Market neutral strategies phần 2 pptx

Questions and Answers About Market Neutral Investing 13lio from long and short positions rather than achieving neutrality via aderivatives contract based on an underlying index.. Levy: I

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Questions and Answers About Market Neutral Investing 13

lio from long and short positions rather than achieving neutrality via aderivatives contract based on an underlying index

Jacobs: This reﬂects the fact that long-only portfolios are generally

con-strained by the weights of the names in the underlying index, whereasmarket neutral long-short portfolios, if properly constructed, are free ofindex weights This is most noticeable when you look at stock under-weights Given that the market capitalization for the median stock in theU.S equity universe is 0.01% of the market’s capitalization, a portfoliothat cannot short can achieve, at most, a 0.01% underweight in the aver-age stock; this underweight is obtained by excluding the stock from theportfolio The manager may have a very negative view of the company,but the portfolio’s ability to reﬂect that insight is extremely limited Themanager that can sell short, however, can underweight this stock by asmuch as investment insights (and risk considerations) dictate

Levy: It’s important to note that the market neutral long-short portfolio

also has greater leeway to overweight stocks, because the manager canuse offsetting long and short positions to control portfolio risk Whereas

a long-only portfolio may have to limit the size of the position it takes inany one stock or stock sector, in order to control the portfolio’s risk rela-tive to the underlying benchmark index, the market neutral long-shortportfolio manager is not circumscribed by having to converge to bench-mark weights to control risk The freedom from benchmark constraintsgives market neutral long-short portfolios greater leeway in the pursuit

of return and control of risk—a beneﬁt that translates into an advantageover market neutral portfolios constructed without shorting

Can I “neutralize” my long-only portfolio by adding a short-only

portfolio?

Buchan: Yes, but you would miss out on the real beneﬁts of market

neu-tral portfolio construction—the added ﬂexibility to pursue returns andcontrol risks that comes from the ability to offset the risk/return proﬁles

of individual securities held long and sold short

Levy: Integrated portfolio optimization results in a single market neutral

portfolio, not a separate long portfolio plus a separate short portfolio

But a long portfolio combined with a short portfolio would be

market neutral?

Jacobs: Yes, but it would offer little advantage over a long-only

portfo-lio that achieved neutrality via derivatives positions

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14 MARKET NEUTRAL STRATEGIES

Wouldn’t it beneﬁt from the diversiﬁcation provided by a

less-than-one correlation between the returns on the long positions

and the returns on the short positions?

Levy: But the same beneﬁt can be achieved by adding to a long-only

portfolio a less than perfectly correlated asset with similar risk andreturn The unique advantages of market neutral long-short portfolioscome only from an integrated optimization

Will my portfolio be market neutral if I have equal amounts

invested long and short?

Levy: Not unless the sensitivities of the positions held long and sold

short are also equivalent If the amounts invested are equal, but thebetas are not, the portfolio will incur market risk (and returns) Aninvestor might want to place a bet on the market’s direction by holdinglarger and/or higher-beta positions long than short if the market isexpected to rise, or vice versa if the market is expected to decline, butthe portfolio in that case is not market neutral

Buchan: It is also important to note that even a beta-neutral portfolio

can retain residual exposures to certain market sectors For example,long positions may overweight the technology sector, relative to theshort positions, resulting in a portfolio that is exposed to systematic risk

in this sector A well-designed beta-neutral portfolio, however, will havesuch exposures only as the result of a deliberate choice on the part ofthe investor

Jacobs: A similar problem arises in ﬁxed-income market neutral

Mar-ket neutral ﬁxed-income portfolios are generally designed to havematching durations for the longs and shorts; this means that, for a givenparallel change in interest rates, price changes in the long and shortpositions will offset each other If the term structure of interest ratesdoes not change in a parallel fashion, however (for example, if longrates change less than short rates), price changes in the long and shortpositions will not be offsetting It is thus important to determine theportfolio’s expected responses to movements in each part of the yieldcurve (the short rate, the 10-year rate) and in each sector (corporates,mortgages, etc.)

Aren’t short positions risky, or at least riskier than

long positions?

