Currency Management in Equity Portfolios

Currency Management in Equity Portfolios

May 2006

White Paper Series

UBS Global Asset Management White Paper Series

This article is taken from UBS Global Asset Management's White Paper Series,dedicated to providing in-depth, innovative investment research. In addition toresearch on specific asset classes, sectors and regions, we conduct studies ofbroader strategic issues, and other investment-related topics that help advancethe intellectual foundation of our industry.

The White Paper Series is an integral part of Global Investment Solutions (GIS).GIS helps UBS Global Asset Management maintain its position as a leading solu-tions provider for institutional and private clients, building on our strength andexpertise in the areas of asset allocation and risk management. GIS offers a rangeof solutions for clients' investment needs, including asset and liability modeling;strategic and active asset allocation; risk management; portfolio management;and education and training.

Introduction

At UBS Global Asset Management our approach to currencymanagement has always been to split apart the decisionsabout which assets should be incorporated into a portfolioand what the currency exposure should be.

The existence of a deep and liquid market in forward for-eign exchange makes this possible. The currency impactresulting from the purchase (or sale) of an asset can be fullyoffset by selling (or buying) currencies corresponding to thecurrency exposure of the asset back into the base currency.

In the case of government bond markets, the currencyexposure of the asset in question is straightforward, as it is100% of the currency of denomination. In the case of equi-ty markets, measuring currency exposure is not so clear cut.Many companies are global, operating in many differentcurrency zones. The currency in which its shares are denomi-nated may bear little relation to the markets in which thecompany operates. Even if a company is based solely in onecountry, it may have considerable exposure to foreign cur-rencies by virtue of sales abroad or imports of componentsand raw materials.

In this paper we acknowledge that consensus wisdom onthe currency exposure of equities is subject to more variableopinion, and we examine the best approach to currencymanagement in equity portfolios. We consider altogetherfive approaches. Our conclusion is that the most effectiveapproach is to assume that the currency exposure of theequity is equal to 100% of its currency of denomination (asin the case of government bonds). This is consistent withthe approach taken at UBS Global Asset Management.

Two-step currency management: “Hedging” and“Strategy”

The construction of a return-seeking currency overlay on aportfolio involves a conceptual two-stage process, eventhough there is only one stage in implementation. The firststep in constructing the overlay is to work out what forward

contracts are required to bring the currency exposure backto neutral (i.e. to benchmark). We refer to this as the“hedge” in this paper. The second step is to work out whatforwards are required to achieve the currency exposures rel-ative to benchmark that are desired by the return-seekingstrategy. We refer to this as the “strategy” in this paper.Bundling these two groups of forward contracts togethergives us the set of forward contracts that is actually imple-mented in the portfolio.

Table (1) shows a simple example of this. Column A con-tains the currency exposure of the benchmark of an equityportfolio, and column B contains the currency exposure ofthe portfolio of equities as it is currently invested. In thisexample, we are not pre-assuming how columns A and Bhave been worked out, since that is the subject of theanalysis in this paper. The percentages in column C are the"hedge"—the forward currency exposures that are requiredto get the currency exposure resulting from the asset strate-gy B—once we know what it is—back to benchmark A.Once we have a method for determining the numbers incolumns A and B, then the numbers in column C are given.

Column D shows what the currency "strategy" is: the cur-rency exposures relative to benchmark that are desired in areturn-seeking context. Finally, column E shows the net setof forward currency exposures that has to be implementedin order to achieve currency strategy D starting from under-lying exposures B. These numbers in D and E are alsoknown once we have determined A and B.

The point here is that we need to measure A and B beforewe can effectively carry out currency management on thisequity portfolio—even if we "already know" what desiredcurrency strategy D we want.

Note that when we measure the performance of currencystrategy, we examine exclusively the performance of theposition represented by column D, not the total set of for-ward contracts in column E. The performance of the under-lying strategy is equal to the total portfolio performance lessthe performance of the currency strategy. That is – the per-

© 2006 UBS Global Asset Management (Americas) Inc. is a subsidiary of UBS AG - All rights reserved.reserved. 1

May 2006 Currency Management in Equity Portfolios

Table 1: Example of construction of currency overlay

1 Percent of portfolio.

Currency exposureresulting Forwards required Net set

from asset to neutralize of contractsBenchmark asset strategy currency Currency to be

weights (%) (%) exposure1 strategy1 implemented1

USD 40 30 +10 -5 +5

EUR 30 35 -5 -5 -10

JPY 30 35 -5 +10 +5

C EA B (A-B) D (C+D)

4 © UBS Global Asset Management (Americas) Inc. is a subsidiary of UBS AG - All rights reserved.reserved.

