Peter Fortune

Senior Economist and Adviser to theDirector of Research, Federal ReserveBank of Boston. The author is gratefulto Ralph Kimball, Richard Kopcke,Katerina Simons, and Curtis Turner,all of this Bank, for constructive com-ments. John N. Doyle at NationalFinancial Services Corporation wasextremely helpful in clarifying broker-dealer margin practices. Anonymousreaders at the Board of Governors ofthe Federal Reserve System havehelped to clarify the study, withoutnecessarily agreeing with its conclu-sions. Any remaining errors are theauthor's responsibility.

Margin Requirements,Margin Loans, andMargin Rates: Practice and Principles

The Board of Governors of the Federal Reserve System establishesinitial margin requirements under Regulations T, U, and X.Regulation T applies to broker-dealers, Regulation U applies to

banks and other lenders, and Regulation X applies to margin loans notexplicitly covered by the other regulations.1 Prior to 1998, Regulation Gapplied to nonbank, non-broker-dealer lenders in the United States, but ithas recently been rolled into Regulation U. These requirements apply to“purpose credit,” defined as credit for the acquisition or sale of securitiessubject to Regulation T requirements. They set a minimum equity posi-tion on the date of a loan-financed transaction.

Recent increases in margin credit, both in aggregate value and rela-tive to market capitalization, have rekindled the debate about using mar-gin requirements as an instrument to affect the prices of common stocks.Proponents of a more active margin requirement policy see Regulation Tand its companions as instruments for affecting the level and volatility ofstock prices by influencing investors’ demand for common stocks. It isargued that an increase in margin requirements will alter the maximumamount of common stock that an investor can buy, thereby affectinginvestors’ demand for stocks.

Other proponents of margin requirement policy see margin require-ments as signals of the Federal Reserve System’s resolve to prevent bub-bles in stock prices from affecting the U.S. economy, believing that theannouncement effects of increased margin requirements will stabilize thestock market. Robert J. Shiller takes this position, arguing that an increasein margin requirements will have a stabilizing effect on the stock marketand on the economy. Believing that we are in a period of “irrational exu-berance,” a term attributed to Chairman Greenspan, Shiller claims in anexuberantly titled Wall Street Journal article that the Fed should return toits pre-1974 policy of actively changing margin requirements in responseto stock market speculation. This, he argues, will mitigate the “distortionsof saving and investment behavior, driven by the public’s illusion of

20 September/October 2000 New England Economic Review

stock-market wealth . . . and the risks of economic dis-locations and massive wealth redistribution . . . if themarket continues to soar and then crashes” (Shiller2000).

Recent increases in margin credit, both in aggregate value andrelative to market capitalization,have rekindled the debate aboutusing margin requirements as aninstrument to affect the prices of

common stocks.

The purpose of this article is to discuss the histor-ical background, accounting mechanics, regulation,and economic principles of margin lending. The firstsection of this study sets the foundation for an under-standing of margin loans. It assesses the data availableon the volume of margin loans, both in the aggregateand at individual brokerage houses. The second sec-tion discusses the history and practice of marginrequirements as well as the accounting frameworkunderlying customers’ accounts at broker-dealers.Together, the two sections establish the framework foran analysis of margin loans.

The third section assesses the extent to which ini-tial margin requirements restrict the amount of marginlending. We argue that the maximum amount of mar-gin debt is less than would obtain if only maintenancemargins were in force, and that the debt limits arisingfrom Regulation T are more restricting in periods ofrising stock prices. This leads to the conclusion thatinitial margin requirements might serve as a mildautomatic stabilizer, limiting margin debt more duringperiods of bull markets than during bear markets.However, the likelihood that this could prevent boomsand crashes is extremely remote.

The fourth section addresses the economics ofmargin loans, demonstrating that they can be inter-preted as implicit put options on the underlying secu-rities. This section can be skipped by readers familiarwith the economics of equity options.

1Regulation X applies to United States citizens borrowing fromnon-U.S. lenders. No Fed margin regulations apply to margin loansto non-U.S. citizens by non-U.S. lenders, even if the purpose is tobuy securities issued by U.S. corporations.

In the fifth section we develop a simple modelfor estimating the effect of this implicit put option onthe margin loan rates charged by brokers. This modelunveils a margin loan rate mystery. While economictheory suggests that margin loan rates should vary fre-quently with the volatility and leverage of individualaccounts, brokers appear to adhere to rigid rate-settingformulas having little reference to the account's char-acteristics. We show that these rates depend primarilyon market conditions and loan size.

Throughout the paper, we focus on margin loansto the customers of broker-dealers, that is, our primaryinterest is in the implementation and implications ofRegulation T. While many of the principles and issuesraised also apply to Regulation U, our interest is in therole of broker-dealers as lenders, and in the implica-tions for investor behavior. A fuller account wouldaddress the pledging of customers’ securities by bro-ker-dealers to obtain loans from financial institutions.

The paper also does not address the importantquestions surrounding lending by offshore brokersand financial institutions. Nor do we address theimportant questions raised by the increased flow ofmoney into the U.S. stock market from foreigninvestors, who are exempt from Federal Reserve mar-gin requirements.

I. Background

Aggregate Margin Loan Data

Figure 1 shows the history of Regulation T mar-gin requirements since 1940. This figure shows therequired margin ratio, defined as the minimum equityper dollar of securities bought or sold. The data shownin Figure 1 are for purchases of equity securities, typi-cally common stocks or convertible bonds. Therequired ratio has been as high as 100 percent and aslow as 40 percent. The last change in the marginrequirements faced by broker-dealer customers was in1974. Clearly, Regulation T has not been actively usedas a policy instrument.

Recent increases in the amount of margin debt,measured by debit balances at broker-dealer marginaccounts, are documented in Figure 2.2 This figureshows the end-of-month ratio of margin account debitbalances at broker-dealers (a measure of margin loans)

2The definition of debit balances is discussed in the nextsection.

September/October 2000 New England Economic Review 21

stock—the conventional interpretation of “margin loan.” It also includes liabilities not associated with thepurchase of common stock. For example, debitbalances include loans against non-equity securities,such as U.S. Treasury securities, corporate bonds, andmunicipal bonds.5 Thus, the aggregate amount of debitbalances will increase if investors are borrowing tobuy debt instruments. Debit balances also include“loans” associated with short sales. A customer mightsell a stock short to lock in the profits on a long posi-tion in the same stock (shorting against the box), or inanticipation of a price decline of common stock. To dothis, he borrows the shares from another investor, usu-ally another customer of the same broker. The marketvalue of the shares borrowed is the short-selling cus-tomer’s liability because he is obligated to return thoseshares on demand. The broker, who has borrowed theshares on the customer’s behalf, adds the market valueof the shorted position to the customer’s debit bal-ances. In this way, debit balances include the marketvalue of short positions. Note that the debit balancesarising from short positions are “margin loans” eventhough no explicit loan from a broker-dealer or otherfinancial institution occurs.6

This complicates the interpretation of changes indebit balances because, other things equal, the amountof margin loans will move directly with security priceswhen short positions are substantial. This can rein-force the impression that margin loans are rising whenstock prices rise, even though the initiating source ofthe margin loan increase is a sale of stocks.

Another source of debit balances is a customer’swithdrawal of cash from his margin account, typicallythrough a check-writing authority or through creditcard use. While the first tranche drawn on is the cus-tomer’s cash (typically a sweep account), overdraftprivileges allow a customer to withdraw cash up to thevalue of his “free credit balances” (defined below).This is treated as a loan against his securities andadded to his debit balances. Thus, debit balances canincrease because customers are taking cash from theiraccounts, not because they are buying securities usingbrokers’ loans.

5The thirst for loans to finance acquisition of municipal bondsis limited by the federal tax code, which excludes interest on theseloans from deductibility.

6While a short sale against the box has no Regulation T marginrequirement, the short side is a debit item. It is included in marginloans, and the customer pays the margin loan rate on the debit balance.

22 September/October 2000 New England Economic Review

to the end-of-month market value of stocks traded on the NYSE and NASDAQ. It also shows the value of theS&P 500 index relative to its trend in order to allowsome judgment about the level of margin loans in bullor bear periods.3 Two observations are noteworthy.First, the loan ratio has averaged between 1 and 1.5 per-cent of the aggregate market value of common stockssince January 1985. Not until early 2000 did the ratioexceed the October 1987 peak of 1.5 percent. This sug-gests that only a small portion of the aggregate value

The ratio of margin loans to stockvalue tends to be high (low) when

stock prices are low (high), in contrast to the conventional viewthat increased margin loans lead

to higher stock prices.

of common stocks is burdened by debt. Second, theloan ratio appears to be negatively related to stockprices. While periods of high or low stock prices (rela-tive to trend) are also periods of high or low absolutelevels of margin loans, the level of margin loans does not change in proportion to a change in the marketvalue of common stocks. As a result, the loan ratiotends to be high (low) when stock prices are low(high). This appears to contrast with the conventionalview that increased margin loans lead to higher stockprices.

Defining Margin Loans

Margin loans are formally called “debit balancesat broker-dealer margin accounts.” (See Box 1.) Debitbalances measure the liability of margin account own-ers to their brokers.4 This liability includes loans bybrokers for the purchase or holding of common

3The trend value of the S&P 500 is computed by using the aver-age rate of increase between the starting and ending dates in this fig-ure. The value relative to trend is the ratio of the actual S&P 500 to itstrend value, defined as S(1+g)t, where S is the starting value, g is theaverage rate of price increase between the starting and ending val-ues of the S&P 500, and t is the time elapsed since the starting date.

4The Federal Reserve System obtains debit balance and freecredit balance data monthly from the New York Stock Exchange,which collects it from member firms.

September/October 2000 New England Economic Review 23

Have Investors Relied More Heavily on MarginLoans?

Many types of accounts do not allow marginloans. Chief among these are retirement accounts suchas IRAs, Keoghs, SEP-IRAs, and 401(k) accounts(unless specifically allowed). Also excluded are trustestate accounts, fiduciary accounts (unless specificallyallowed), and accounts established under the UniformGift/Transfer to Minors Acts (UGMA/UGTA). Whilean investor’s mutual fund shares are marginable, thebrokerage account of a mutual fund is excluded frommargin status by the Investment Company Act of 1940(see Fortune 1997).7

The mix of accounts will affect judgments aboutthe relative size of margin loans. A firm with low mar-gin loans relative to total customer assets might have asmaller share of customer assets in margin accounts,although those margin accounts might be fully mar-gined. Thus, the ratio of debit balances to stock marketcapitalization, shown in Figure 2, might understate theimportance of margin loans because stock market cap-italization is an aggregate amount including cashaccounts as well as margin accounts. Unfortunately,many firms do not report the value of assets in margin

The use of margin loans appears tohave increased significantly after

1986. This increase might be due, inpart, to changes in the federal tax

code that year.

accounts, and no data are available on the aggregatevalue of margin accounts.