Levy: It’s true that the exposure of a long position is limited, because

the security’s price can go to zero but not below Theoretically, a shortc02.frm Page 14 Thursday, January 13, 2005 12:12 PM

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position has unlimited exposure because the security’s price can risewithout bound In practice, however, this risk is considerably mitigated.First, the short positions will be diversiﬁed across many securities Sec-ond, a substantial (undesirable) increase in the price of a security thathas been shorted will in all likelihood be at least partially offset by a(desirable) increase in the price of correlated securities held long Third,because long and short positions must be kept roughly balanced tomaintain neutrality, shorts are generally covered as they rise in price,limiting potential losses

If you’re using short positions to create a market neutral

strategy, doesn’t that mean the strategy must be leveraged?

Jacobs: Not necessarily The amount of leverage of a given strategy is

within the investor’s control Although Federal Reserve Board tion T permits leverage of up to two-to-one for equity strategies, forexample, the investor can choose not to lever Thus, given an initial $100

Regula-in capital, the Regula-investor could Regula-invest $50 long and sell short $50; theamount at risk is then identical to that of a $100 long-only investment

Then wouldn’t you want to avoid leverage in order to avoid the

risk it entails?

Buchan: Actually, some leveraged market neutral strategies may be

much less risky than unleveraged long-only strategies For example,shorting a Treasury bond futures contract and owning the bond that isdeliverable against the futures contract at expiration is a much less riskystrategy than a long-only small-cap equity strategy Furthermore,restricting the choice of market neutral strategies to those that areunleveraged can produce a “leverage paradox,” whereby, in order toachieve a desired return, one may end up choosing an unleveraged strat-egy that is inherently riskier than a strategy that could be “levered up”

to produce the same return at less risk

Jacobs: In addition, by using all the strategies out there at the

appropri-ate leverage levels (which for some may be no leverage), you can takeadvantage of the typically low correlations among all the strategies,rather than just a subset This will produce the least risky portfolio ofstrategies, as you have the opportunity to diversify risks across manydifferent markets

Levy: Furthermore, long-only portfolios can use leverage, too However,

long-only strategies that borrow to leverage up returns expose the wise tax-free investor to a possible tax liability, as gains on borrowedc02.frm Page 15 Thursday, January 13, 2005 12:12 PM

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other-16 MARKET NEUTRAL STRATEGIES

funds are taxable as unrelated business taxable income Borrowing stock

to initiate short sales does not constitute debt ﬁnancing, so proﬁts ing from closing out a short position do not give rise to unrelated businesstaxable income (UBTI)

result-Buchan: In general, when judging any market neutral strategy, the

ques-tion should be whether the level of leverage is prudent with respect tothe strategy Clearly, if the strategy involves buying Asian technologystocks and shorting European ﬁnancial stocks, there is a signiﬁcantamount of risk (so much, in fact, that few investors would consider such

a strategy market neutral) Conversely, if the strategy involves buyingstock in a company and then shorting the same company’s AmericanDepositary Receipt (ADR) against the long position, the risk would berelatively small

Jacobs: The same is true for ﬁxed-income arbitrage: The level of prudent

leverage is dependent upon the strategy Buying Japanese governmentbonds and shorting European corporate securities is very risky; not onlyare the corporates inherently riskier (and less liquid), but you’re arbi-traging between two very different interest rate regimes But buying U.S.Treasuries and selling short Eurodollar futures (buying a so-called TEDspread), is not, as a trade, very risky

Buchan: Basically, it’s not the leverage per se that matters, but rather the

leverage times the risk of the underlying position; or, more succinctly,it’s the net exposure that matters

So some market neutral strategies are riskier than others?

Buchan: Clearly, but this is true of investment strategies in general With

market neutral, the riskiness depends to a large extent on the underlyinginstruments Mortgage securities, for example, are commonly perceived asquite a bit riskier than government bonds Even here, however, it is difﬁcult

to generalize Mortgage securities cover a wide range, from highly liquidpass-throughs to unique tranches of collateralized mortgage obligation(CMO) deals; therefore, it is misleading to lump all the different types ofmortgage securities in the same group Many mortgage securities areexposed to liquidity risk and prepayment risk (or, in more formal terms,exhibit negative convexity), and may be difﬁcult to value But some famil-iarity with these securities reveals that they are not that different from othertypes of bonds Take the prepayment risk: as individuals prepay their mort-gages, pass-through securities exhibit negative convexity; when interestrates fall, they increase in value by less than a similar ﬁxed-rate governmentc02.frm Page 16 Thursday, January 13, 2005 12:12 PM

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security and, conversely, when interest rates rise, they fall by more than thesimilar government security But the investor is compensated for theseadverse outcomes with a higher yield Thus, the salient question for the

pass-through investor is whether the yield on the security adequately

com-pensates for the adverse price risk

Levy: This is essentially no different from ordinary government bonds.

