiration.Say you are long cash and short future, and the market is rallyingsharply. If the position is properly hedged, the market movement inand of itself is of no consequence. However, the short future positionneeds to be ®nanced because the exchange will request margin deposits to cover the losses generated by the up-move. The theory says that ifyou cannot ®nance these margin calls at a rate equal to that of theposition, you are losing the rate differential. In a stable interest rateenvironment, this is clearly not a serious concern, but in case of aliquidity squeeze, it may become just that.44This second example con®rms that the carry of the position, even inthe comfortable situation of an absolute convergence, is not risk free.Interestingly, both examples refer to a squeeze as a possible source oflosses. When a trader builds a position, he or she intuitively knows thelevel of noise inherent in all the secondary parametersÐinterest rates,borrowing costs, dividendsÐand will trade accordingly. If during thelife of the position these parameters exit the con®dence interval he orshe priced, he or she is most certainly going to lose from these unexpected moves, and these small accumulated losses may signi®cantlydamage the original pro®tability when the arbitrage was locked.
44
Liquidity ``squeezes'' tend to develop recurrently at the end of calendar years, as wewill see when we examine the market for overnight funds.
CHAPTER 1 INTRODUCTION
41
Naturally this is a dynamic process, and a trader faced with theseannoying losses would draw obvious conclusions and adjust.Whatever he or she does, however, there is always a chance that unexpected moves will spoil the party.Returning to our original question, this means that carrying anarbitrage position is generally risk free, but it requires at least asmuch attention as initiation and expiry. Furthermore, it is clear fromthis discussion that arbitrageurs are not indifferent to the uncertaintyabout the time frame between execution and exit: With equal pro®tability, opportunities with short and known carry are much moredesirable.45
Nonconvergence
Nonconvergence refers primarily to a situation at expiry in which bothlegs of the arbitrage do not come together as expected. In the case of aspeculative position there is no real expiry; therefore, an alternativeview of the same concern is to acknowledge that the convergencehas not materialized after a reasonable amount of time. The magnitudeof what is reasonable here is dictated essentially by judgment andsupported by historical data or precedents if the strategy has beentraded before. In any case, as we said before, every position of thattype should have embedded in it a speci®c time horizon, and successusually depends on how disciplined the traders are in taking losses.Because the convergence is precisely what drives the position in the®rst place, it should be the focus point of testing and modeling effortsprior to engaging any capital in trading. In particular, the most important question can be formulated with a simple probabilistic approach.Assuming the execution and carry are ¯awless, what is the probabilityof failure and associated loss that make the arbitrage a pro®table proposition overall? Consider that historical convergence occurs within afew months with a probability of 80 percent and generates on aggregate a 5 percent return after transaction and ®nancing costs. If P standsfor the maximum expected loss in the 20 percent of cases in whichconvergence fails, it must be such that we still keep a weighted pro®t:80%  5%
20%  P  0 ) P  20%
Therefore, if we cannot be assured that, on average, losses remainbelow 20 percent when we are wrong, the whole strategy is question45
See, for example, James Dow and Gary Gordon, ``Arbitrage Chains,'' Journal of Finance,49, Papers and Proceedings of the Fifty-Fourth Annual Meeting of the American FinanceAssociation, 1994, pp. 819±849, for a discussion of trading horizon in arbitrage situations.
42
THEORY AND TOOLS
able. This is a very simplistic approach, but it has an enormous advantage in forcing us to quantify average pro®ts, maximum losses, andsuccess rates in a consistent way.Incidentally, this simple formalism is powerful enough tohandle the case of an absolute convergence. Consider that there is a0.01 percent chance that a major exchange fails and that a future is notsettled on a price equal to that of its underlying index. This corresponds to 1 in every 10,000 daysÐthat is, every 40 years. Applyingthe above formalism and denoting p the pro®t associated with anindividual transaction of index arbitrage:99:99%  p
0:01%  P  0 ) P  9999  p
Based on these assumptions, if we believe that we cannot lose morethan 9999p even if the exchange fails, index arbitrage is a pro®tablestrategy over the long term. Is that reasonable? Assume that indexarbitrage generates a 0.20 percent return.46 The above condition statesthat P should be under 20 percent for us to break even on average.Therefore, the ultimate question is: Are we going to lose more than 20percent of the total nominal of the position if the market breaks down?This is clearly an interesting question, and the answer is most likelyyes: In most cases exchange members are directly liable when one ofthem fails, which would be the most likely cause of a general breakdown. For the whole system to collapse, there would have to be massive losses, and 20 percent is certainly a low estimate as to what woulddisappear to ®ll this gap.47 As becomes evident, this whole exerciseopens more doors than we like, and an arbitrageur should practice itactively to make sure he or she has an appropriate grasp of the riskinvolved.Leaving aside the problem of expiry, there is another convergencefailure that we need to consider to be exhaustive, and that is the effectof a disproportionate divergence after we have taken a position. Wesaid earlier that arbitrageurs should know when to take a loss, andcertainly the apparition of an exceptional divergence is one situation in
46
We will come back to the examination of pro®tability. The ®gure 0.20 percent is basedon the hypothesis that an arbitrageur captures the whole bid-ask spread on the S&P500 index, independently of any other pro®t.47As an interesting exercise, consider that 1929 was the closest we know of to a generalmarket breakdown, and note that it happened once in the century, that is, with aprobability of 1 over 25,000 days. The above calculation indicates a 50 percent acceptable loss for a pro®t of 0.20 percent.