Figure 3 addresses the question of intensity ofmargin loan use by focusing only on margin accounts.This figure shows the aggregate amount of debit bal-ances at broker-dealers per dollar of potential margindebt. We define potential margin debt as the sum ofactual debit balances at margin accounts and free cred-it balances at margin accounts, as reported by broker-dealers to the NYSE. Free credit balances are defined

7The Act of 1940 allows mutual funds (open-end investmentcompanies) to borrow only from banks for short-term liquidityneeds. Unregulated funds, like hedge funds, have no such restrictions.

under Rule 15c3-3 of the Securities Exchange Act of1934 as “liabilities of a broker-dealer to customerswhich are subject to immediate cash payment to cus-tomers on demand . . . .” The amount of cash that canbe withdrawn from a margin account, the free creditbalance, is calculated as the excess of the value of mar-gin securities over the Regulation T margin requiredby the Fed; it is equivalent to the "margin excess" asdefined in Regulation T. For example, suppose that anaccount has $100,000 of margin securities and $25,000of debit balances. Suppose also that Regulation Trequires a 50 percent margin, or equity of at least$50,000. The customer can borrow up to $50,000, and,having borrowed only $25,000, he has $25,000 of addi-tional debt capacity that he can use for cash with-drawal.8

Because free credit balances measure the unuti-lized margin loan capacity, the sums of debit balancesand free credit balances are the maximum debit bal-ances. The ratio of actual debit balances to maximumdebit balances, shown in Figure 3, is useful for two rea-sons. First, it isolates the debit balance position at mar-gin accounts, eliminating the non-margin accountsfrom the comparison. Second, it relates actual margin loans to a measure of margin loan capacity, providingan indicator of the intensity with which thoseinvestors who can borrow against securities actuallydo so.

Figure 3 demonstrates a strong upward trend inthe use of margin debt at margin accounts. In 1985,margin account owners borrowed only 15 percent ofthe maximum allowed margin loans, but by the springof 2000 they were borrowing over 40 percent of margindebt capacity. While this indicates an increasingreliance on margin loans, it also suggests that, on aver-age, margin account owners do not use nearly 60 per-cent of debt capacity. Note that while the aggregatevalue of margin loans has increased sharply in recentmonths, no recent surge has occurred in the intensityof use of margin loans relative to margin loan capacity;the ratio marches upward but at a reasonable, steadyrate.

It is of some interest to note that the use of mar-gin loans appears to have increased significantly after1986. This increase might be due, in part, to thechanges in the federal tax code in that year. Prior to the Tax Reform Act of 1986, interest payments were

8As noted below, a customer can borrow more—up to the debtallowed by the house maintenance margin—if the funds are not usedfor the acquisition of securities. This can be done by transferring securi-ties from the Margin Account to the Good Faith Account.

24 September/October 2000 New England Economic Review

Structure of Accounts

The Federal Reserve Board specifies a struc-ture of accounts that broker-dealers must establishto implement Regulation T. The chief accounts ofinterest are the Cash Account, the Margin Account,the Good Faith Account, and the SpecialMemorandum Account (SMA).

A customer’s Cash Account requires full pay-ment for securities within five business days of thetrade date. It does not allow debit balances beyondthis time for the purpose of purchasing or sellingsecurities, and it cannot be used for short sales.a

Failure to make full payment can result in freezingof the Cash Account so that no additional purchasescan be made without payment on the trade date.

The Margin Account records transactions in,and holdings of, both margin securities and othersecurities, as defined in Regulation T and discussedabove. Securities held in a Margin Account must bein “street name,” that is, the broker-dealer is the legalowner, and they must agree to allow brokers to lendtheir securities for short sale by other customers.

Securities not held in the Margin Account canbe held in a Good Faith Account. This can includenon-equity securities, such as nonconvertible cor-porate debt, options on non-equity securities, andrepurchase agreements involving non-equity secu-

rities. It can also include exempted securities,defined in section 3(a)(12) of the SecuritiesExchange Act of 1934, such as U.S. Treasury bondsand municipal bonds. These securities are not sub-ject to Federal Reserve margin requirements, butthey must meet the “good faith” margin require-ments set by the broker-dealer and the exchanges.

The Special Memorandum Account (SMA) isan adjunct to the Margin Account. It measures theaccount's “buying power,” defined as the amount ofmargin securities that can be bought subject toFederal Reserve margin requirements. The buyingpower is calculated as the SMA divided by the ini-tial margin ratio; with a 50 percent initial marginratio, the buying power is precisely twice the valueof the SMA.

According to Regulation T, the followingitems can be recorded in the SMA: receipts of inter-est and dividends, deposits of cash (includingdeposits to meet maintenance margin calls), pro-ceeds from security sales, and “margin excess trans-ferred from the margin account.” Regulation Tallows transfers from the SMA to be used as marginfor new purchases. However, exchange rules do notallow these transfers to be used for maintenancemargin calls.

Margin excess is defined in Regulation T asMargin Account equity exceeding the Regulation Tinitial margin requirement. It is also called theMargin Account's free credit balance. For example,

Box 1: Margin Requirement Accounting

aCash accounts can have debit balances associated with certainpurposes, such as payment of sales proceeds prior to settlement.

deductible regardless of the purpose of the loans. After 1986, many loans were classified as personal loans forwhich interest deductibility was phased out. The onlyimportant loans still eligible for interest deductibilityare mortgage loans (up to $1 million), home equityloans (up to $100,000), and loans to finance purchasesof securities that generate taxable income. Thus, after1986, margin loans might have been used as substi-tutes for loans that had lost the deductibility privilege.Instead of using equity to buy stocks and borrowing tobuy an automobile, an investor might use equity tobuy the auto and borrow to buy stocks.

Margin Debt at the Firm Level

As shown above, aggregate margin loan datasuggest that the average brokerage customer has sub-

stantial equity in his account. However, the use ofmargin debt varies across firms, reflecting a range of exposures to debt-related risk. Figure 4 shows theyear-end 1999 amount of debit balances per dollar ofaggregate customer assets at several brokerage firms.As noted above, the average ratio of margin debt tomarket capitalization is about 1.5 percent. The tradi-tional full-service brokerage firms in Figure 4, MerrillLynch and PaineWebber, have loan ratios near thataverage. But the online trading firms have higherratios: DLJDirect, TD Waterhouse, and Ameritradehave ratios between 5.8 and 7.2 percent, and E*Tradehas a loan ratio of almost 10 percent.

The reasons for these differences are varied.Online firms might have customers who trade moreactively and who choose a higher leverage than thetypical customer of a traditional brokerage house.

September/October 2000 New England Economic Review 25

if the Regulation T requirement ratio is 50 percent,and a customer holds 1,000 shares of common stockin his Margin Account, each share priced at $100, hecan borrow a maximum amount of $50,000; if hedoes so, his margin account equity is $50,000, andthere is no margin excess. Should the stock pricerise to $130, the value of the stock will be $130,000,the Margin Account‘s equity will be $80,000, andthe maximum margin loan is $65,000. The marginexcess, or free credit balance, is the additional loanthat can be made, or $15,000. The margin excess canbe transferred to the SMA to add to the account's“buying power.” Thus, the $15,000 margin excessallows purchase of an additional $30,000 of marginsecurities.

The SMA is increased when margin excessoccurs, as when security prices rise, but it does notdecline when the Margin Account's equity declines.Thus, the SMA records the maximum margin excessexperienced in the account. This asymmetry allowsthe broker to avoid the costs of customer transac-tions motivated solely by the desire to maintain hismaximum buying power. For example, if a marginexcess emerges, a customer can always preserve itsbuying power by withdrawing the excess margin incash, then using the cash at a later date to buy addi-tional securities. Our customer who enjoyed the$15,000 margin excess could take it out in cash, thenuse that cash at a later date to buy $30,000 of securi-ties even after stock prices decline. This optionwould preserve the maximum buying power evenif the stock price has fallen after its initial increase.

The high volume of records changed, checks cut,and contacts with customers that this behaviorwould elicit has led to the practice of simply pre-serving the maximum margin excess in the SMA.Thus, there can be a “phantom” portion of the SMAthat does not represent underlying account equity.

If the margin accounts equity falls short of theRegulation T ratio, no Fed call is made for addition-al margin because Regulation T applies only at thetime of purchase or short sale. However, underRegulation T, additional purchases in a marginaccount with deficient equity must meet the 50 per-cent Regulation T margin requirement.

Loans Against Open Positions

A customer cannot use an open position, thatis, an existing position in margin securities thatwere purchased at a previous time, to borrow morein a Margin Account than the amount allowed byRegulation T. This is true even though the housemargin requirement is lower than the Regulation Trequirement.

However, if there is a margin excess in theMargin Account (security value exceeds theRegulation T requirement), that excess can be with-drawn and deposited in a Good Faith Account. Thebroker-dealer can lend an amount up to the levelallowed by the house margin requirement. The bor-rower must specify, in writing, that the loan is anonpurpose credit, with the loan proceeds used fora purpose other than purchase of securities.

Thus, a broker who encourages very active trading, or,at the extreme, day-trading, might show higher loanpositions relative to asset values in margin accounts.9

However, this conclusion might be premature.Brokerage houses differ in their mix of accounts, withfull-service brokers probably having a larger propor-tion of non-margin accounts, such as IRA and trustaccounts. While data on assets held in margin accountsare difficult to find for individual firms, it is likely thatonline brokerage houses have a higher ratio of marginaccounts to cash accounts than full-service houses. Ifso, the data in Figure 4 would overstate the differencein margin account loan intensity between traditionaland online brokerage houses.

9For day-traders who close their positions by day’s end,Regulation T requires no initial margin, since it is calculated on thedebit balance at the end of the day. However, Regulation T doesrequire that margin be posted equal to end-of-day losses.