Zero-coupon bonds, for example, have lots of positive convexity, on arelative basis, and will therefore often yield less than coupon bonds.There are also liquidity and valuation issues, just as with corporatebonds Most corporate bonds are illiquid, in the sense that it can cost alot to trade them By this measure, many mortgage securities are actu-ally more liquid than corporates In addition, in valuing a corporatebond, one has to estimate the probability of default and the correspond-ing likely recovery rates—just as one has to estimate future mortgageprepayment rates under differing economic scenarios

Buchan: So mortgage securities are different from but, in general, not

necessarily riskier than other bonds used in market neutral strategies

Jacobs: Ken’s comment about the liquidity of corporates reminds me

that one should also take into account, when evaluating the risk of aparticular strategy, the liquidity of the underlying markets, which may

be of critical importance especially for highly leveraged strategies Andanother concern I might add is the availability of opportunities in a par-ticular strategy; to the extent that this may limit the ability to diversifyone’s portfolio, it can have a considerable impact on risk

Aren’t market neutral strategies best exploited only in certain

situations or by investors with special information?

Jacobs: I’ve heard it said that market neutral equity strategies only make

sense if pricing inefficiencies are larger or more frequent for potentialshort positions (that is, among stocks that tend to be overpriced) thanfor potential long positions (stocks that tend to be underpriced) Butgreater inefficiency of short positions is not a necessary condition formarket neutral investing to offer benefits compared with long-onlyinvesting These benefits reflect the added leeway to pursue return andthe greater control of risk that derive from the strategy’s freedom frombenchmark weight constraints

Levy: It’s also frequently heard that merger arbitrage does not work

unless it’s based on insider information But, as it is practiced in thec02.frm Page 17 Thursday, January 13, 2005 12:12 PM

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institutional investment community, merger arbitrage is usually based

on a public announcement, where the identity of the target, the identity

of the buyer, and the rough terms of the transaction are disclosed Evenafter such an announcement is made, a spread between the acquirer andthe target tends to persist until the deal closes This spread reﬂects thevery real risks that the deal will not close or, if it does close, it will take

a lot longer than expected, reducing the investor’s annualized return.Managers able to analyze these risks correctly have been able to usemerger arbitrage to add signiﬁcant value on a risk-adjusted basis overthe past decade

Buchan: A lot of people think convertible bond hedging follows a

four-year cycle in terms of returns Historically, the strategy has formed for a quarter or two every three to four years, in 1987, 1990,

underper-1994, 1998, and 2002, and then proceeded to enjoy a strong recovery inthe ensuing year But what’s behind this pattern? Some of the returns toconvertible bond hedging may come from a liquidity premium the con-vertible holder collects in return for holding a relatively illiquid security

If this is the case, then we should see convertible bond hedgers performing when liquidity is prized, as these less liquid assets getmarked down In fact, regressing the return of convertible hedgers as auniverse on a liquidity measure (such as the spread between Treasurybills and LIBOR) shows that, when the most liquid instruments arehighly valued, convertible bond hedging does poorly for the quarter(typically down 2% to 7%) So the question is not whether convertiblebond hedging has an inherent four-year cycle but, rather, what makeshighly liquid instruments more valuable every four years?

under-But won’t market neutral long-short positions be riskier in

general than the positions taken by an index-constrained

long-only portfolio?

Jacobs: Although a market neutral long-short portfolio may be able to

take larger long (and short) positions in securities with higher (andlower) expected returns compared with a long-only index-constrainedportfolio, proper integrated optimization will provide for selections andweightings made with a view to maximizing expected return at the risklevel desired by the investor

But surely trading costs will be higher?

Levy: The trading costs will largely be a reﬂection of the leverage in the

portfolio If a market neutral equity portfolio takes advantage of the fulltwo-to-one leverage allowed, for example, it will engage in roughlyc02.frm Page 18 Thursday, January 13, 2005 12:12 PM

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twice as much trading as a comparable long-only portfolio with thesame capital and no leverage As in any investment strategy, however, it

is important in market neutral to estimate expected returns net of ing costs A market neutral portfolio should not trade unless thosetrades offer a return above and beyond the cost of trading

trad-But surely management fees will be higher for market neutral

than for long-only strategies?