Currency Management in Equity Portfolios May 2006

formance of the assets held, with their currency exposureneutralized back to benchmark (by whatever method is cho-sen to do this).

In this paper we are focusing exclusively on the first part ofthe process—namely, how we estimate currency exposuresA and B.

Determining the best hedge for equity portfolios

The issue here is therefore how we identify the currencyexposures in columns A and B in table 1 on the precedingpage—where the underlying portfolio is an equity portfolio.The hedge (column C) is the difference between A and B.

As mentioned in the introduction, for some asset classes,such as government bonds, this is a trivial exercise since thecurrency exposure is simply 100% of the currency in whichthe asset is denominated. But for equity portfolios, the truecurrency exposure is less clear. A company may operate inmany different currency zones than the one in which itsshares are listed. For example, Nestlé is listed on the Swissstock exchange and its shares denominated in CHF, but onlya comparatively small proportion of its activities are based inSwitzerland. Although payment for the shares would bemade in CHF, it could be misleading to think that the assetbought had a high exposure to the CHF. In fact, Nestlé’sshare price, when measured in CHF, can exhibit a positivecorrelation with the USDCHF exchange rate, reflecting thefact that much of the company’s activities take place in theUS.

Even if a company is based solely in one country, it may wellbe exposed to foreign exchange rate movements by virtueof foreign sales or foreign imports.

Given all the above, it is clearly not necessarily the case thatthe currency exposure of an equity should be purely the cur-rency where the firm is located at all times.

Nonetheless, we require a consistent and operationally effi-cient method, driven by an underlying set of assumptions,to make a conclusion about what the currency exposure inequity portfolios is—and consequently a conclusion aboutwhat the best hedge of that currency exposure will be. If nosingle method is always guaranteed to be correct, we needto find the best feasible method.

To address this issue, we compared five approaches to thehedging of currency risk in equity portfolios, with eachmethod embodying different assumptions about what thecurrency exposure of equities should be.

Candidate methods of hedging currency risk of equities

[1] No hedge

With the first method, no hedge is applied. The assumptionunderlying this is that there is no way to come up with cur-rency exposures on a forward-looking basis; therefore, thereis no hedging method to reduce currency risk, and thehedge is simply to do nothing. This method serves as abenchmark to judge if other methods are superior.

[2] Nominal hedge

With this method, currency exposure is assumed to be100% of the denomination of listing2.

[3] Foreign sales hedge

In this method, foreign sales data are used to obtain a proxyfor currency exposures, and the assumption is that foreignsales determine the true currency exposure of the equity.Since foreign sales data are relatively stable over time, onecan apply last year’s figures for the current year. A problemwith this is that detailed, company-specific breakdowns offoreign sales are not widely available, although the propor-tion of a company’s sales coming from outside its domesticlocation is available. Therefore, we break down the foreignportion of sales according to the trade statistics of the coun-try where the company’s headquarters is located. The for-eign sales concept is perhaps intuitively superior in an era ofglobalisation, although it is probably mitigated in practice byinternal corporate hedging, which is not generally disclosedto the market

[4] Regional exposure hedge

This method is similar to the foreign sales method, butmakes use of region exposures of stocks. The UBS GlobalAsset Management equity risk model already applies region-al exposures to stocks, which are estimated simultaneouslywith industry and size effects when the risk model is set. Itis possible to transform these region exposures into currencyexposures. The four regions are North America (assigned to100% USD), Europe (100% EUR), Asia (100% JPY) andEmerging Markets (a third each USD, JPY and EUR). Thisconcept also has intuitive appeal, similar to the foreignsales-based currency exposure concept.

[5] Regression hedge

This method uses a backward-looking regression to informus of what the implied currency exposures of an equity is.Using the previous year’s data, the stocks’ local returns areregressed onto its local currency exchange rates versus thethree major currencies USD, JPY and EUR. This yields astock’s realized currency exposure in USD, JPY, EUR and thecurrency in which the stock is denominated. If we assume

2 In this study if the shares were listed in more than one currency, the location of headquarters was taken to determine currency denomination.

that the currency exposure is stable, and that the historicregression is a good forward-looking guide, then thismethod has empirical appeal.