II. Margin Requirement History and Practice

Prior to the Great Depression, the amount ofcredit that could be extended against securities was amatter of brokerage house policy. The Crash of 1929and the subsequent depression in both stock pricesand economic activity were attributed, in part, toexcessive use of debt to buy common stocks. At thetime, brokers would lend as much as 90 percent of themoney that customers paid for stocks, leaving only a10 percent equity margin to cushion declines in stockprices. This lending, it was argued, not only stimulat-ed demand for common stocks, thereby elevatingstock prices and encouraging a subsequent crash, butalso promoted a sharper decline in prices when cus-tomers’ equity positions vanished and brokers mademargin calls requiring a deposit of additional cash and

26 September/October 2000 New England Economic Review

September/October 2000 New England Economic Review 27

Table 1 summarizes the current requirements forseveral categories of securities. Nonexempt equitysecurities are those equities that come underRegulation T’s requirements; the primary examplesare common stocks traded on registered exchanges,convertible bonds, and equity or index options. Non-equity securities are all securities not classified as equi-ty securities; the most prominent examples are non-convertible corporate bonds, reverse repurchases onnon-equity securities, and options on non-equity secu-rities. Exempted securities are those exempted fromany Regulation T requirements, primarily U.S.Treasury bonds and municipal bonds. At present,nonexempt equity securities have a 50 percent marginrequirement. If the transaction is a short sale, the salesproceeds are set aside as collateral and are not avail-able to the customer. The Federal Reserve System’sregulations do not impose margin requirements fornon-equity securities but require only that margins onthese securities meet the “good faith” requirementsimposed by lending brokers, subject to any exchangerequirements. There are no Regulation T requirementsfor exempted securities. While initial margin require-ments limit the extension of credit at the time of atransaction, maintenance margin requirements limit acustomer’s debt against open positions. As a rule, bro-ker-dealers set house margins for most common stocksabove the required exchange margins. House marginpolicies also consider the characteristics of the individ-ual accounts; house margins are higher for concentrat-ed accounts (those with a disproportionately largeposition in a few stocks) and for high-volatility stocks.For example, until recently Charles Schwab had mar-gin requirements as great as 100 percent (no loan value allowed) for a short list of stocks. At this writing,Schwab requires maintenance margins above 50 per-cent, and as high as 80 percent, for over 110 stocks,mostly in the Internet and technology sectors.

Implementation of Regulation T MarginRequirements

Regulation T implements margin requirementsin two ways. The first is by defining “margin securi-ties,” those securities that can be used as collateralagainst broker loans. The second is through setting themargin requirement ratios for each class of marginsecurities, that is, the minimum equity required fornewly purchased securities, expressed as a percentageof the acquisition’s value.

securities to restore customer equity. As we show later,margin calls can also force liquidation of shares valuedat a multiple of the value of the margin call, therebyexacerbating the effect on stock prices.

In 1933, the New York Stock Exchange estab-lished a requirement that member firms’ customerscould borrow no more than 50 percent of the value ofsecurities held. Because the standards were expressedin terms of account equity, or “margin,” rather thanaccount debt, these standards became known as “mar-gin requirements.”

The Crash of 1929 and the subsequent depression in both stockprices and economic activity wereattributed, in part, to excessive use

of debt to buy common stocks.

The NYSE’s margin requirements applied to“open positions,” defined as existing holdings of secu-rities. Thus, they were “maintenance” margins, not ini-tial margins applying only to new acquisitions. NYSEmember firms were free to establish more stringent“house” maintenance margins than this “exchange”standard. Minimal equity standards are now requiredat all registered exchanges: At the NYSE, the exchangemargin requirements are set under Rule 431; theNASD’s Rule 2520 controls over-the-counter exchangemargins.10 Under the current Rule 431 and Rule 2520,broker-dealers must require customers to have a main-tenance margin equal to at least 25 percent of a longposition in stocks and 30 percent of a short position.Brokers typically require a higher ratio, on the order of30 to 35 percent for long positions.

The sweeping securities legislation of the 1930swent well beyond the self-regulation efforts of thesecurities industry by establishing federal standardsthat security lenders must meet. The SecuritiesExchange Act of 1934 (15 U.S.C. 78a) created a federalpower to limit lending against newly acquired securi-ties. The authority to set these standards was given tothe Board of Governors of the Federal Reserve System,which has implemented it under the several regula-tions cited at the outset.

10The commodities futures exchanges set good faith marginsfor financial futures contracts.

Table 1

Initial and Maintenance Margin Requirements for Common Stocks, Bonds, and Options, December 31, 1999Type of Regulation T NYSE Rule 431Security Type of Transaction (Initial margin) (Maintenance Margin)

Nonexempt Equity Securities• Common Stocks • Long • 50% of market value • Greater of 25% of market

Convertible Bonds value or $5 per shareEquity Mutual Funds • Short • 50% of market value • Greater of 30% of market

value or $5 per sharea

• Short against Box • None • 5% of long market value

• Equity/Index Options • Buy Options • 100% of cost • None

• Write Covered Options • None on option • None on optionplus 50% of stock’s 25% of lower of strike price market value or stock’s market value

• Write Uncovered Options • None • 100% of option premium(equity and narrow index) plus 20% of underlying

security value less out-of-the-money valueb

• Write Index Options • None • 100% of option premium(broad-based) plus 15% of underlying

security value less out-of-the-money valueb

• Spreads • None • 100% of long cost plus(long side must expire first) excess of short put

(long call) strike overlong put (short call) strikeb

• Straddles • None • Greater of short put or short call requirementplus option market valueof other sideb

Nonexempt Non-Equity Securities• Nonconvertible • Long or Short • None • Greater of 20% of market

Corporate Bond value or 7% of principala

• Mortgage-Related • Long or Short • None • 5% of market valueSecurity

Exempted Securitiesc

• U.S. Treasury Bond • Long or Short • None • Sliding Scale by maturitya

or less than one year = 1% to U.S Treasury Bond over 20 years = 6%

Mutual Fund

• U.S. Treasury Bond • Long or Short • None • 3% of principal for Zeros(Zero Coupon) over 5 years in maturitya

• Municipal Bond • Long or Short • None • Greater of 7% of or principal or 15 % of

Municipal Bond market valuea

Mutual FundaIn addition, short sale proceeds must be set aside as collateral.bThe minimum margin allowed is equal to the short option proceeds plus 10 percent of the underlying equity orindex value.cExempted securities are defined in section 3(a)(12) of the Securities Exchange Act of 1934. This category includesgovernment and municipal securities, bank-administered trust funds, and interests in securities issued by life insur-ance companies in connection with “qualified plans.” All other securities are non-exempt.

28 September/October 2000 New England Economic Review

While common stocks traded on registeredexchanges have long been included in the definition ofmargin securities, foreign stocks and OTC stocks werenot, until recently, margin securities under RegulationT definitions; the exceptions were stocks explicitlyincluded on a List of Marginable OTC Stocks. Con-vertible bonds, non-investment-grade debt securities,and listed equity options were not margin securitiesuntil recent amendments.

Recent amendments have broadened the defini-tion of margin securities. Amendments in 1996 extend-ed margin security status to bonds that are convertibleinto a margin security, thereby adding convertible cor-porate bonds to margin status. Amendments in 1998extended margin security status to non-investment-grade debt securities, and also allowed listed calloptions to be used as partial margin for short sales ofthe underlying security. The 1998 amendments alsobroadened the range of both over-the-counter (OTC)and foreign stocks that could be bought on margin;margin status was extended to all NASDAQ-tradedstocks and to any foreign stocks included in a specifiedlist of foreign stock price indices. Finally, the 1998amendments created a “good faith” account for non-equity securities.11 Regulation T sets no marginrequirements for non-equity securities, requiring thatthey meet the “good faith” margins required by thebroker-dealers and the exchanges.

The Securities Exchange Act of 1934 was createdin an environment where derivative securities did notexist. The Board of Governors has the authority to set margin requirements for stock-index futures, but thishas been delegated to the Commodities FuturesTrading Commission (CFTC). There are no federalmargin requirements for other futures contracts.

Security Prices and Margin Calls

One of the concerns about price-destabilizingbehavior is the possibility that price declines triggermaintenance margin calls. These calls can be met bydeposit of new cash or margin securities, or by sale ofthe margined securities and repayment of debt. In thissection, we discuss the use of security sales to meetmargin calls.

Suppose that the value of the 1,000 shares ofstock purchased at $100 per share in the previousexample plunges to $65 per share, or $65,000. The

11Non-equity securities are securities that are not “equity secu-rities” as defined in section 3(a)(11) of the Securities Exchange Act of1934. These include non-convertible corporate bonds and mortgage-related securities.

September/October 2000 New England Economic Review 29

Account's equity would decline from $50,000 to only$15,000. Assuming a 25 percent house margin require-ment, the house maintenance margin required is$16,250. The actual margin is only $15,000, giving theaccount a margin ratio of about 23 percent. The brokerdetermines that there is a house margin deficiency of$1,250 and issues a maintenance margin call for thatamount.

If the investor has no funds to meet the margincall or is unwilling to use any available funds for thispurpose, the broker will sell enough securities torestore the maintenance margin requirement. In thiscase, the broker will sell 76.92 shares12 at $65, receivingsales proceeds of $5,000 that are used to retire an equalvalue of debt. The values of stocks and debt thatremain are $60,000 and $45,000, respectively, and theMargin Account's equity is $15,000, precisely 25 per-cent of the value of the margined stock. The mainte-nance margin ratio is restored.

This example is summarized in Table 2. Each rowshows the Margin Account for stock prices differing by$2.50 per share. The top row, for a price of $130, showsthe account in the first example discussed above. Row13, in large bold font, shows the initial position. Row26, in bold italic font, shows the account when thestock price has fallen to $66.67, below which margincalls occur. Row 27 shows the example given above ofa price decline to $65 per share. If the stock price fallsto $50 (Row 33), the customer’s equity is completelywiped out and the broker will sell all of the $50,000 of stock to repay the original debt.

Thus, the relationship between account equityand stock price is “kinked”: For stock prices at orbelow $50, the account equity is zero.13 But as stockprices rise above $50, account equity rises in the sameproportion. As we shall see later, the use of marginloans converts the account to a call option on theunderlying securities.

One result from Table 2 is worth noting. Margincalls have a multiplier effect on stock sales whenforced liquidation occurs. When stock prices fallenough to create margin calls, the customer must sellshares valued at a multiple of the margin call in orderto restore the maintenance margin. This occurs

12If D is the margin debt, S is the value of the margin securities,and m is the maintenance margin ratio, a margin call is made whenD > (1-m)S. The margin call amount is D – (1-m)S, and the number ofshares that must be sold is (1/m) times the margin call amount.

13This assumes that the margin loan is a nonrecourse loan. Inreality, margin loans are recourse loans, and the customer is legallyliable for any losses the broker suffers from negative account equity.Of course, recovery of losses is typically a matter of dispute, requir-ing arbitration or litigation.

