AIM 37-7:Computeafirm’sleverageandconstruct afirm’s balance sheet given the followingtypesoftransaction*:purchasing long equity positionsonmargin, enteringintoshort sales, and tradinginderivatives.
Purchasingstockonmargin orissuing bondsareexamplesof usingleverage explicidy m increase returns.However, thereareodier transactions that haveimplicitleverage.Itis
importanttounderstandtheembedded,leverage inshort positionsandderivatives,suchas opdonsandswaps. By constructingeconomicbalance sheetsforinvestorsand/orfirms,it is
possible tomeasure dieimplicit leverageof these transactions.
Margin LoansandLeverage
First,consider marginloans. The stockpurchasedwith themargin loaniscollateralfor the loan. The haircut (h) isdie borrower’s equity and1-h isloaned against the market valueof the collateral. Theleverageiscalculatedas 1I it.TheFederal Reserve requires that an investor put upa minimumof 50% equity(be.,h= 50%)inastock purchase using borrowed funds.
First,assume thatafirm has$100cash investedby theowners (i.e., noborrowedfunds).
The balance sheetin thiscase Is:
Liabilities and Equity Assets
Debt $0
.Cash $ioo -Equity $ioo
TLandOE
$100
Totalassets $100
Tfdiefirm uses the cash to purchasestock, die balance sheetis:
Liabilities and Equity Assets
Debt $0
$100 $1on
$100
Stock -Equity
TLandOE
$100 Totalassets
Thus,dieleverageratio isequal to1 (i.e.,$100/ $100or1.0/ 1.0)
CrossReferencetoCARP Assigned Reading— VIall,Chapter 12
Nest,assume that thefirm uses50% borrowed fundsandinvests 5l>%(i.e., h-50%)
equity to buyshares of stock.Immediatelyfollowingdietrade, the marginaccountbalance sheethas50% equity anda$50 marginloan from thebroker.That is:
Liabilities and Equity Assets
Margin loan $50
£100 $50
Stock Equity
TLandOE
$100 $100
Totalassets
The full economic balancesheetasa result of theborrowed funds (remember,owners put in
$100ofequityinitiallyso thefirmnowhas$100of stockand$50of cash) is:
Liabilities and Equity Assets
Cash $50 Maigin loan $50
Slade Jlilll 36100
$150 Equity
TL andOE
$150 Totalassets
Thus,dieleverage ratio has increased to1.5(i.e.,$150 f $100or 1i0.667).Notethat the broker retainscustodyof the stockto useascollateralfor the loan.
ShortPositionsandLeverage
In ashorttrade,dieinvestorborrows thesharesof stock and sells them.The transaction lengthens the balance sheet because diecashgeneratedfrom the shortsalealongwith the valueof the borrowedsecuritiesappearonthe balance sheet.
Assumethe firm borrows$100of stockandsellsitshort. The firm hasanassetequal to die proceedsfromselling thestockand aliabilityequal to the valueof the borrowedshares.
However,die firmcannot use the cashfor otherinvestments as it iscollateral.Itensures that the stockcan berepurchasedandreturned tothelender.Itis inasegregatedshortaccount.
In dieeventdiat the stockpriceincreasesrather than decreases, the firm mustalsoput$50 ina marginaccount.
Immediately followingthe trade, themargin accountand shortaccounthas $50 equity and a$50 marginloanfrom the broker.
Liabilities and Equity Assets
$150duefrom broker:
Margin
Short saleproceeds Totalassets
$100
$50 Borrowedstock
$100 Equity
TLandOE
$50
$150 $150
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Topic37 GossReferencetoGARPAssigned Reading—Malz, Chapter 12 The firm’s fulleconomicbalance sheetgiven the short saleis:
Liabilities And Equity Assets
$50 Borrowed stock $100 Cash
Due from broker SI50 Equity $100
TLandOE
$200 $200
Totalassets
Thus,dieleverageratio hasincreased to2.0 (i.e.,$200/$100or 1/ 0.50), Theleverageis
higherinthis case thanin the previous marginexample becausethe fullvalueof the stock isborrowedinashort transaction.Leverageisinherentin theshortposition hut isachoice in thelongposition.Thefirm onlyborrows 50% of the balance of the stockinthelong position,
If die short posidon playsahedgingrolein dieportfolio, the position will reducemarket risk. Thismeansthatleveragewilloverstatethe overall riskbecause itignoresthepotential riskreducing benefitsoftheshort positions.As such,adistinctionmust be madebetween grossandnetleverage.Grossleverageisdie valueof all theassets, including cashgenerated byshortsales,divided bycapital. Netleverageis theradoof thedifferencebetween thelong andshort posidonsdivided by capital.