Analysis of hedging methods

We compared empirically how effective each of the fivemethods is in removing the currency risk of equity holdings.This was done by systematically applying the method ofhedging to various universes of global equities—such as thetop 1500 stocks by year 2004 market capitalisation, and soon.

The logic underlying the analysis is as follows: if the select-ed method is highly effective at removing currency risk fromequity portfolios, then it follows that the assumptionsbehind that method are highly accurate ones to make aboutwhat the true currency exposures of equities are. If amethod is less effective—it fails to remove much currencyrisk—then the assumptions behind it do not so accuratelydefine the true currency exposure of equities. By this logic,those assumptions behind the method which takes out themost currency risk should be the best assumptions for howto estimate currency exposure of equities.

The means of measuring how much currency risk remains ina hedged equity holding is to regress the returns of thatequity (ex-post the chosen hedging method) onto theexchange rates of the JPY, EUR and USD (three currencies,therefore two independent exchange rates) and the respec-tive local currency of the stock (one additional exchangerate if the local currency is none of USD, EUR and JPY). Theresult of this regression informs us whether foreignexchange risk has been removed or remains: The greater theextent to which exchange rate movements can explain thehedged equity returns, the worse the hedge is. This gives ameasure of comparison across hedging methods. We simu-lated this analysis on randomly generated long/short portfo-lios of either 25 or 100 stocks; in addition the analysis wasperformed on each single stock in the relevant universe. Wethen amalgamated the results into a population histogramdivided into quartiles. For a method that is an effectivehedge, the remaining currency risk for the population willbe small, whilst for an ineffective method, it will be higher.A comparison of methods should therefore indicate whichmethod is superior. If we cannot improve on an existingmethod, there is no basis for exploring alternatives further.If we can—then the expected improvement under the supe-rior alternative would need to be assessed relative to thedifficulty of implementing it.

Results and conclusion of analysis

The results of the analysis are presented in detail in the firstappendix on page 6. Here we focus on the major resultsand conclusions drawn from them. The analysis of these

methods showed that method 2 is empirically the most sat-isfactory method of hedging currency risk. In other words,nominal hedging—assuming that the foreign exchangeexposure of equity is that of its listing currency—is the mosteffective way to remove currency risk from the portfolio,and this assumption is the most valid general assumption tomake about the currency exposure of equities.

Methods 3 and 4 are approximately as effective as method2, but not quite. However, methods 3 and 4 would beviable alternatives to method 2 if they were superior inother ways.

In fact, the operational difficulty (and operational risk) ofmethods 3 and 4 is somewhat greater than method 2.Difficulties arise in the following ways:

� If the currency exposure is assumed to be different fromthe listing currency of a stock, appropriate measurementtechnology needs to be in place so that hedging amountscan be determined.

� Reporting of portfolio exposure to underlying investorsand other interested parties is based on nominal (listingcurrency) exposure, generally industry wide. If we werenot treating the foreign exchange exposure of stocks asbeing their listing currency exposure, reporting technolo-gy that communicated this fact would need to be devel-oped.

� Performance attribution of portfolios separately accountsfor currency exposure, and its effect on performance andthis methodology (Singer-Karnosky) also assumes that anysecurity’s currency exposure is that of its listing currency.If we switched to a different assumption, performanceattribution philosophy and methodology would need toreflect that switch in the same way as reporting.

Methods 1 and 5 are significantly inferior to methods 2, 3and 4. Method 5 also attracts the same operational difficul-ty issues as methods 3 and 4 above. Method 1 would incurthe two issues of how to report currency exposure and howto attribute currency performance.

The conclusion of this exercise is that nominal hedgingis marginally the most superior method from a riskmanagement perspective, and significantly superiorfrom an operational perspective. The perceived intu-itive superiority of methods 3 and 4 may be disregard-ed given that they do not appear to produce superiorresults.

