Buying long is the most common strategy, at least from an individual investor’s perspective. A hedge fund buying long has some cash and simply exchanges it for the security that it wants to hold. In a sense, the transaction can be represented as a swap (see Figure 5.1). Once the transaction has been concluded, the hedge fund has no further commitment. It fully owns the security and enjoys all its benefits (dividends, coupons, voting rights, etc.).

Selling is simply the opposite of buying long. A hedge fund wanting to sell a security that it no longer wishes to hold exchanges it for cash (see Figure 5.2). Once the transaction has been concluded, the hedge fund has no further commitment. It fully owns the cash, and can use it for any purpose.

Buying long and selling are called cash transactions, because they do not involve any loan and do not require any collateral. All the flows take place at the same time, and do not involve any future commitment. By contrast, other transactions are based on some form of lending and therefore require the posting of collateral and repayment of the loan. In this case, a securities company – typically a brokerage firm – will lend some securities or some cash to the hedge fund and will hold other assets in the fund’s account as collateral for the loan. The collateral in this case is termed margin and can be made up of cash, securities or other financial assets.

The two major transactions requiring collateral are buying on margin and selling short. Both are usually confusing for neophyte investors. While conventional security transactions involve only two parties, the buyer and the seller, margin transactions involve a third party, the security lender. This is because both buying on margin and selling short imply borrowing an asset. When buying on margin, the hedge fund borrows some cash; when selling short, the hedge fund borrows a security. In the following, we attempt to clarify the differences between these two strategies by looking at the detailed flows they generate.

Later, once the hedge fund has enough cash and no longer needs the loan, it will pay it back with interest, and receive back its collateral. The cash may come from the sale of the security that was bought on margin, or from any other source (see Figure 5.4).

There are several reasons for a hedge fund to buy on margin. First, buying on margin is an efficient way of borrowing against the securities already held in a portfolio, using them as collateral. The proceeds of such a loan can be used for both investing and non-investing needs. The interest rate charged is usually lower than in bank loans, and the repayment terms are much more flexible. Second, buying on margin increases the buying power and allows a greater amount of securities to be purchased per dollar of capital (i.e. leverage). Indeed, a fund manager buying on margin does not need to fully pay for his purchase – he just needs to post some collateral. With little cash or even no cash, it is therefore possible for him to take a position and enjoy its rise in price without really paying for it.

Brokerage firms also find several advantages in margin trading. They make money on both the margin accounts (from the interest they charge on the loans) and the trading (from the higher commissions they receive, due to the larger transaction sizes that leverage allows). Since margin loans are always secured by collateral, the default risk of a borrower is relatively limited. Indeed, the only risk is that the collateral plus the securities held in the margin account decline in value to a point where they are worth less than the loan balance itself. This raises two new questions. First, which type of collateral should be accepted? Second, how can one prevent the value of the collateral from dropping below the balance of the loan? To answer these questions and to prevent the excessive use of credit to purchase securities, most regulatory bodies and exchanges have enacted rules that govern margin trading. Whatever the country, these rules should cover three dimensions: minimum margins, initial margins and maintenance margins.

To open a margin account with a broker and before any trade takes place, an investor must deposit a minimum margin. This rule primarily targets small investors; it is not really relevant to hedge funds, because the corresponding amount is small. For instance, in the United States, the National Association of Securities Dealers (NASD) and the New York Stock Exchange (NYSE) now impose a minimum of $25 000 in cash or fully paid securities in order to open a margin account.⁷⁷ Of course, amounts differ in other countries and markets.

The initial margin requirement represents the minimum amount of funds an investor must put up to purchase securities on credit. For example, with a 50% initial margin requirement, the maximum amount of credit an investor can obtain from his broker to purchase stocks is 50% of the stocks’ value. An investor willing to buy one share of common stock valued at $100 per share must do so with at least $50 of his own funds or additional collateral.

In the US, the Federal Reserve sets the initial margin requirement as part of its monetary policy. Since 1934, it has changed 23 times, and even at one time reached a full 100% payment. The current rate, set in 1974, is 50%. As a matter of comparison, the initial margin requirement in the 1920s was usually around 10%. It resulted in high levels of margin debt and unstable stock prices, and created perfect conditions for the stock market crash in 1929.