30 September/October 2000 New England Economic Review

Tab

le 2

Ana

lysi

s of

Mar

gin

Cal

lsa

Orig

inal

Pos

ition

Va

lued

at D

iffer

ent P

rices

Mar

gin

Cal

ls, S

hare

s S

old

, and

Deb

t Rep

aid

P

ositi

on A

fter M

argi

n C

alls

Sha

res

Pric

eVa

lue

Deb

tM

arg

in

M

arg

inS

hare

s S

old

Sha

res

Rem

aini

ng

D

ebt

Deb

tE

qui

ty

M

arg

inN

PS

DE

qui

tyR

atio

C

allb

Valu

ebN

umb

er

Num

ber

Val

ue

R

epai

d

R

emai

ning

R

emai

ning

R

atio

Row

(1)

(2)

(3)

(4)

(5)

(6)

(7)

(8)

(9)

(10)

(11)

(12)

(13)

(14)

(15)

110

0013

0.00

1300

0050

000

8000

0.6

20

00

1000

1300

000

5000

080

,000

.62

210

0012

7.50

1275

0050

000

7750

0.6

10

00

1000

1275

000

5000

077

,500

.61

310

0012

5.00

1250

0050

000

7500

0.6

00

00

1000

1250

000

5000

075

,000

.60

410

0012

2.50

1225

0050

000

7250

0.5

90

00

1000

1225

000

5000

072

,500

.59

510

0012

0.00

1200

0050

000

7000

0.5

80

00

1000

1200

000

5000

070

,000

.58

610

0011

7.50

1175

0050

000

6750

0.5

70

00

1000

1175

000

5000

067

,500

.57

710

0011

5.00

1150

0050

000

6500

0.5

70

00

1000

1150

000

5000

065

,000

.57

810

0011

2.50

1125

0050

000

6250

0.5

60

00

1000

1125

000

5000

062

,500

.56

910

0011

0.00

1100

0050

000

6000

0.5

50

00

1000

1100

000

5000

060

,000

.55

1010

0010

7.50

1075

0050

000

5750

0.5

30

00

1000

1075

000

5000

057

,500

.53

1110

0010

5.00

1050

0050

000

5500

0.5

20

00

1000

1050

000

5000

055

,000

.52

1210

0010

2.50

1025

0050

000

5250

0.5

10

00

1000

1025

000

5000

052

,500

.51

1310

0010

0.00

1000

0050

000

5000

0.5

00

00

1000

1000

000

5000

050

,000

.50

1410

0097

.50

9750

050

000

4750

0.4

90

00

1000

9750

00

5000

047

,500

.49

1510

0095

.00

9500

050

000

4500

0.4

70

00

1000

9500

00

5000

045

,000

.47

1610

0092

.50

9250

050

000

4250

0.4

60

00

1000

9250

00

5000

042

,500

.46

1710

0090

.00

9000

050

000

4000

0.4

40

00

1000

9000

00

5000

040

,000

.44

1810

0087

.50

8750

050

000

3750

0.4

30

00

1000

8750

00

5000

037

,500

.43

1910

0085

.00

8500

050

000

3500

0.4

10

00

1000

8500

00

5000

035

,000

.41

2010

0082

.50

8250

050

000

3250

0.3

90

00

1000

8250

00

5000

032

,500

.39

2110

0080

.00

8000

050

000

3000

0.3

80

00

1000

8000

00

5000

030

,000

.38

2210

0077

.50

7750

050

000

2750

0.3

50

00

1000

7750

00

5000

027

,500

.35

2310

0075

.00

7500

050

000

2500

0.3

30

00

1000

7500

00

5000

025

,000

.33

2410

0072

.50

7250

050

000

2250

0.3

10

00

1000

7250

00

5000

022

,500

.31

2510

0070

.00

7000

050

000

2000

0.2

90

00

1000

7000

00

5000

020

,000

.29

2610

0066

.67

6666

750

000

1666

7.2

50

00

1000

6666

70

5000

016

,667

.25

2710

0065

.00

6500

050

000

1500

0.2

312

5050

0077

923

6000

050

0045

000

15,0

00.2

528

1000

62.5

062

500

5000

012

500

.20

3125

1250

020

080

050

000

1250

037

500

12,5

00.2

529

1000

60.0

060

000

5000

010

000

.17

5000

2000

033

366

740

000

2000

030

000

10,0

00.2

530

1000

57.5

057

500

5000

075

00.1

368

7527

500

478

522

3000

027

500

2250

07,

500

.25

3110

0055

.00

5500

050

000

5000

.09

8750

3500

063

636

420

000

3500

015

000

5,00

0.2

532

1000

52.5

052

500

5000

025

00.0

510

625

4250

081

019

010

000

4250

075

002,

500

.25

3310

0050

.00

5000

050

000

0.0

012

500

5000

010

000

050

000

00

nmf

a Thi

s hy

pot

hetic

al e

xam

ple

ass

umes

an

initi

al m

arg

in re

qui

rem

ent o

f 50

per

cent

and

a m

aint

enan

ce m

arg

in re

qui

rem

ent o

f 25

per

cent

.bTh

e va

lue

of th

e m

argi

n ca

ll is

max

[D –

(1 –

m)S

, 0].

The

valu

e of

sha

res

sold

(and

deb

t rep

aid)

to m

eet t

he m

argi

n ca

ll is

(1/m

)*va

lue

of m

argi

n ca

ll.

September/October 2000 New England Economic Review 31

because the margin ratio is defined as equity per dollarof security value, and because the act of selling stocksand using the proceeds to repay debt does not itselfalter the account's equity; it reduces the assets (securi-ties) by an amount equal to the reduction in liabilities(margin debt). The route through which liquidationraises the margin ratio is the decline in value of securi-ties held in the account arising from security sales.Because the restoration of the margin ratio arises fromthe reduction in value of stocks held, not from the useof sales proceeds to repay debt, forced liquidationsmust be a multiple of the initiating cause—the margincall.

If, for example, the maintenance margin ratio is25 percent, each dollar of margin call forces the sale offour dollars of stock.14 In Table 2, a stock price declinefrom $66.67 per share to $65 will reduce the accountequity by $1250, creating a margin call of only $1250.But $5000 of stock must be liquidated to restore the 25percent maintenance margin ratio.

Thus, margin calls, if not met by deposits of cashor margin securities, trigger a sale of shares by a multi-ple that is greater the lower the maintenance marginratio. This adds to the destabilizing effects of marginloans.

The Interest Rate on Margin Loans

Brokers charge interest on debit balances,whether those balances arise from cash loans to buysecurities, from withdrawal of cash, or from short sales of securities. For the equity buyer, the advantage of amargin loan is measured by the difference between theloan rate and his opportunity cost of funds, both meas-ured after taxes. An asymmetry works against theshort seller: He must pay the margin loan rate on thevalue of the open short position, but he typicallyreceives no interest on the sales proceeds.15

Brokers obtain the funds for margin loans fromseveral sources. First, internal funds can be used tomake the loans. Second, the broker can use customers’cash deposits, paying customers the interest theywould normally receive. Finally, brokers can borrowthe money from commercial banks or other lenders,subject to appropriate collateral. At year-end 1999,about $157.8 billion was loaned by commercial banks

14In general, if m is the maintenance margin ratio, 1/m ofstocks must be sold to restore each dollar of deficiency.

15Interest on the proceeds from a short sale is kept by the bro-ker unless it pays a short-interest rebate to the customer whose secu-rities were borrowed. Short-interest rebates are uncommon exceptfor very large customers.

to broker-dealers on security collateral; this is equal toalmost 70 percent of total debit balances at broker-dealer margin accounts. This overstates the use ofbank credit to finance broker-dealer margin loansbecause brokers borrow for other purposes, such ascarrying their own securities.

The rate charged by banks on security loans tobrokers, the “broker call money rate,” is reported infinancial papers such as The Wall Street Journal. Figure5 shows the broker call money rate and the federalfunds rate at the end of each month from January 1989through July 2000. Because margin loans are call loans,allowing brokers to request immediate payment fromtheir customers, they are equivalent to an overnightloan. The federal funds rate is the interest rate onovernight interbank loans, so it is the cost of overnightmoney for banks that lend in the call money market.Over the period shown, the broker call money rate hasaveraged about 1.5 percentage points above the federal funds rate. The differential charged by banks hasbeen fairly stable, with short-run volatility in the dif-ferential arising primarily from month-to-month fluc-tuations in the fed funds rate.

The rate charged their margin customers by bro-kers is typically quoted as a premium over the bro-ker’s "base lending rate." A widely used base lendingrate is the broker call money rate, though some brokersuse the bank prime rate and others define their ownbase rate using information on a range of market inter-est rates. The premium over the lender’s cost ofmoney, however defined, covers the broker’s cost ofrecording, monitoring, and managing the loan, as wellas a risk premium for the possibility that the cus-tomer’s assets might become insufficient to repay themargin loan.

Table 3 reports the base rates and margin loanrates advertised by an unscientific sample of broker-age firms at the end of July 2000. Table 3 also reportsthe premium charged by each broker over the brokercall money rate. Full-service brokers (Morgan StanleyDean Witter, Merrill Lynch, and PaineWebber) appearto have the highest margin loan rate structure, espe-cially for smaller loans. Online discount brokers havesignificantly lower rates, and one, Brown & Co., hasrates at or below the broker call money rate.

The differences in loan rates reflect the differentpricing strategies adopted. Brokers receive incomeboth from commissions on trades and from marginloan interest. Online brokers compete with traditionalbrokers by having lower transaction costs. Their pric-ing strategy might require lower margin loan rates to

attract active traders who are inclined to borrow andwho, therefore, have higher trading volumes.Traditional brokers, on the other hand, might wantmore stable trading and enjoy higher commissions ona smaller volume per account.

III. Initial Margin Requirements and MarginDebt

One argument in favor of increased initial mar-gin requirements is that this would reduce the chanceof destabilizing margin calls in the event of a stockprice plunge. As long as the initial margin requirementexceeds the maintenance margin requirement, it isargued, Regulation T adds an extra cushion of equityto the Margin Account, enhancing the protection of thelenders and reducing the probability that investorswill be forced to sell in a declining market.

In this section, we consider how much initialmargin requirements might restrict margin debt, rela-tive to a world in which only maintenance marginsexisted. To do this, we derive (in Box 2) a measure ofthe maximum margin credit allowed under RegulationT and compare it to the maximum margin creditallowed if only house maintenance requirements exist.

This ratio is then calculated for the period September1988 to July 2000 for a hypothetical account.

The ratio is defined as Dx/Dm, where Dx is themaximum margin debt allowed under Regulation Tand Dm is the maximum margin debt that would beallowed if only maintenance margin requirementsapplied. If the ratio Dx/Dm is, say, 0.70, initial marginslimit debt to no more than 70 percent of the amountallowed by maintenance margins alone.