© UBS Global Asset Management (Americas) Inc. is a subsidiary of UBS AG - All rights reserved.reserved. 5


Appendix 1: Detailed risk study

1. Data

The analysis was done using currency and equity return datafrom 2000 up to 2004. The sample of companies availableincluded all the stocks within the UBS Global AssetManagement equity risk model (about 10,000). We furthersegregated this sample into the top 1,500, 500 and 100stocks according to market capitalization. The results pre-sented in table 2 below pertain to the top 1,500 stocks,which are close to the universe of the MSCI World index.We also show the results based on other strata, includingthe full sample set, and on individual stocks in figures 1 to4.

The foreign sales and country data required for method 3were as at 2004. These data sets are relatively stable overtime so employing the figures as at 2004 should not lead toa severe bias favoring this method in 2004 and disfavoringit in 2001, 2002 and 2003.

As mentioned above, estimates of regional exposures (formethod 4) were taken from the UBS Global AssetManagement equity risk model. This model was estimatedon data from 1999 until 2003 but as in the case of the for-eign sales, this should not lead to a severe bias.

For the regression estimates (method 5) we estimated cur-rency exposures each year and then applied these to com-panies in the following year. For the purpose of this exerciseonly the three major currencies—USD, JPY and EUR—plusthe base currency were included as regression co-efficients.Including more currencies than this would have increasedthe risk of picking up other (noncurrency related) effects.

2. Long/short portfolio construction

The results presented below were based on randomly sam-pled long/short portfolios. Over 100 long/short portfolioswere generated containing 25 long and short positionseach; a further set of over 100 portfolios was generatedeach containing 100 long and short positions.

For the long/short portfolios with 100 active positions, thesizes of the positions were similar to a well-diversified globalequity strategy with a risk relative to its benchmark of ca.5%. For these portfolios the estimation error is small, and,therefore, the forecasting errors are mainly due to thechange in the currency exposures and not due to estimationerror. For the long/short portfolios with 25 active positions,the size of the positions is similar to a concentrated globalequity strategy with a relative risk of ca. 10%.

3. Results

Table 2 below shows the median currency risk after applyingthe different hedging methods. The “No Hedge” columnrefers to method 1 (the “do nothing” strategy), and, there-fore, gives an indication of the currency risk in long/short

portfolios: i.e., 1.95% for those with 25 positions and1.05% for those with 100 positions.

Applying a nominal hedge (method 2) reduces the currencyrisk to 1.43% (for long/short portfolios with 25 positions)and 0.77% (for long/short portfolios with 100 positions).

Methods 3 (foreign sales hedge) and 4 (region exposurehedge) achieve similar results to method 2, though they arenot quite as good. In contrast method 5 (the regression esti-mate hedge) performs very poorly and achieves hardly anyreduction in risk compared to the “do nothing” strategy.

The final column of table 2 shows the local equity marketrisk, which is included so as to give some measure of themagnitude of currency related risk in relation to overall port-folio risk. Currency risk is approximately 20% of local equitymarket risk; this can be reduced to approximately 15% byapplying a hedging strategy on the lines of method 2.

In Figure 1 on the following page, the top two panels showthe currency risk from Table 1 in a graph. The bottom twopanels are the corresponding figures for the smaller universeof the top 500 stocks in market capitalization with no sub-stantial difference in pattern. A logarithmic scale is used.

Figure 2 on the following page graphs the currency risks forindividual stocks. Whereas for long/short portfolios andhedged individual stocks the currency risk is independentfrom the base currency, this is no longer the case for non-hedged individual stocks, and the risk numbers shown inthis case are relative to the USD.



No Hedge Nominal Foreign Region Regression Equity

Hedge Sales Exposure Estimate Local

Hedge Hedge Hedge Risk

2001 2.30 1.63 1.82 1.90 2.06 12.1

2002 2.12 1.64 1.77 1.78 1.74 10.9

2003 1.85 1.48 1.50 1.48 1.81 10.7

2004 1.53 0.96 1.02 1.17 1.39 8.2

Mean 1.95 1.43 1.53 1.58 1.75 10.5

No Hegde Nominal Foreign Region Regression Equity

Hedge Sales Exposure Estimate Local

Hedge Hedge Hedge Risk

2001 1.21 0.85 0.90 0.89 1.19 6.2

2002 1.22 0.90 0.96 0.97 0.93 5.6

2003 0.96 0.80 0.74 0.77 0.92 5.3

2004 0.81 0.54 0.58 0.61 0.75 4.2

Mean 1.05 0.77 0.80 0.81 0.95 5.3

Long/Short 25

Long/Short 100

Table 2: Currency risk (% per annum) after applyingdifferent hedging approaches

Figures refer to median value over 100 randomly generated portfolios.Universe consists of top 1,500 stocks in terms of market capitalization