Derivatives andLeverage
Derivatives allowaninvestortogainexposure toanasset orriskfactorwidioutactually buyingorsellingtheasset.Derivativesalsoallowinvestorstoincreaseleverage.Although derivativesaregenerallyoff-balancesheet,theyshouldbeincludedon dieeconomicbalance sheet as dieyaffectaninvestor’sreturns.Derivativesaresyntheticlongandshort positions.
Toestimate the economic balancesheet,find thecash-equivalentmarketvaluefor each
typeofderivative.Derivativesinclude:
• Futures,forwardcontracts,and swapcontracts.Thesecontractsarelinearand symmetricto theunderlyingassetprice. Theamountof the underlyinginstrument
representedby the derivativeissetat the initiationofthecontractsovaluescan be
representedon theeconomichalance sheetbydie market value of theunderlyingasset.
Thesecontractshavezero net presentvalues (NPVs)atinitiation.
• Optioncontracts.Thesecontractshaveanon-linearrelationship tothe underlying
assetprice. Theamountof the underlyingrepresentedby die optionchangesover time.
Thevaluecan befixedatanysingle pointin timebythe option delta.Thus,onthe economicbalancesheet,the cashequivalent market valuescan berepresented hythe deltaequivalentsrather dian themarkeL valuesof die underlyingassets.Thesecontracts
donothavezeroNPVsatinitiationhecause the valueIsdecomposedintoailintrinsic value(whichmayhe zero)anda timevalue (whichislikelynotzero),
In this next example, thecounterparty isassumed cohe die primebroker or broker-dealer executing the positions. Thismeansthatmarginwill be assessedhyasinglehrokerona
portfoliobasis.
Topic
CrossReferencetoCARPAssigned Reading—Mali, Chapter 12
First,assume diefirmentersa1-monthcurrencyforwardcontractandis short$100against theeuroandthe1-month forward exchangerate isSi.25 pereuro.The balance sheetis:
Liabilities andEquity Assets
$100 equivalentof£40bankdeposit Brokerloan $100
Now",assume diefirm buysa3-monthat-the-moneycall option on astock index with an underlyingindex valueof$100.The call’s deltaiscurrendy50%. Thetransaction is equivalent tousinga$50broker loan tohuy$50of the stock index. Thatis:
Liabilities andEquity Assets
$50Jongindexposition 450 Broker loan 450
Next,assume thefirmentersashort equity position viaa total returnswap(TRS). Thefirm pays the total return on$100ofABCstock and thecostofborrowingtheABCstock
(i.e.,the short rebate).Thisisequivalent to cakingashort positionin ABC.Assumingthe marketpriceofABCis$100,wehave:
Liabilities and Equity Assets
£100duefrom broker 4100 BorrowedABCstock $100 (proceedstramshortsale)
Finally,assumethefirmaddsshort protection oncompanyXYZviaa5-year credit default swap (CDS) witha notional valueof$100.This positionisequivalent toalongposition in a par-value 5-year Heating ratenote (FRN) financed witha termloan.
The firm’scombinedeconomic balancesheet thatincludesall of thederivatives positionsis:
Liabilities and Equity Assets
Short-termbrokerJoan 4150
Cash $50
Duefrom broker $150
$50margin
$100 Termloan
$100short saleproceeds Equivalentof£40bankdeposit Longequity index
$100 BorrowedABC stock $100
$50
$100 Equity
$450 TLandOE XYZ FRN $100
$450 Totalassets
Thefirm has increaseditsleverage to 3.5in itslongpositions. Tlielong positions combined with the short position (theABCTRS) meansdie firm hasgainedeconomicexposure to securitiesvaluedat$450 using$50 of cash.
Notice thatcomputing leverageiscomplexwhen derivadvesare used.Also,correctly interpretingleverageisimportantsincerisk maybe mitigatedif short positionsareused
tohedge.Forexample,currencyand interestrateriskscan behedged accurately, tdowever, the posidonsareof thesame magnitudeastheunderlyingassets.Ifdie positionsarecarried
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Topic37 CrossReferencetoGARPAssigned Reading—MaJz,Chapter 12
ontheeconomicbalancesheet,leveragewill be overstated andother material risksin the portfolio may be ignored,