Box 2 shows that the formula for this ratio at anytime, t, is

T

(Dx/Dm)t = 1/{[(1–m)/(1–x)]∑wt–i(Pt/Pt–i)}, (1)i=0

where T is the period over which stocks have beenacquired, x and m are the initial and maintenance mar-gin ratios, respectively, and the weights, wt–i, are theproportions of cumulative purchases attributable toeach prior period. Thus, if $100,000 of net stock pur-chases have occurred since the account's inception,and if $5,000 of this was bought 10 periods in the past,the weight for that purchase is wt–10 = 0.05. Note thatthe weights sum to one (∑ wt–i = 1), so Dt

x/Dtm is the

reciprocal of a weighted average of price increases.According to this formula, initial margins restrict max-

32 September/October 2000 New England Economic Review

September/October 2000 New England Economic Review 33

imum debt levels by a greater amountthe higher the initial margin ratio, thelower the maintenance margin ratio, andthe lower the average rate of priceincrease since the leveraged purchase ofmargin securities.

We have used equation (1) to calcu-late, for a hypothetical account, theextent to which the Regulation T initialmargins restrict the use of broker loans.This hypothetical account assumes thatan investor began buying stocks inJanuary 1975 and followed a dollar-cost-averaging strategy, purchasing the samedollar volume of stocks in each monththrough March 2000. It also assumes thatstocks are held for five years, so theweighted average in equation (1)includes only 60 months of stock prices(T=60). Finally, the initial maintenancemargin required is 50 percent and themaintenance margin required is the 25percent minimum set by the NYSE andNASD.

The reader should note that the cal-culation just discussed is designed toindicate how much existing Regulation Tinitial margin requirements would limitthe maximum margin credit allowed,compared to the maximum margin creditallowed if only existing maintenancemargin requirements acted as brakes ondebt. It does not tell us how muchRegulation T restricts actual margin debtbecause many margin accounts are notfully margined.

Figure 6 shows the results for thisdollar-cost-averaging investor. The flatred line labeled “ratio excluding pricehistory” shows the value of the debtratio if only the margin ratios (x and m)are considered and if prices had stayedconstant. In this case, the debt ratio is0.67, meaning that initial margins allowonly two-thirds of the debt that would bepossible if only maintenance marginswere applied.

The black line in Figure 6 shows thedebt ratio if the actual five-year weight-ed average of price increases is applied.In this case, the debt ratio is as high as

Table 3

Margin Loan Rates at Selected Brokerage Firms July 31, 2000Margin Loan Rate (%)

Firma Loan Size Advertised Premiumb

Full Service BrokersMerrill Lynch Under $50,000 11.500 3.250 (O 8.875%) $50,000 – $99,999 10.500 2.250

$100,000 – $499,999 9.625 1.375 $500,000 – $999,999 9.500 1.250 $1,000,000 – $4,999,999 9.375 1.125

Morgan Stanley Dean Under $25,000 11.625 3.375 Witter(B 8.250%) $25,000 – $49,999 11.125 2.875

$50,000 – $99,999 10.375 2.125 $100,000 and over 9.875 1.625

PaineWebber Under $25,000 11.625 3.375 (O 9.125%) $25,000 – $49,999 11.125 2.875

$50,000 – $74,999 10.625 2.375 $75,000 – $100,000 10.125 1.875 $100,000 and over 9.875 1.625

OnLine BrokersBrown & Co Below $49,999 8.250 .000 (B 8.25%) $50,000 – $99,999 8.000 – .250

$100,000 – $499,999 8.750 – .500$500,000 and over 7.250 –1.000

E*Trade Under $25,000 10.250 2.000 (B 8.250%) $25,000 – $49,999 9.750 1.500

$50,000 – $99,999 8.000 – .250 $100,000 and over 7.750 – .500

Fidelity Investments Under $10,000 10.550 2.000(O 8.550%) $10,000 – $24,999 10.050 1.500

$25,000 – $49,999 9.550 1.000$50,000 – $99,999 9.050 .500$100,000 – $1,999,999 8.800 .250$2,000,000 – $5,000,000 8.550 .000

Charles Schwab Under $10,000 10.750 2.500(O 8.750%) $10,000 – $24,999 10.250 2.000

$25,000 – $49,999 9.750 1.500$50,000 and over 9.250 1.000

DLJDirect Under $25,000 10.125 1.875(O 8.625%) $25,000 – $49,999 9.625 1.375

$50,000 – $99,999 9.125 .875$100,000 – $249,999 8.875 .625$250,000 – $999,999 8.625 .375$1,000,000 and over 8.125 – .125

National Discount Under $10,000 10.615 2.365Brokers (O 8.625%) $10,001 – $24,999 10.115 1.865

$25,000 – $49,999 9.375 1.125$50,000 – $149,999 8.875 .625$150,000 – $249,999 8.625 .375$250,000 and over Negotiable na

Speedtrader Under $10,000 10.750 2.500(B 8.250%) $10,000 – $29,999 10.500 2.250

$20,000 – $49,999 10.000 1.750$50,000 and over 9.000 .750

aFirm names are followed by designation of the base lending rate and its July 31, 2000, value:(B) is the Broker Call Money Rate; (P) is the Prime Rate; and (O) is all other base rates.bThe premium is calculated as the excess of the advertised rate over the broker callmoney rate on July 31, 2000 ( 8.25%).

34 September/October 2000 New England Economic Review

This box demonstrates the effect of initial mar-gin requirements on potential margin loans. Itassumes that in the absence of initial marginrequirements on new positions, the customerwould be limited only by maintenance marginrequirements on open positions.

Let Dt be the value of the outstanding brokerloan at the end of a period, and dt the value of thenewly issued broker loan during that period. Also,let nt be the number of newly purchased shares, andPt be the price of each share at the end of the tth peri-od. Finally, let T be the number of periods duringwhich the investor has purchased stock, x be the ini-tial margin ratio (0 ≤ x ≤ 1), and m be the mainte-nance margin ratio (0 ≤ m < x). Note that this analy-sis requires that the initial margin ratio exceed themaintenance margin ratio; if not, initial marginshave no influence on the level of margin debt.

The amount of a new margin loan during aperiod must be no greater than that allowed by ini-tial margin requirements, so

T

dt ≤ (1 – x) ∑ntPt , (2.1)i=0

from which the maximum outstanding debtallowed by initial margins (Dt

x ) can be derived asthe sum of all current and past values, or

T

Dtx = (1 – x)∑nt–iPt–i . (2.2)

i=0

The maintenance margin requirement, on theother hand, states that outstanding debt can be nogreater than (1 – m) times the market value of thesecurities. Noting that the current market value is

the current price times the sum of all sharesacquired up to the current time, maximum margindebt under the maintenance margins is

T

Dtm ≤ (1 – m)Pt ∑nt–i. (2.3)

i=0

From (2.2) and (2.3) we can calculate the ratioof maximum debt allowed under maintenance mar-gins to maximum debt allowed under initial mar-gins. After slight manipulation, this ratio is

T

Dtm/Dt

x ≤ [(1 – m)/(1 – x)]∑Wt–i(Pt/Pt–i) (2.4)i=0

i = 0,…, TT T

where wt–i = ∑[Pt–int–i/∑Pt–int–i] and ∑Wt–i = 1.i=0 i=0 i=0

Thus, the ratio of maintenance debt to initialdebt is proportional to a weighted average of theprice ratio between current price and the price atwhich the shares were bought. The amount of debtallowed under initial margin requirements dependson the initial and maintenance margin ratios, on thetiming of stock purchases, and on the price increas-es since shares were purchased.

The reciprocal of equation (2.4), Dtx/Dt

m, pro-vides a direct measure of the debt restriction frominitial margins. This ratio is 1 if initial margins areno more restrictive than maintenance margins; it is0.5 if initial margin requirements allow only 50 per-cent of the debt allowed by maintenance marginrequirements. This is discussed in the text and usedas the basis for Figure 6.

Box 2: Margin Debt, Initial Margins, and Maintenance Margins

0.67 (in early 1982), and as low as 0.36 (in late 1987).For most of the period, the debt ratio is between 0.40and 0.60, indicating that initial margin requirementsrestrict margin debt to a level well below the levelallowed by maintenance margin requirements.

It should be kept in mind that this is a hypotheti-cal brokerage account. If the portfolio were held instocks with a house margin well above the minimum25 percent allowed by the NYSE and NASD, the effectof initial margins would be smaller. Indeed, if themaintenance ratio is above the initial margin ratio, asmany houses require for certain volatile stocks, initial

margin requirements will not affect the level of debt. Thus, the extent to which initial margin require-

ments limit margin debt does not depend only on themargin ratios. The history of stock prices is also impor-tant, and in periods of rising prices, Regulation Timposes more severe limitations than it does in peri-ods of declining prices. In this sense, Regulation Tmight serve as an automatic stabilizer, limiting margindebt more in bull markets than in bear markets. This isnot likely to serve as an effective tool to prevent specu-lative bubbles, although it might inhibit trading byaggressive speculators.

September/October 2000 New England Economic Review 35

IV. The Economics of Margin Loans

In the first section of this article, we noted thattaking out a margin loan to buy securities is equivalentto buying a call option on the underlying securities. Itis an axiom of finance theory that this is also equiva-lent to buying a put option having a strike price equalto the amount of margin debt. In effect, the marginedcustomer can “put” the securities to the broker-dealerat a price equal to the debt.

The purpose of this section is to explain thatequivalence. Those readers already familiar with it canskip directly to the fifth section, where the value of theimplicit put option is used to explain the interest ratecharged on margin loans.

Margin Loans as Implicit Options

Figure 7 shows the relationship between theaccount equity and the share price for a fully marginedposition in common stocks, assuming the data andresults in Table 2. The account equity is zero for ashare price of $50 or less, and rises linearly with theshare price as it increases above $50. To repeat the

construction of the data in Table 2, the initial positionis at point A, with the investor buying a share at $100,borrowing $50 and paying the remaining $50 in hisown funds.

As the share price declines, the investor’s equitydeclines. At point M the share price is $66.67, and theinvestor’s equity is $16,667, precisely 25 percent of thestock’s value. Any further price decline will trigger amargin call. If no additional cash or securities aredeposited, forced sale of stocks will result. At point Dthe price is $50, and the broker has sold all of theshares to meet margin calls and repay debt. The customer has lost all of his equity.