Figure 1: Long/short portfoliosMedian currency risk of random portfolios with holdings from selected universes

Figure 2: Individual stocks Median currency risk (vs. USD) across selected universes

top 1500 mkt 25 long/short top 1500 mkt 00 long/short

top 500 mkt cap 25 long/short top 500 mkt cap 100 long/short

factor universe top 1500 mkt cap

top 500 mkt cap top 100 mkt cap

4. Detailed results 2004

For the year 2004, Figures 3 and 4 below and on page 9show the distribution of currency risk across either a select-ed stock universe or across the 100 randomly createdlong/short portfolios. The blue box indicates the 1st quartile(lower border) and the 3rd quartile (upper border), themedian (red line within the blue box), the extent of the datarange (black line), and possible outliers that go beyond 1.5inter-quartile ranges (red 'plus' signs outside the box).

Note that in these charts, “unh” = method 1, “nom” =method 2, “fsa” = method 3, “reg” = method 4, and “est”= method 5.

The qualitative assessment of the different hedging methodscomes to the same conclusion as if looking only at themedian values. The pattern for the 2001, 2002 and 2003data is basically the same and therefore has not beenincluded here.



Figure 3: Long/short portfoliosMedian currency risk of random portfolios with holdings from selected universes

unh nom fsa reg est10

-3

10-2

10-1


-3

10-2

10-1


-3

10-2

10-1


-3

10-2

10-1


-3

10-2

10-1


-3


-3

10-2

10-1


-3

10-2

10-1


-3

10-2

10-2

10-1


-3

10-2

10-1


-3

10-2

10-1

10-1


-3

10-2

10-1

2004 top 500 mkt cap 25 long/short 2004 top 500 mkt cap 100 long/short

2004 top 1500 mkt 25 long/short 2004 top 1500 mkt 100 long/short

curr

ency

ris

kcu

rren

cy r

isk

Appendix 2: Mechanics of currency overlays

The implementation of a currency overlay on a portfolioinvolves the use of forward currency contracts in order tomanage currency exposure separately from that of theunderlying assets. A brief example will illustrate how thisworks. Suppose that a US investor wishes to buy Germangovernment bonds but does not wish to gain exposure tothe euro (EUR). He can do this by agreeing to sell EUR backinto USD at a future date at the time when he initially buysEUR in order to effect his purchase of government bonds.The forward price of EURUSD is fixed in advance and isequal to the spot exchange rate (how much USD theinvestor had to pay to get the EUR required for his Germanbond purchase), adjusted by the interest rate differential.This relationship can be expressed algebraically as:

where eef is the forward EURUSD exchange rate (expressedas US dollars per euro), es is the spot EURUSD exchangerate; rrUS and rrEU are the nominal interest rates in US dollarsand euro, respectively, applicable for the time periodbetween the forward settlement date and the spot settle-

ment date. This relationship between the spot and forwardrates holds strictly3: assuming no change in the interest ratedifferential between the two currencies, any change in thespot rate will be reflected one for one in a change in theforward rate.

The interest rate adjustment reflects an arbitrage condition:a currency with a higher interest rate relative to anothermust trade at a discount in the forward market (i.e., it ischeaper to buy forward than spot) to reflect the fact that itearns a higher interest rate in the intervening period. If thiswere not the case it would be possible to earn riskless profitby buying the higher-yielding currency in the spot marketand simultaneously selling it in the forward market.

Conceptually, a combined spot purchase and forward saleof a foreign currency is exactly the same as if an investorheld on to his domestic currency (placing it on deposit) andborrowed the foreign currency in order to effect his pur-chase. Thus, there is no currency risk but there is a gain orloss involved equal to the interest rate differential betweenthe two currencies.