Jacobs: If one considers management fees per dollar of securities

posi-tions, rather than per dollar of capital, there is not much difference

between market neutral and long-only And management fees per active

dollar managed may be lower with market neutral than with long-only.Index-constrained long-only portfolios contain a substantial “hiddenpassive” element; as their active positions consist of only those portions

of the portfolio that represent overweights or underweights relative tothe benchmark, a large portion of the portfolio is essentially passiveindex weights This is not true of market neutral Because a market neu-tral portfolio is independent of benchmark weights, its positions can befully devoted to performance (i.e., to either enhancing return or reduc-ing risk)

Levy: Also, most market neutral strategies are managed on a

perfor-mance-fee basis, so the fee will reﬂect the manager’s value-added

Should one use a single manager or multiple managers for a

market neutral strategy?

Jacobs: Some investors choose to create a market neutral strategy by

combining a long-only portfolio with a short-only portfolio or with aderivatives position that neutralizes the long portfolio’s market risk Inthese cases, the manager of the long portfolio may differ from the man-ager of the short portfolio or from the overlay manager that looks afterthe derivatives positions As we have noted, however, these types ofmarket neutral strategies cannot beneﬁt from the full ﬂexibility afforded

by long-short portfolio construction This goes back to our previouscomments on integrated optimization: Only an integrated optimization,which considers long and short positions simultaneously, results in aportfolio that is free of benchmark weight constraints, hence able toexploit fully the risk-reducing and return-enhancing beneﬁts of marketneutral construction using long and short positions An investor seekingthese beneﬁts from a market neutral strategy should have it managedunder a single roof

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Buchan: But the same may not hold if you are considering multiple

mar-ket neutral strategies In general, the value-addeds are much less

corre-lated across market neutral managers than across long-only equity

managers The reason is there are many more styles of market neutral

investing (over 20) than there are of equity investing (growth vs value,

large cap vs small cap) As long as the managers have the same expected

return, one can lower the risk of an overall fund more by using many

market neutral managers than by using many long-only equity managers

Is market neutral too complicated for most investors to

understand?

Buchan: There are two parts to market neutral investing—the strategy

and the securities As I have noted, the strategy itself is typically no

more complex than what is being done on a long-only basis, with regard

to benchmark-relative investing There, the issue is how the portfolio

will perform relative to the benchmark; here, the issue is how one

secu-rity (or basket of securities) will perform relative to another The other

issue is the type of securities used to implement the market neutral

strat-egy Clearly, there are securities that are simple to evaluate and

securi-ties that are more complex But this is independent of whether or not

they are being used in a market neutral strategy

How will it ﬁt into a plan’s overall structure?

Jacobs: First, it is important to understand that market neutral does not

constitute a separate asset class The asset class to which a market neutral

portfolio belongs depends upon how the portfolio is constructed A

mar-ket neutral portfolio is essentially a cash investment (albeit with higher

volatility than cash); its value-added is the portfolio’s return relative to

the interest receipts from the short sale proceeds But one can combine a

market neutral portfolio with various derivatives positions to obtain

exposures to any number of assets—equity, bonds, currency For example,

a position in stock index futures combined with a market neutral

portfo-lio results in an “equitized” portfoportfo-lio; its value-added is the portfoportfo-lio’s

return relative to the equity index return from the futures position

Levy: Plan sponsors can take advantage of this ﬂexibility to simplify a

plan’s structure Using market neutral, they can exploit superior security

selection skills (whether in the bond market, the stock market, or the

currency market), while determining the plan’s asset allocation mix

sep-arately, via the choice of derivatives In this sense, market neutral can be

said to simplify a plan sponsor’s decision-making

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Kenneth N Levy, CFA

PrincipalJacobs Levy Equity Management

n market neutral equity investing, the investor buys “winners”—securitiesthat are expected to do well over the investment horizon—and sellsshort “losers”—securities that are expected to perform poorly Unliketraditional equity investing, market neutral investing takes full advan-tage of the investor’s insights: whereas the traditional investor wouldact and potentially beneﬁt only from insights about winning securities,the market neutral investor can act on and potentially beneﬁt frominsights about winners and losers