The relationship between equity and share pricein Figure 7 has the characteristics of a call option onthe stock with a strike price of $50 per share. This pro-vides a useful interpretation of a margined position: Itis equivalent to creating a call option on the underly-ing security with the strike price equal to the initialdebt position. If the share price exceeds $50, the calloption is in-the-money and the investor can exercise itby selling the shares and repaying the loan. If theoption is out-of-the-money, the investor’s account hasbeen closed out by forced sales of the stock.

36 September/October 2000 New England Economic Review

states that purchase of a call option with strike price Xis equivalent to purchase of the underlying stock pluspurchase of a put option with strike price X plus bor-rowing an amount equal to the present value of thestrike price. Thus, the put–call parity relationship is

C(X, T) = S + P(X, T) – Xe–rT, (2)

where C(X, T) and P(X, T) are the premiums on calland put options with strike price X and an expirationdate T periods in the future, S is the current shareprice, and r is the riskless interest rate.

The logic of this relationship is simple. At themargin loan’s expiration date in T periods, the initialdebt of Xe–rT is paid off by giving the lender X dollars.Thus, equation (2) says that at the expiration date,when T = 0, the call premium must equal the stockprice plus the put premium less the strike price, that is,C (X,0) = S + P (X,0) – X. There are two possibilities: Ifthe call option expires in the money (C > 0), the putoption must be out-of-the-money and will expire with-out value (P = 0); the value of the call at expiration is,

Note that the account equity does not becomenegative if the stock price falls below $50 per share.This reflects the assumption that margin loans are non-recourse loans, for which the borrower has no person-al liability. The importance of this assumption is dis-cussed below.

The interpretation of a margined account as a calloption allows a reinterpretation of the margin loan asan embedded put option (see Fortune 1995 for a re-view of the economics of options). In other words, amargin loan is also equivalent to a put option writtenby the broker-dealer, allowing the investor to “put”the underlying security to the broker when prices fallsufficiently far. The next section briefly outlines theeconomic theory of margin loans as implicit, orembedded, put options.

Valuing the Put Option in a Margin Loan

We have shown that a margin loan creates a calloption-like payoff structure for a customer’s marginaccount. In this section, we show that this is equivalentto creating a put option on the underlying securities.To see this, note that the “put–call parity theorem”

September/October 2000 New England Economic Review 37

the low stock price is precisely offset by the profit onthe put option, leaving a zero equity for all pricesbelow D*. Thus, the kinked solid line OD*A’ shows theexpiration-date account equity at all possible shareprices. The account equity line OD*A’ in Figure 8 isidentical at each stock price to the account equityshown by the heavy kinked line in Figure 7.

This analysis is not without important assump-tions. It assumes that margin loans, like listed options,have a precise expiration date, and that both loan pay-off and option exercise cannot occur before the expira-tion date. In short, it assumes that options areEuropean-style, rather than American-style, and thatprepayment penalties or other limits exist to inhibitearly margin loan payoff. This is, of course, not a pre-cise description of reality, for in the United States onlyindex options are European-style; all equity optionsare American-style and can be exercised at any time upto the expiration date. Furthermore, margin loans arewithout specific payoff dates so the customer canrepay them at any time.

In addition, our analysis assumes that marginloans are nonrecourse loans. That is, the customer haslimited liability and need not compensate the brokerfor losses that occur if the account's equity becomesnegative. In fact, customers are personally liable forbroker’s losses arising from margin loans, and brokers

then, S – X. This is the call’s intrinsic value and is pre-cisely what the payoff of the call option will be underthese conditions.

Alternatively, if the call option expires withoutvalue (C = 0), the put option expires with value P = X – S.This is the put option’s intrinsic value and will be pre-cisely the amount received if the put is exercised at thetime of expiration. So when the put–call parity rela-tionship in equation (2) holds, each option will beproperly priced at the expiration date. But if an asset isproperly priced at one point in time, it must, in an effi-cient market, be properly priced at all points in time. Ifnot, investors can engage in profitable arbitrage torestore equality. In short, equation (2) must hold at anytime at or prior to expiration.

The put–call parity theorem can be applied to amargined position in common stocks by noting thatthe initial value of the loan, D, must lead to a paymentof DeRT at expiration of the loan, where R is the marginloan rate charged by the broker. Thus, the strike priceX can be interpreted as X = DeRT when the amount D isborrowed from the broker to buy S of common stock.The put–call parity relationship, thus modified, is

C(DeRT, T) = S + P(DeRT, T) – De(R–r)T. (2')

Thus, the margined account is equivalent to buy-ing a share of stock outright, borrowing D dollars fromthe broker at interest rate R, and purchasing a putoption on one share with a strike price equal to thedebt to be paid off at expiration, DeRT. Figure 8 showsthe put cum stock and loan position at the expirationdate of the options and of the margin loan. The lineAA’, sloping upward at 45 degrees, is the account'sequity from a purchase of a share of stock at price S,assuming the amount D was borrowed from the bro-ker when he bought the shares. At expiration, theinvestor must pay DeRT (shown as D* in Figure 8) andhis account equity will be S – D*, measured by thelength of the vertical line to point a. The solid line seg-ment D*A’ shows the account's equity if the stock priceexceeds D* at the expiration date of the margin loan.The dotted segment AD* shows the negative equityresulting from a long position if the share price isbelow D*.

The dotted line D*C, sloping upward to the left,shows the profit from the put option at strike price D*when it expires in-the-money, that is, when the shareprice is below the strike price D*. As the stock pricedeclines below D*, the negative equity resulting from

38 September/October 2000 New England Economic Review

have several advantages in successful recovery.Brokers not only have the authority under marginagreements to sell securities, they can also use equityin other accounts held by the broker to satisfy losses ina margin account. In addition, margin agreementsrequire binding arbitration to resolve disputes, aprocess tending to favor brokers relative to litigation.However, the recovery process can be neither success-ful nor easy. Customers typically find reasons to dis-pute their liability, and while the requirement of bind-ing arbitration of disputes tilts the scales in favor ofbrokers, it does not always avoid expensive litigation,nor does it always lead to successful recovery. Thissuggests that margin loans, while legally recourseloans, might be in a limbo, somewhere betweenrecourse and nonrecourse.

In spite of these strong assumptions, the analysisjust presented, arguably, is a reasonable approxima-tion to an accurate description of the marginedaccount, and it can be made more accurate at theexpense of some complications that are not necessaryto the fundamental argument. For example, we caninterpret the time-to-expiration as a single day, allow-ing the analysis to apply to all but day-tradingaccounts, which are closed out at the end of each day.We can also explicitly introduce American-styleoption-valuation models, rather than the simplerEuropean-style valuation models, such as the Black–Scholes model. Furthermore, the partial recoursenature can be introduced into a more complexanalysis.

V. A Model of the Margin Loan Rate

The Margin Loan Rate and the Implicit Put Option

As noted above, brokers charge a margin loanrate that exceeds their own cost of funds, measured bythe broker call loan rate charged by banks. Becausebrokers do not explicitly charge borrowers for theimplicit put options embedded in margin loans, thepremium of the margin loan rate over the broker’s costof funds (denoted by R – r in the above section) can beinterpreted as compensation for the implicit optionand for any transaction costs associated with the loan.In the remainder of this study, we develop measures ofthe potential effect of the put premium on the marginloan rate.

The interest rate equivalent of the value of theput option can be fairly readily computed. In Box 3 we

derive a relationship between the “theoretical” marginloan rate and the riskless interest rate. We define thetheoretical margin loan rate as the rate that would becharged if only the value of the implicit put optionwere added to the interest rate paid by the broker; thisexcludes any costs of managing the margined account.Box 3 shows that the amount by which the theoreticalmargin loan rate exceeds the rate paid by the broker,denoted as R – r, is a risk premium that dependsdirectly on the value of the implicit put option per dol-lar of margin loan. To repeat, the daily margin loanrate is described by

R = r + p/T, (3)

where p = P/D* is the put premium per dollar of mar-gin loan, D* is the amount of the loan taken out atinception,16 and T is the number of days until the loanis repaid. Thus, the daily margin loan rate is the dailyriskless rate plus the put option value allocated to eachday.

The risk premium can be determined using stan-dard option-pricing models. The most familiar is theBlack--Scholes model (see Box 4; Black and Scholes1973; Fortune 1996).17 According to the Black–Scholesmodel, the put premium (P) depends on five variables:the market value of the underlying stock (S), the strikeprice (in this case the value of the broker loan at expi-ration, D), the riskless rate of interest (r), the number ofdays until expiration (T), and the volatility of thereturn on the stock, measured by its standard devia-tion and denoted by �. The details are outlined inBox 4.

The foundations of this model are complex, butthe implications are simple. First, the value of a putoption will be inversely related to the price of theunderlying stock: A stock price decline will increasethe put premium because it puts the option further in-the-money; a stock price increase reduces the put pre-mium because it places the option further out-of-the-money. In short, stock price changes after the marginloan is taken out will affect the amount of equity,hence the equity cushion protecting the broker; thiswill change the value of the put option.

Second, the volatility of stock returns will be animportant determinant of the put option’s value. A

16In Box 2 the amount of the loan at inception is De-RT, that is, itis the amount to be paid off at expiration, D, discounted at the mar-gin loan rate to its present amount. This is D* in equation (3) and itrepresents the loan actually taken out at inception.

17This assumes that the put option is a European option, exer-cisable only on the expiration date, or that it is an American-styleoption with no dividend paid on the underlying stock.

Suppose that margin loans are made at thebroker loan rate, denoted by R, that the risklessinterest rate is r, and that the broker loan and theput option expire after T periods. An investor canborrow from the broker at rate R, or he can obtainfunds by selling holdings of (say) U.S. Treasurysecurities earning the interest rate r. This secondstrategy is equivalent to borrowing at the risklessinterest rate. Thus, the investor can take out a mar-gin loan at rate R or borrow at rate r.

A purchase of S dollars of common stock attime t, financed, in part, by a broker loan of amountDe–RT, requires payment of D dollars at expirationafter T periods. The amount of out-of-pocket cost tothe investor is S – De–RT at inception, and the valueof the investor’s equity at time T is ST – D if positive,or zero; this value is denoted as max[0, ST – D].

If, instead, the investor purchases S dollars ofstock at time t, sells the riskless security in amountDe–rT, and pays P dollars for a European put optionwith strike price D expiring after T periods, his ini-tial investment of S + P – De–rT will have a value ofmax(0, ST – D) at expiration. If ST – D > 0, the put’svalue is zero and the position is worth ST – D;if ST – D < 0, then P = D – ST, and the position haszero value.