When settlement of the forward contract is due, an investorcan maintain his currency hedge by performing a spot trans-action to settle the forward trade and simultaneously enter-ing into another forward trade at a later date. Consider the



Figure 4: Individual stocksCurrency risk (in un-hedged case vs. USD) distribution across selected universes


-2

10-1

100


-2

10-1

100


-2

10-1

100


-2

10-1

100


-2

10-1

100


-2

10-1

100


-2

10-1

100


-2

10-1

100


-2

10-1

100


-2

10-1

100


-2


-2

10-1

100

( )( )rree EU

US

sf +

+•=

1

1

3 Technically it is known as covered interest rate parity.

2004 top 500 mkt cap 2004 top 100 mkt cap

2004 factor universe 2004 top 1500 mkt cap

curr

ency

ris

kcu

rren

cy r

isk

example of the US investor who buys German bonds andthen hedges the currency exposure by selling EUR forwardback into USD. Imagine he had originally implemented thiscurrency hedge at time S0 for settlement date S1. Whendate S1 is reached our US investor can maintain his currencyhedge by buying EURUSD to settle the original forward saleand simultaneously selling EURUSD again at a later date S2(see diagram (1)). This is often referred to as rolling a for-ward contract.



Diagram 1: Illustration of rolling a forward foreign exchange contract

Sale of EURUSD for

settlement at time S1

Purchase of EURUSD for


Sale of EURUSD for


S0 S1 S2time

Sale of EURUSD for


Purchase of EURUSD for


Sale of EURUSD for


S0 S1 S2time

Previously published papers in the White Paper Series include:

Aaron Meder. "Slaying the pension (deficit) dragon.” UBS Global Asset Management, September 2005.

Renato Staub. "Top-down modeling of a market covariance matrix.” UBS Global Asset Management, May 2005.

Renato Staub. "Capital Market Assumptions." UBS Global Asset Management, February 2005.

Renato Staub. “Asset Allocation vs. Security Selection—Baseball with Pitchers Only?” UBS Global Asset Management,November 2004.

Edwin Denson. “Dynamic Alpha Strategy.” UBS Global Asset Management, September 2004.

Tom Clarke. “Market Behaviour Analysis.” UBS Global Asset Management, August 2004.

Tom Clarke and Jonathan Davies. “Active Currency Management, Mean Reversion and Trading Rules.” UBS Global AssetManagement, June 2004.

Brian Singer. “Asset Allocation Revival.” UBS Global Asset Management, March 2004.

Brian Singer, Renato Staub and Kevin Terhaar. "An Appropriate Policy Allocation for Alternative Investments." Journal of Portfolio Management, Spring 2003.

Renato Staub and Jeffrey Diermeier. "Segmentation, Illiquidity and Returns."Journal of Investment Management, First Quarter 2003.

Author:

Tom ClarkeManaging Director, Global Investment SolutionsTel. +44-20-790 [email protected]

Jonathan DaviesExecutive Director, Global Investment SolutionsTel. +44-20-790 [email protected]

Günter Scharz, Ph.D.Executive Director, Global Investment SolutionsTel. +41-44-235 [email protected]

To request any of our white papers, please contact:

April PowellTel. +1-312-525 [email protected]



This publication is intended for limited distribution to clients and associates of UBSGlobal Asset Management. Use or distribution by any other person is prohibited.Copying or distributing any part of this publication without the written permissionof UBS Global Asset Management is prohibited.

Past performance is no guarantee of future results. The information and opinionscontained in this document have been compiled or arrived at based upon informa-tion obtained from sources believed to be reliable and in good faith. All such infor-mation and opinions are subject to change without notice and this document is forinformation purposes only. It is not intended to be construed as an offer or a solici-tation to buy or sell any securities. A number of the comments in this documentare based on current expectations and are considered “forward-looking state-ments.” Actual future results, however, may prove to be different from expecta-tions. The opinions expressed are a reflection of UBS Global Asset Management’sbest judgment at the time this report is compiled, and any obligation to update oralter forward-looking statements as a result of new information, future events, orotherwise is disclaimed. UBS AG and/or its affiliates may have a position in andmay make a purchase and/or sale of any of the securities or other financial instru-ments mentioned in this document.

UBS Global Asset Management is a business group of UBS AG. In the UnitedStates, it provides investment advisory services through UBS Global AssetManagement (Americas) Inc. and UBS Global Asset Management Trust Company.

2006 by UBS Global Asset Management (Americas) Inc.C6-0303 05/06www.ubs.com/globalam-us

Currency Management in Equity Portfolios

Documents

Transcript of Currency Management in Equity Portfolios