CHAPTER 1 INTRODUCTION
43
which this skill might be needed. However, this is not the whole storybecause even in a fairly certain convergence situation, arbitrageursmay be driven to cut their positions even in the face of an extraordinaryopportunity. This seemingly contradictory situation is similar to thenotorious martingale about the roulette game. If you keep betting onthe same color, twice the previous amount after each loss, statisticallyyou have to break even after a ®nite amount of time. The main reasonthis does not work in practice is the limited amount of capital most ofus have access to. If we keep losing and losing, chances are we will runout of money before we can make everything back.48 In terms of arbitrage, even if the position is perfectly hedged, a divergence in the market actually costs money, through actual ¯owsÐin the case of margincalls, for example. The paper or actual loss may trigger managementdecisions to cut a position, at the worst time because the opportunityhas never been as good, and at a considerable loss.49 This is in essencewhat happened to LTCM50: The fund literally disappeared as a resultof actual ¯ows and paper losses, and it declared bankruptcy when itbecame apparent that the spreads it carried would not correct in theshort run. There is no certainty that the underlying positions were truearbitrage; however it seems that the spreads did actually come back tosomewhat normal levels in 1999.Therefore, the convergence risk can take several forms and be ofmajor importance at any time during the life of the position. As shouldbecome more and more apparent, this risk drives the implementationof the strategy and the different tools to evaluate it.
CONVERGENCE CONTINUUMAlthough the above presentation looks like a precise segmentation,in practice, things are naturally not that simple. Absolute convergence stands out in the crowd because it is usually easily identi®ed.48
In addition, to make sure that nobody ever tries his or her statistical chance, mostcasinos impose restrictions on the size of the bets.49See Andrei Shleifer and Robert W. Vishny, ``The Limits of Arbitrage,'' The Journal ofFinance, 52, 1997, pp. 35±55, for a complete model of this phenomenon.50LTCM (Long-Term Capital Management) was a very famous hedge fund established inthe 1990s by some of the most respected ``®nancial minds.'' It failed in 1998 as a result ofheavyÐand naturally unexpectedÐlosses in Russia and other emerging markets. Themanagers claimed to be doing ``arbitrage'' all along. For more information on LTCM,see ``Hedge Funds, Leverage and the Lessons of Long-Term Capital Management,''Report of the President's Working Group on Financial Markets, April 1999, USGPO.
44
THEORY AND TOOLS
Explicit and hypothetical situations are much less apparent. Forexample, pair trading between similar companies can be managedas preemptive risk arbitrage: If the industry is mature and prone toconsolidation, choosing the right pair based on strategic criteria iseasier and safer than pure statistical analysis. Furthermore, tradingstrategies based simply on mean-reversion expectations can be considered akin to arbitrage strategies because of the assumed underlying divergence-convergence pattern, and they are much moredeveloped than our restricted exposeÂ suggests. Indeed, mean reversion in stock prices is a property that has been extensively studied,51and many traders or fund managers run sophisticated models toexploit it.Therefore, our classi®cation is somewhat too restricted to re¯ectthe reality prevalent in the marketplace. Market participants involvedin arbitrage, in a very general sense, expect a convergence that canexist in any state from absolute to hypothetical, from public to proprietary, and they can vary signi®cantly over time. To account for thisvariety, we need to consider a broader scale, tabulated on the level ofcertainty about the eventual convergence, as in Table 1-9. We willapply this framework in more detail when we examine practicalarbitrage situations at the end of this book. What should be clearalready is the fact that qualifying a particular trading strategy as anarbitrage has necessary logical implications: valuation, risk analysis,and virtually all important characteristics related to this position aredictated by this quali®cation.