In a security market equilibrium, all securitiesor combinations of securities that yield identicalvalues at any future date must have the same valueat any other date. If not, investor arbitrage willoccur that restores the equality of values. Becausethe value of the two strategies is the same atexpiration, equilibrium requires that S – De–RT =St + Pt – De–rT. After some rearrangement, thisreduces to e(R–r)T = 1 + (Pt/De–RT). Taking logarithms

Box 3: The Broker Loan Rate and the Implicit Put Option in Margin Loansof each side, using the approximation that, for smallvalues of x, ln(1 + x) = x, we derive the approxima-tion

R ≈ r + (Pt/De–RT)/T. (3.1)

The daily margin loan rate that makes theinvestor indifferent between taking out a broker’sloan and selling his own riskless securities to buystock is equal to the riskless rate plus the daily valueof the put per dollar of margin loan. The last is sim-ply the total value of the put (per dollar of loan onthe day the margin loan is taken out) divided by thenumber of days until the loan’s expiration. Theinvestor will pay a premium for the margin loanbecause of the value of the put embedded in theloan. In a competitive market, the broker whoplaces the same value on the put will charge justthis rate to compensate for the embedded put thathe has written.

The theoretical premium charged by the bro-ker will be very small if the customer has a largeequity in the account, either because initial andmaintenance margins are high, or because theinvestor chooses to borrow less than initial marginsallow, or because the stocks have very low volatility.

But if the value of the put option is high, eitherbecause there is little equity in the account orbecause the stock in the account is very volatile, thebroker loan rate might substantially exceed the risk-less rate. The amount of the broker loan rate premi-um will depend on those factors that determine thevalue of a put option. Of particular importance willbe the account’s margin and the volatility of thereturn on the margined security.

higher volatility will increase the chances that the putoption expires in-the-money, thereby raising the putpremium. Third, the put premium is directly related tothe strike price; a higher (lower) strike price places theput option more (less) in-the-money, giving it greater(smaller) value. Thus, the greater is D, the higher thestrike price will be, and the greater will be the putoption’s value. Finally, the value of the put will beinversely related to the riskless interest rate and direct-ly related to the time remaining to expiration. A higherriskless interest rate reduces the present value of thestrike price, reducing the effective strike price, and a

longer time to expiration means a greater chance thatthe put will expire in-the-money.

All of the five variables affecting the put premiumare out of the investor’s control except the amount ofthe margin loan. Within the allowed ranges (debt can-not be negative or greater than margin requirementsallow), the investor has full control over the strike price.If he chooses a higher debt level, the value of the implic-it put option will increase, and the broker will recoverthat value by charging a higher margin loan rate. Alower debt level will reduce the value of the put optionand should be accompanied by a lower loan rate.

September/October 2000 New England Economic Review 39

40 September/October 2000 New England Economic Review

A shortcoming of the Black–Scholes model is thatit assumes that stock prices follow a log-normal distri-bution, that is, the logarithm of the price is normallydistributed. This gives a very small probability of thelarge declines in stock prices that will have greatesteffect on the put’s value. As noted in Box 4, the actualdistribution of stock prices does not conform to thelog-normal. Rather, the probability of large changes isgreater than normal, and the distribution is negativelyskewed, with large declines being more frequent thanlarge increases.

To reflect this reality, a modification of theBlack–Scholes valuation model is used. This is theJump-Diffusion model, which grafts onto the simplediffusion process a “jump variable” that reflects theeffect of a random number of discrete shocks to the

stock price, each shock being drawn from a normalprobability distribution with a zero mean and variance�2. In the Black–Scholes model, the volatility of stockreturns over one time period is the simple diffusionvolatility, �, and the volatility over T periods is �√T. Inthe Jump-Diffusion model, the volatility over one peri-od is √(�2 + ��2), where � is the expected number ofjumps in one period of time; the volatility over Tperiods is √[(�2 + ��2)T].

The theoretical margin loan rate will vary direct-ly with the broker’s base lending rate; this studyassumes the base rate is the broker call money rate,currently 8.25 percent. The loan rate should also varydirectly with the value of the implicit put per dollar ofmargin loan, and inversely with the time for which thebroker expects the loan to be outstanding (30 days in

Using the information developed in Box 3, thetheoretical margin loan rate, at a daily rate, is

R = r + p/T, (4.1)

where p = (Pt/De–RT) is the put value per dollar ofinitial margin loan. That is, the daily margin loanrate is the daily riskless rate plus the value of theput per dollar of loan, divided by the number ofdays the loan is outstanding. The value of the putoption is, therefore, crucial to the theoretical marginloan rate.

Several option valuation models are availableto assess the value of the implicit put option. Themost basic of these is the Black–Scholes model. Analternative, richer, model is the Jump-Diffusionmodel, which allows the underlying security’s priceto take discontinuous “jumps” rather than follow asmooth distribution of movements. We will discussboth models.

The Black–Scholes Option Pricing Model

The Black–Scholes model assumes that a secu-rity price evolves according to a simple diffusionprocess described by

dlnS = �dt + (�√dt)z, (4.2)

in which S is the security price, dlnS is the instanta-

neous change in its logarithm (the instantaneousrate of return), and dt is a small interval of time. Theparameters � and � are the mean return and thevolatility of return, respectively. The variable z is arandom variable following a standard normal dis-tribution.

According to the Black–Scholes model, if theevolution of a security’s price is described by a sim-ple diffusion process, a European-style put option’spremium (or price), denoted by P, depends on fivevariables: the market value of the underlying stock(S), the strike price (X), the riskless rate of interest(r), the period until expiration (T), and the volatilityof the return on the stock (�). The put premium isdescribed by

P = – SN(– d1) + Xe–rTN(– d2), (4.3)

where d1 = [ln(S/X) + (r + 1�2 �2)T]/�√T d2 = d1 – �√T.

The term N(– d) represents the cumulativevalue of a standard normal distribution, that is, theprobability that a standard normal random variableis no greater than the value – d. The probability lim-its d1 and d2 are as shown above.

The strike price, X, is the amount of the loan(including accumulated interest) to be repaid atexpiration in T periods; thus, X = D because the ini-tial loan, De–RT, accumulates to the value D.

Box 4: The Value of the Implicit Put Option

September/October 2000 New England Economic Review 41

our examples). This means that the margin loan rateshould change frequently as the volatility of thestock’s return changes, as the loan’s expiration dateapproaches, and as the leverage in the portfoliochanges with the prices of the underlying securities. Ifthe broker were to apply the same analysis in settinghis margin loan rates, each customer would becharged a different rate each day as the characteristicsof his portfolio change. In short, there would be a com-plex menu of margin loan rates depending on the spe-cific circumstances of the account.

Table 4 reports the results using the Jump-Diffusion model. This is done for four values of thesimple diffusion volatility: 20, 30, 40, and 50 percent.The 20 percent volatility is roughly the level exhibitedby the S&P 500 stock price index. For each of thesesimple volatilities, the theoretical loan rate premium is

computed for six levels of jump volatility (�): 0, 10, 20,30, 40, and 50 percent. Thus, the range of total volatili-ties in Table 4 is from 20 percent to about 70 percent.18

Note that the results for a zero jump volatility arethose for the Black–Scholes model because only simplevolatility is relevant in that situation.

The theoretical margin loan rate is reported inTable 4 for two levels of margin protection. The first isfor a 50 percent margin, the Regulation T level. Thisprovides such a large equity cushion that the premiumis negligibly small at all volatilities. Thus, accountsmeeting the Regulation T level of equity should pay amargin loan rate equal to the base lending rate. If this

18Recall that the total volatility is √(�2 + �2). We assume that themean number of jumps is one per day, as found in Fortune (1999).

The value of p in (4.1) is, then, the put optionvalue, P, divided by the initial margin loan, De–RT.

The Jump-Diffusion Option Pricing Model

A shortcoming of the Black–Scholes model isthat it assumes that stock prices follow a simple log-normal probability distribution in which the proba-bility of large changes is small. Yet we see that actu-al stock prices are subject to short and significantchanges that do not seem to fit the normal distribu-tion: The tails of the actual distribution are fatterthan the normal (abnormally high probabilities oflarge changes), and the distribution is negativelyskewed, with a higher probability of sharp pricedeclines than of equally sharp price increases.

A valuation model that incorporates theseproperties is the Jump-Diffusion model proposedby Press (1967) and Merton (1976). The Jump-Diffusion model builds on the Black–Scholes modelbut allows for occasional jumps upward or down-ward, with skewness in the results. It has been usedrecently in modeling stock returns by Kremer andRoenfledt (1993) and by Fortune (1999).

The Jump-Diffusion model modifies the simplediffusion model by grafting onto it a “jump variable.”This jump variable is defined so that during any shortinterval of time, the change in the log of the stockprice can be affected by a discrete number of shocks.The size of each shock’s effect is a random variabledrawn from a normal distribution with mean � andstandard deviation �. The number of shocks in an

interval of time is described by a Poisson distributionwith parameter �; this parameter is the expectednumber of shocks in an interval, so �T shocks areexpected over T periods. The modified diffusionprocess describing the return on the security is

ndlnS = �dt + (�√dt)z + ∑xi , (4.4)

i=0

where xi is distributed as N(�,�).

The Jump-Diffusion model for valuing aEuropean-style call option with T periods untilexpiration is

�

C = ∑[e–�T(�T)n/n!]Cn , (4.5)n=0

where Cn is the Black--Scholes value of a call optionwhen exactly n jumps occur. The Black--Scholesvalue for n jumps is defined as above, but the vari-ance of the return in the Black--Scholes model is �2 +n�2/T; that is, the total variance is the simple diffu-sion variance (�2) plus the multiple n/T, times thejump diffusion variance (�2). The factor (n/T) canbe any value from zero to infinity.

To calculate the jump-diffusion value, onesimply calculates the Black--Scholes value for eachpossible number of jumps (n), multiplies each ofthese values by e–�T(�T)n/n!, then sums over all theproducts from n = 0 to a very large value of n (from,say, n = 0 to n = 100). We have done this using a sim-ple Gauss program.

42 September/October 2000 New England Economic Review

tenance margin requirement. The account's leveragedoes not matter.

But Table 4 shows that the primary considerationin setting a margin loan rate should not be the absoluteloan size. Rather, it should be the account's leverageand the volatility of the return on the margin securi-

were the representative accountupon which brokers base their loanrates, there should be no premiumfor default risk.

The second level of protectionis the 25 percent margin requiredunder NYSE and NASD rules. Atthis margin level the implied loanrate premium is substantial, partic-ularly at high volatilities. Forexample, at a 25 percent margin amargin loan on an account with asimple volatility of 20 percent(roughly equal to the S&P 500’svolatility) requires no premium ifthere is no jump volatility, but a3.25 percent premium is requiredat a 50 percent jump volatility. Whenthe simple volatility is 50 percent,the loan rate premium is 1.46 per-cent to 10.5 percent, depending onthe jump volatility.