To achieve market neutrality, the investor holds approximatelyequal dollar amounts of long and short positions Furthermore, thesecurities are selected with careful attention to their systematic risks.The long positions’ price sensitivities to broad market movementsshould virtually offset the short positions’ sensitivities, leaving the over-all portfolio with negligible systematic risk

This means that the portfolio’s value does not rise or fall justbecause the broad market rises or falls The portfolio may thus be said

to have a beta of zero This does not mean that the portfolio is risk-free

It will retain the risks associated with the selection of the stocks heldlong and sold short The value-added provided by insightful securityselection, however, should more than compensate for the risk incurred

I

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MECHANICS

Exhibit 3.1 illustrates the operations needed to establish a market tral equity strategy, assuming a $10 million initial investment Keep inmind that these operations are undertaken virtually simultaneously,although they will be discussed in steps

neu-The Federal Reserve Board requires that short positions be housed

in a margin account at a brokerage firm The first step in setting up along-short portfolio, then, is to find a “prime broker” to administer theaccount This prime broker clears all trades and arranges to borrow theshares to be sold short

Exhibit 3.1 shows that, of the initial $10 million investment, $9 lion is used to purchase the desired long positions These are held at theprime broker, where they serve as the collateral necessary, under FederalReserve Board margin requirements, to establish the desired short posi-tions The prime broker arranges to borrow the securities to be soldshort Their sale results in cash proceeds, which are delivered to thestock lenders as collateral for the borrowed shares.1

mil-Federal Reserve Board Regulation T (“Reg T”) requires that a gined equity account be at least 50% collateralized to initiate shortsales.2 This means that the investor could buy $10 million of securitiesand sell short another $10 million, resulting in $20 million in equitypositions, long and short As Exhibit 3.1 shows, however, the investorhas bought only $9 million of securities, and sold short an equalamount The account retains $1 million of the initial investment in cash.EXHIBIT 3.1 Market Neutral Deployment of Capital (Millions of Dollars)

mar-Source: Bruce I Jacobs and Kenneth N Levy, “The Long and Short on Long-Short,” Journal of Investing (Spring 1997).

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Market Neutral Equity Investing 23

This “liquidity buffer” serves as a pool to meet cash demands on theaccount For instance, the account’s short positions are marked to marketdaily If the prices of the shorted stocks increase, the account must postadditional capital with the stock lenders to maintain full collateralization;conversely, if the shorted positions fall in price, the (now overcollateral-ized) lenders release funds to the long-short account The liquidity buffermay also be used to reimburse the stock lenders for dividends owed onthe shares sold short, although dividends received on stocks held longmay be able to meet this cash need In general, a liquidity buffer equal to10% of the initial investment is sufﬁcient

The liquidity buffer will earn interest for the market neutralaccount We assume the interest earned approximates the Treasury billrate The $9 million in cash proceeds from the short sales, posted as col-lateral with the stock lenders, also earns interest The interest earned istypically allocated among the lenders, the prime broker, and the marketneutral account; the lenders retain a small portion as a lending fee, theprime broker retains a portion to cover expenses and provide someproﬁt, and the long-short account receives the rest The exact distribu-tion is a matter for negotiation, but we assume the amount rebated tothe investor (the “short rebate”) approximates the Treasury bill rate.3The overall return to the market neutral equity portfolio thus has twocomponents: an interest component and an equity component The perfor-mances of the stocks held long and sold short will determine the equity com-ponent As we will see below, this component will be independent of theperformance of the equity market from which the stocks have been selected

Market Neutrality

The top half of Exhibit 3.2 illustrates the performance of a market tral equity portfolio It assumes the market rises by 30%, while the longpositions rise by 33% and the short positions by 27% The 33% returnincreases the value of the $9 million in long positions to $11.97 million,for a $2.97 million gain The 27% return on the shares sold shortincreases their value from $9 million to $11.43 million; as the shares aresold short, this translates into a $2.43 million loss for the portfolio.The net gain from equity positions equals $540,000, or $2.97 millionminus $2.43 million This represents a 6.0% return on the initial equityinvestment of $9 million, equal to the spread between the returns on thelong and short positions (33% minus 27%) As the initial equity investmentrepresented only 90% of the invested capital, however, the equity compo-nent’s performance translates into a 5.4% return on the initial investment(90% of 6.0%) (Of course, if the shorts had outperformed the longs, thereturn from the equity portion of the portfolio would be negative.)