OTHER EXAMPLESCross-Exchange Listings
A cross-exchange listing is a classic example of an arbitrage situationbecause there is no complexity whatsoever in capturing value out ofthe arbitrage. The only skill required is execution, and the arbitrage cantheoretically be handled automatically without any human intervention on hundreds of stocks at the same time if both legs accept electro51
See, for example, Werner F. M. De Bond, and Richard H. Thaler, ``Anomalies: AMean Reverting Walk Down Wall Street,'' Journal of Economic Perspectives, 3, 1,winter 1989, pp. 189±202, and Eugene F. Fama and Kenneth R. French,``Permanent and Temporary Components of Stock Prices,'' Journal of PoliticalEconomy, 96, 2, April 1988, pp. 246±273, for early articles on the subject. This isexactly the property we propose to explore later with technical trading rules.
CHAPTER 1 INTRODUCTION
45
TABLE 1-9ValuationConvergence typeConvergence riskExecution riskHedgeRisk of carryTime horizonWindow of opportunityPro®tabilityaRobustnessbImplications
Absolute3ÐÐÐÐÐÐÐÐÐÐ"HypotheticalTheoreticalMark to marketPublicHighly proprietaryLow to nonexistentCriticalCriticalLowFixed quantityFixed quantity or deltaImportantLowKnown or boundedUnknownVery shortLonger10  11  10StrongWeakPricingNone (Inef®cient market?)
a
The term 10  1 denotes repeated opportunities with relatively low pro®ts. By contrast, 1  10indicates infrequent but highly pro®table trades.bBy robustness, we denote the ability of the position to resist a jump in the price of one or bothlegsÐfor example, bad earnings on one of the two securities, or a general and unexpectedmarket movement of signi®cant amplitude.
nic order submission. Obviously, this type of arbitrage requires anef®cient access to both markets in terms of transaction costs and information ¯ows.A slightly more elaborate version of this arbitrage appears whenone of the legs is an American Depository Receipt (ADR)Ðthat is, thesame share listed in domestic currency.52 The carry of the position maygenerate a foreign exchange risk that needs to be monitored closely.Domestically, the equivalent of cross listing is the proliferation ofthe electronic communications network (ECN), driving trading awayfrom traditional platforms. These networks carry already more than 20percent of all trading volumes. This fragmentation of exchanges, insharp contrast to what is happening on the international scene, is theconsequence of the current structure of the market, especially that ofthe NASDAQ. All ECN sponsors believe they can address this problemand propose better and cheaper executions. Whether they can sustainsuch trading volumes remains to be seen and is mostly dependent ontraditional exchanges' competitive response.In general, because of its simplicity, a strategy based on cross listing is unlikely to generate signi®cant pro®ts either because the price52
As we will see later, the abbreviation ADR may also be applied to derivativesÐforexample, the Nikkei 225 contract listed on the Chicago Mercantile Exchange versusthe same contract listed in Osaka.
46
THEORY AND TOOLS
difference in itself is very small, or because the level of liquidity isrelatively low as associated with ``abnormal'' prices.53 Nevertheless,it is clear that many traders keep an eye on these opportunities.