Thus, while the implicit putapproach implies no loan rate pre-mium for a newly created positionmeeting Regulation T marginrequirements, or higher, it goes along way toward explaining theobserved loan rate premiums(Table 3) when the account’s equityhas deteriorated from its initiallevel.

The Margin Loan Rate Mystery

The results reported in Table 3conflict markedly with thoseshown in Table 4. Table 3 showsthat brokers tend to set a marginloan rate structure that varies withthe absolute size of the loan, notwith the leverage in the account (asmeasured by the loan size relativeto the value of margin securities) orthe account's volatility. For exam-ple, Charles Schwab and Co.charges a loan rate of 9.25 percent for a margin loan of$50,000. This rate applies to a newly created accountwith $100,000 of common stocks, just meeting theRegulation T requirement. It is also the rate charged acustomer with an existing position in common stocksvalued at $77,000, just over Schwab’s 35 percent main-

Table 4

Margin Loan Rate Premium and Margin Loan RateImplied by the Jump-Diffusion Valuation Modela

Volatility (%) Margin Loan Interest Rate (%) Simpleb Jumpb Call Money 50% Margin 25% Margin

(�) (�) (r) (R–r) R (R–r) R

20 0c 8.25 .00 8.25 .00 8.25

(S&P 500 level) 10 .00 8.25 .00 8.25

20 .00 8.25 .01 8.26

30 .00 8.25 .16 8.41

40 .00 8.25 1.01 9.26

50 .00 8.25 3.25 11.50

30 0c 8.25 .00 8.25 .01 8.26

10 .00 8.25 .02 8.28

20 .00 8.25 .12 8.37

30 .00 8.25 .58 8.83

40 .00 8.25 1.94 10.19

50 .00 8.25 4.71 12.96

40 0c 8.25 .00 8.25 .26 8.51

10 .00 8.25 .35 8.60

20 .00 8.25 .73 8.98

30 .00 8.25 1.71 9.96

40 .00 8.25 3.71 11.96

50 .01 8.26 7.07 15.32

50 0c 8.25 .00 8.25 1.46 9.71

10 .00 8.25 1.70 9.95

20 .00 8.25 2.46 10.71

30 .00 8.25 4.01 12.26

40 .01 8.26 6.63 14.88

50 .04 8.29 10.50 18.75 aAll calculations assume the account equity is just at the 50 percent margin required byRegulation T or at the 25 percent maintenance margin required by NYSE Rule 431 andNASD Rule 2520. The notation is: simple volatility, �; jump volatility, �; Call Money Rate, r;Theoretical Margin Loan Rate, R; risk premium, R-r.bThe simple volatility is the standard deviation of the rate of return associated with thesimple diffusion model underlying Black-Scholes valuation. The jump volatility is the stan-dard deviation associated with discrete “jumps” in the rate of return. The total volatility is√(�2 + �2). c The margin loan rate with �=0 is the Black-Scholes value.

September/October 2000 New England Economic Review 43

ties. An account held in common stocks that just meetsthe 50 percent Regulation T requirement has so muchequity that the margin loan rate should not be muchhigher than the broker’s cost of funds. This is true for awide range of both simple and jump volatilities. But anaccount with a margin of 25 percent (the NYSE andNASD requirements) should have a very high premi-um over the broker’s cost of funds.

This highlights a mystery that is encountered inother loan markets. Interest rates tend to be set withless reference to credit and market risks than economictheory would suggest. This appears to be true inspades for margin loans. That it is a persistent phe-nomenon only underscores the mystery, for the marketfor brokerage services is highly competitive and cus-tomers can readily seek better deals from otherbrokers.

One explanation is that brokers might control therisks in a variety of ways, allowing them to adjust therisk profiles across accounts to a common level towhich a standardized loan rate schedule can apply. Forexample, we know that brokers set house marginrequirements at higher levels, sometimes well abovethe Regulation T level, for stocks that are particularlyvolatile. Brokers also set higher maintenance marginsfor accounts that are concentrated in a few securities.In addition, they limit the ability of individual cus-tomers to take leveraged positions. For example, thereare several levels of permissible option trading activi-ty, ranging from no option trading through permissionlimited solely to purchases of options, up to permis-sion to write uncovered options. The permitted trad-ing activity depends on the customer’s account equity,his experience, and his demonstrated knowledge ofoption trading risks. In short, brokers might controlloan risk by setting limits on quantities rather than bysetting loan prices.

Another explanation might be that relating theinterest rate to leverage rather than size carries addi-tional costs. The rate charged would differ among cus-tomers, and it would change frequently for any cus-tomer. This could create confusion and distrust amongcustomers, leading to a higher level of grievances andto costly broker time spent explaining the rate struc-ture rather than executing trades.

The apparently high loan rates might reflect thefact that many customers do not shop around as readi-ly as they could. Investor inertia gives brokers theadvantage of a “flypaper effect”; money tends to staywhere it first was placed. This is undoubtedly a factorexplaining why investors who want to invest on mar-gin do not rush to Brown & Co., which charges both

low commissions and margin loan rates below the callmoney rate. The flypaper effect argues that charging alower rate to attract new customers will erode the mar-gin loan revenue from existing customers with little

Interest rates tend to be set with lessreference to credit and market risksthan economic theory would suggest.

This mystery is encountered inother loan markets as well.

gain in accounts, but raising the rate will give morerevenue from existing accounts and, perhaps, not losea large number of new accounts. Investors who are notattentive to loan rate competition may encourage theirbrokers to set a margin loan interest rate schedule thathas little relationship with the underlying costs andrisks faced by brokers.

VI. Summary

The goals of this study are to describe themechanics of margin requirements (particularly in theequity markets), to lay out the history and practice sur-rounding the Federal Reserve System’s regulationsaffecting initial margins (particularly Regulation T), tolay out the economic principles underlying the analy-sis of margin loan risks faced by brokers and their cus-tomers, and to examine the potential effects of theserisks on the interest rates charged on margin loans.

The first and second sections discuss the back-ground for margin loans and margin loan require-ments. The distinction is made between initial marginrequirements that are set by the Federal ReserveSystem and maintenance margin requirements set bysecurity exchanges and broker-dealers. We addresssome reasons that debit balances are an imperfectmeasure of the use of credit to buy securities. We showthat recent increases in margin loans, to about 1.5 per-cent of the value of stock market capitalization, maynot reflect a more intense use of margin loans. In fact,there has been no recent surge in margin loans relativeto debt capacity in margin accounts. In short, while thequantity of margin loans has increased, the capacity toborrow against securities has also risen as a result of

Kremer, Joseph W. and Rodney L. Roenfeldt. 1993. “Warrant Pricing:Jump-Diffusion vs. Black-Scholes.” Journal of Financial andQuantitative Analysis, June, pp. 255-72.

Merton, Robert. 1976. “Option Pricing When Underlying StockReturns Are Discontinuous.” Journal of Financial Economics,January/March, pp. 125-44.

Parry, Carl E. 1949. “A Short History of Regulations T and U.” Boardof Governors of the Federal Reserve System, mimeo (May).

Press, J.S. 1967. “A Compound Events Model of Security Prices.”Journal of Business (July), pp. 317-35.

Shiller, Robert. 2000. “Margin Calls: Should the Fed Step In?” TheWall Street Journal, Monday, April 10, p. A46.

References

Black, Fischer and Myron Scholes. 1973. “The Pricing of Options andCorporate Liabilities.” Journal of Political Economy, May/June, pp.637-59.

Fortune, Peter. 1995. “Stock, Bonds, Options, and PortfolioInsurance: A Rose by Any Other Name…” New England EconomicReview, July/August, pp. 25-46.

____________. 1996. “Anomalies in Option Pricing: The Black-Scholes Model Revisited.” New England Economic Review,March/April, pp. 17-40.

____________. 1997. “Mutual Funds, Part I: Reshaping the AmericanFinancial System.” New England Economic Review, July/August ,pp. 45-72.

____________. 1999. “Are Stock Returns Different Over Weekends?A Jump Diffusion Analysis of the “Weekend Effect.” New EnglandEconomic Review, September/October, pp. 3-19.

44 September/October 2000 New England Economic Review

the margin debt. This premium is required to compen-sate the broker for the implicit put option he giveswhen making a margin loan.

In the fifth section we develop a simple model ofthe link between the put premium and the margin loanrate, and apply it to determine the characteristics thatshould explain the high margin loan rates that typical-ly prevail. We demonstrate that the value of the putoption depends on the volatility of the return onunderlying securities, as well as on the account’s lever-age as measured by the size of the margin loan relativeto the value of securities. We find that, if an accountmeets the 50 percent initial margin currently set by theFed, the value of the implicit put embedded in a mar-gin loan is negligibly small because 50 percent marginprovides such a large equity cushion that the chancesthe put option will end up in-the-money are veryremote. However, an account just meeting the 25 per-cent maintenance margin required by the New YorkStock Exchange and the NASD will have a valuableimplicit put option, and a broker is justified in charg-ing a substantial premium over the base lending rate.

We also find that margin loan rates are not set asour theory suggests. Interest rates tend to be setaccording to the absolute size of the margin loan,while our theory suggests that size should be far lessimportant than the volatility of security prices and theleverage in the account. We term this the “margin loanrate mystery” and briefly discuss several reasons for it.

rising stock prices. It is not clear that this exposes thefinancial system to more risk.

The third section focuses on the extent to whichinitial margins provide an extra cushion of equity toprotect brokers and their customers from margin callsand forced sales. We demonstrate that the amount bywhich the Fed’s initial margins restrict the potentialamount of margin debt depends on the history of stockprices as well as on the initial and maintenance marginratios. Initial margin requirements (in excess of main-tenance margin requirements) will limit margin debtmore strictly after periods of rising prices. In effect, ini-tial margin requirements act as a mild automatic stabi-lizer, restricting loans more severely to aggressiveinvestors when security prices have been rising.However, any stabilizing influence from this directionwill have little or no effect on prevention of specula-tive bubbles.

The fourth section addresses the economic prin-ciples underlying the credit risk created by marginloans. Here we show that holding securities partiallyfinanced by a margin loan is equivalent to a brokergiving his customer an implicit put option on theaccount: If the account’s value declines, the customercan put securities to the broker, either by allowingforced sales of securities or, in extreme circumstances,by abandoning the account. We note that the marginloan rate should be above the broker’s cost of funds,the premium reflecting the credit risk associated with