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We assume the short rebate (the interest received on the cash proceedsfrom the short sales) equals 5% This amounts to $450,000 (5.0% of $9million) The interest earned on the liquidity buffer adds another $50,000(5.0% of $1 million) (A lower rate would result, of course, in a lowerreturn.) Thus, at the end of the period, the $10 million initial investmenthas grown to $11.04 million The long-short portfolio return of 10.4%comprises a 5% return from interest earnings and a 5.4% return from theequity positions, long and short

The bottom half of Exhibit 3.2 illustrates the portfolio’s mance assuming the market declines by 15% The long and short posi-tions exhibit the same market-relative performances as above, with thelongs falling by 12% and the shorts falling by 18% In this case, thedecline in the prices of the securities held long results in an ending value

perfor-of $7.92 million, for a loss perfor-of $1.08 million The shares sold short, ever, decline in value to $7.38 million, so the portfolio gains $1.62 mil-lion from the short positions The equity positions thus post a gain of

how-$540,000—exactly the same as the net equity result experienced in theup-market case The interest earnings from the short rebate and theliquidity buffer are the same as when the market rose, so the overallportfolio again grows from $10 million to $11.04 million, for a return

of 10.4% (Obviously, if the shorts had fallen less than the longs, orinterest rates had declined, the return would be lower.)

A market neutral equity portfolio is designed to return the sameamount whether the equity market rises or falls A properly constructedmarket neutral portfolio, if it performs as expected, will incur virtually

no systematic, or market, risk; its return will equal its interest earningsplus the net return on (or the spread between) the long and short posi-tions The equity return spread is purely active, reﬂecting the investor’sstock selection skills; this return spread is not diluted (or augmented) bythe underlying market’s return

ADVANTAGES OF MARKET NEUTRALITY AND SHORT SELLING

Exhibit 3.2 highlights one obvious beneﬁt of a market neutral equityapproach—elimination of market risk In a market neutral portfolio, thereturns to active investing are no longer hostage to the sometimes over-whelming effects of broad market moves Of course, this freedom comes

at a price: The market neutral portfolio also does not beneﬁt from thepositive return that equity, as an asset class, has historically enjoyed(although, as we will see in Chapter 8, the investor can recapture thisequity risk premium by using derivatives)

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Another obvious advantage of a market neutral approach to equityinvesting is that it allows the investor to exploit insights about poor per-formers as well as good performers Long positions in stocks that areundervalued and short positions in stocks that are overvalued make use

of all available market information to enhance returns Not being able

to use insights about overvalued as well as undervalued stocks is like

tearing the Wall Street Journal in half and reading only the good news.

Some of the return advantages of a market neutral equity strategycan be illustrated by comparing the return payoffs of a very basic long-plus-short portfolio with those of a long-only portfolio.4

Exhibit 3.3 shows the payoffs to a long-only portfolio The line forthe market portfolio can be viewed as the return to a long passive posi-tion in the market The beneﬁt of active management is presumably anexcess return, or alpha This excess return shifts the active long portfo-lio’s payoff upward relative to the long market portfolio

Exhibit 3.4 shows the payoffs to the short portfolio The short marketportfolio can be viewed as the return to a short passive position in theEXHIBIT 3.3 Payoffs to a Long Portfolio

Source: Bruce I Jacobs and Kenneth N Levy, “Long/Short Equity Investing,” Journal of Portfolio Management (Fall 1993).

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market When an investor sells short, however, proceeds are generated,and those proceeds earn interest The short market portfolio line can thus

be shifted upward by the amount of interest, as shown in the ﬁgure Activemanagement should produce an excess return, or alpha, on top of the mar-ket-return-plus-interest line The payoff line for the active short portfoliothus recognizes the short passive market return, the interest received onthe short-sale proceeds, and the excess return due to active management

A long-plus-short portfolio combines the long portfolio and theshort portfolio discussed above Exhibit 3.5 shows that the payoff forthis long-plus-short portfolio equals the alpha from the short portfolioplus the alpha from the long portfolio plus the interest earned on theproceeds from the short sales

A Question of Efﬁciency

Exhibits 3.2 and 3.5 assume symmetric market-relative returns for thelong and short positions; that is, the long positions and the short posi-EXHIBIT 3.4 Payoffs to a Short Portfolio

Source: Bruce I Jacobs and Kenneth N Levy, “Long/Short Equity Investing,” Journal of Portfolio Management (Fall 1993).

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