Ex-Dividends
Traditional wisdom says that the price of a stock should go down bythe amount of the dividend on the day it goes ``ex.''54 This hypothesisis institutionalized, for example, by the fact that NYSE open orders aremodi®ed by the amount of dividend on an ex-day: The price of a buylimit order is actually reduced in the specialist's book by the amount ofdividend.However, this description is valid only in a world without taxes.In reality, in the United States dividends are taxed as income for mostinvestorsÐand corporationsÐand therefore, depending on the speci®cs of a particular investor's tax status, it may be advantageous tosell the stock just before the ex-date. Because of the multitude ofindividual particularities, it is therefore virtually impossible to predictby what amount the price of the stock will actually fall.Now consider the situation of a tax-advantaged investor, ortrader.55 He or she enjoys a tax bracket lower than the majority ofmarket participants and could potentially lock an arbitrage by buyingthe stock on the day before ex-date at close and then selling it backjust on open the next day. If the stock falls by less than the dividend,the loss generated by the decline in price is advantageously compensated by the cash dividend. This works because the tax rateembedded in the market price decline is higher than the investor'sown rate.5653
As an illustration of this point see K. Kato, S. Linn, and J. Schallheim, ``Are ThereArbitrage Opportunities in the Market for American Depository Receipts?'' Journalof International Financial Markets, Institutions and Money, 1, 1992, pp. 73±89.54By de®nition, an ex-dividend day is the ®rst day on which the stock trades without itsdividend privilege.55Index arbitrageurs in the United States enjoy such advantages because the tax shieldfrom interest expenses resulting from the carry of the position is more than enough tooffset the total amount of dividends paid by the stocks in the position.56A variant of this arbitrage is to trade a derivative of the stock highly dependent on thedividend, like an American call. See, for example, Avner Kalay and Marti G.Subrahmanyam, ``The Ex-Dividend Day Behavior of Option Prices,'' Journal ofBusiness, 57, January 1984, pp. 113±128, or Ki-Young Chung and Herb Johnson,``Dividend Spreads,'' Journal of Business, 61, July 1988, pp. 299±319. These articlesare not recent, but they describe how ex-day behavior may be taken advantage ofwith options.
CHAPTER 1 INTRODUCTION
47
Naturally as it is presented here, the arbitrage is not risk freebecause if the stock falls by more than the dividend due to a broadmarket move, the position is losing. One solution is to hedge itÐforexample, with an index futures. Does this work? In theory yes; inpractice it is less certain. After accounting for transaction costs andexecution risk, only those stocks with a high dividend yield are possible candidates, and those are precisely the ones that everybody monitors for this exact reason. On the other hand, in countries where the taxcode has an intricate treatment of dividends there are real opportunities.57 What is important here is to recognize that an arbitrage basedon dividends is intimately dependent upon the local tax code, and achange in this code may result in more or less opportunities for arbitrageurs.58
Closed-End FundsIntroductionClosed-end funds are investment vehicles that issue only a limitednumber of shares and, in contrast to open-end funds, shares cannotbe issued or redeemed on an ongoing basis. Only at the statedmaturity will the fund be opened and all the assets liquidated.Before that date, a majority of shareholders must support the opening for it to happen. In any case the ordinary or extraordinaryconditions under which the fund is susceptible to open are statedin the fund's charter.The shares are usually traded on an exchange, and because theirmarket price may be different from the underlying net asset value(NAV), the funds trade at a discount or premium. Figure 1-4 showsfor example the premium of the Japanese Equity Fund (JEQ) fromOctober 1998 to October 1999. This fund is managed by DaiwaInternational Capital Management, and it invests in non®nancial stockslisted on the Tokyo Stock Exchange.57
In particular, the question of tax rebate on dividends is an important driver of dividend-related arbitrages. See the chapter dedicated to stocks for a discussion of issuesrelated to dividends taxation.58See, for example, Ameziane Lasfer, ``Ex-Day Behavior: Tax or Short-Term TradingEffects,'' Journal of Finance, 50, Papers and Proceedings of the Fifty-Fifth Annual Meeting,American Finance Association, Washington, D.C., January 1995 (July 1995), pp. 875±897,for a discussion of the impact of the 1988 Income and Corporation Taxes Act on exday stock price movements, or Ravinder K. Bhardwaj, and LeRoy D. Brooks, ``FurtherEvidence on Dividend Yields and the Ex-Dividend Day Stock Price Effect,'' Journal ofFinancial Research, 22, winter 1999, pp. 503±514.
48
THEORY AND TOOLS
In fact, the existence of premiums and discounts on closed-endfunds remains to this day one of the biggest mysteries in modern®nance. These funds have been traded consistently at a discount overthe years, both in the United States and the United Kingdom, as shownin the charts in Figure 1-559:There is no clear explanation of why this situation exists and persists. Numerous factors have been put forward to account for whatappears to be a persistent inef®cient market, with some success, butnone has provided a de®nitive answer. Examples of the most commonreasons are the following:. Unrealized capital appreciation (
): Investors face built-in capitalgains tax liability from a substantial amount of unrealized capitalappreciation.. Distribution policy (= ): This policy has tax implications forinvestors with regard to current or deferred tax liabilities. Inaddition, to the extent that a fund is trading at a discount, apartial liquidation of assets in the form of a dividend allowsinvestors to capture part of this discount, making it relativelymore attractive.. Restricted, or letter, stock ( ): Stocks in the fund carry restrictiveclauses and cannot be sold before the end of a