The maintenance margin represents the minimum amount of funds an investor must have on his margin account to maintain an open position. It is expressed as a fixed percentage of the total market value of the securities held on margin. For instance, in the US, the NASD and the NYSE impose a minimum 25% maintenance margin requirement on their customers.

The positions purchased on margin are marked-to-market each day, which results in their regular revaluation. The gains, or losses, associated with the daily price changes are applied to the margin account. If the value of the margin account falls below the maintenance margin, the hedge fund receives a margin call. This is basically a request to deposit additional collateral. The fund manager can respond either by selling a part of his open position to reduce his exposure, or by depositing additional cash and/or new securities, until the maintenance margin requirement is met. The cash transferred due to a margin call is referred to as the variation margin.

Of course, security lenders prefer having a collateral made of stable assets, such as cash or T-bonds, while hedge funds prefer using risky securities (including the shares they purchased on margin) to secure their loans.⁷⁸ Most of the time, security lenders use a haircut table, which defines those securities that are accepted as collateral and the rule to determine their marginable value (usually a percentage of the market value). The riskier the asset considered, the more severe the haircut – for instance, cash and T-bills are usually taken at 100% of their value, while a diversified portfolio of stocks may only be accepted at 50 to 70% of its value.

Regulators may change the minimum margin rules whenever market conditions justify it. Brokerage houses must follow these rules, but they may freely apply more stringent requirements to their clients if they want to. In practice, most brokers officially request higher margins than the minima set by regulators and exchanges, but they may further differentiate their margin requirements and haircut tables by individual stocks and by the trading behaviour and credibility of their customers.

The current market value of the purchase is $100 000. In accordance with the 50% initial margin requirement, the hedge fund would need to deposit collateral or safe securities worth $50 000 into its margin account. The broker would lend the remaining $50 000 and execute Understanding the Tools Used by Hedge Funds 125 the purchase transaction. The hedge fund account would then appear as follows:

If the stock price goes up, say to $12, the value of the assets will increase to $120 000. On the liability side, the corresponding gain would be credited to the fund’s equity. The fund’s equity would then cover 58.33% (70 000/120 000) of the market value of the stocks held long. The hedge fund account would appear as:

As an illustration, let us say that the stock price falls to $6 per share. The hedge fund account appears as follows:

Note that if the hedge fund manager ignores the margin call or is not reachable, the broker is entitled to protect his interests without prior notice and bring the equity coverage into an acceptable range by selling a portion of the long stock position. The fund manager has no right to control such liquidation decisions. For instance, in the case of a diversified portfolio, the broker can freely decide which securities among the ones collateralized will be sold. The fund will be held responsible for any losses incurred during this process.

Note that a huge increase in naked short selling could create a virtually unlimited quantity of shares, even to the point that a normal market based on supply and demand could be seriously distorted. One of the arguments frequently used against naked short selling is that brokers and dealers accommodate stock price manipulation by permitting naked short sales to occur when there is no possibility of actually delivering shares to the buyers. However, naked short sales are not always associated with an attempt to manipulate prices. In fact, they can even sometimes protect investors from price manipulation. For instance, market makers such as intermediaries on the NYSE or the Nasdaq may choose to sell short if there is a sudden but temporary series of buy orders on a stock with no real fundamental justification. Their short sale will avoid an unjustified run-up in the stock’s price and stabilize the market.

During a short sale operation, the securities lender has in essence turned his security position into cash while still retaining the economic benefits of ownership. This implies that there are in fact two positions to consider when analysing a short sale: a “real” position occupied by the buyer of the security sold short, and a “phantom” position held by the entity lending the security to the hedge fund. As a consequence of the phantom position, the hedge fund is responsible for any corporate action with respect to the stock lender. For instance:

Technically, short selling does not require any initial investment – it just requires finding a security lender and having enough collateral. Nevertheless, short selling involves important risks:

The cost and difficulty of short selling is determined by supply and demand in the securities lending market. Generally, it is relatively easy to borrow most large cap stocks in established markets at a cost varying from 25 to 75 basis points per year. It is much harder to borrow securities that have low institutional ownership or that are in high demand for borrowing – typically the stocks many people believe to be overpriced. The cost may then increase dramatically, and the recall risk may be high. This leads to an interesting paradox: the securities lending market works well, except when everybody wants to use it to sell short, in which case it works very badly.⁸¹ This paradox explains why most hedge fund managers do not want to disclose their short positions – the cost of borrowing securities rises when other investors are also trying to short.⁸² A key indicator to monitor is therefore the short interest, i.e. how many shares have already been sold short. Last but not least, secrecy might be preferred if the short seller wants to avoid being sued or harassed by the firm he is currently shorting.

If we ignore all lending and execution costs, it should be clear that a hedge fund engaged in a short position will make money only if the repurchase price is lower than the original sale price; the hedge fund will incur a loss if the repurchase price is higher than the sale price. Consequently, the most obvious reason to short is to profit from an overpriced security or market. More sophisticated hedge fund strategies may also use short selling as a hedge for other long positions with offsetting risk, or as a way to speculate on spreads, i.e. the difference between two securities, as we shall see in Part II of this book.

Short selling relies heavily on securities lending, i.e. the practice of security holders making their securities available for a small fee to sellers in the market, on condition that equivalent securities be returned to them at a future date. Securities lending existed in the US in the 19th century, but it only really gained momentum in the 1970s and 1980s with the liberalization of regulations that had previously hampered the practice. Today, available official data suggest that the US market size of open securities loan positions is close to $3 trillion.

The primary source of securities lending remains portfolios of beneficial owners, such as institutional investors, pension funds and insurance companies. These investors are willing to generate additional revenue on their long-term strategic holdings and they are motivated by the desire to reduce custody fees for their portfolios. Although the returns on securities lending are relatively small, particularly for the most liquid securities, a few basis points may matter in a field as highly competitive as asset management. The second source of securities lending is financial firms such as banks and broker-dealers acting as either agents on behalf of beneficial owners, or as principal. For them, securities lending has turned out to be a business in its own right, much more than an extension of a firm’s basic inventory management process. Most broker contracts allow the lending of securities held in their margin accounts, and several firms even borrow securities in advance, with the expectation that others will shortly be prepared to pay more to borrow them (Box 5.2).

The current market value of the short sale is $100 000. First, the hedge fund has to check with its broker to ensure that the shares are available for borrowing. Then, it needs to deposit safe securities worth $50 000 into its margin account, and leave the proceeds of the short sale as collateral.⁸⁴ The hedge fund account would then appear as follows:

If the stock price climbs from $10 to $11, the (absolute) value of the short position increases. Since the value of the assets does not change, the corresponding loss is absorbed by the equity. The new hedge fund account would then appear as:

One may wonder which stock price will create the first margin call. With a 30% maintenance margin, we have:

Once again, prime brokers have a key role to play in the short-selling process. Large prime brokers are more likely to have access to hard-to-borrow securities. In addition, they can often offer some sort of cross-margining facilities, i.e. positions held by the hedge fund in various instruments which all require collateralization are grouped and margined together, taking into account offsetting risks and hedges. Such an approach allows for the most efficient use of a hedge fund’s capital and optimizes the collateral management process.

Since short selling increases the supply of long sale orders in the market, which in turn increases the potential for both disorderly and manipulative trading, the common conjecture seems to be that short sale restrictions can reduce the severity of price declines. Consequently, many regulators have imposed a series of specific short sale constraints that mechanically impede short selling, or at least restrict it to some market participants and/or some liquid securities. These constraints vary from one market to another (see Figure 5.11), but some examples are:

In addition, several exchanges require short sales to be executed only in a plus tick or more commonly in a zero-plus tick situation (Table 5.1). A plus tick (also known as an up-tick) rule means that the short sale can only take place at a price higher than the last previous transaction in that security. A zero-plus tick rule requires the short sale to take place at a price that can be the same as the immediately preceding transaction but higher than the last transaction in that security at a different price.⁸⁵ Both rules are intended to prevent the short selling of a stock that is already declining in price in order to avoid sending stock prices into a free fall. Not surprisingly, no exchange has yet prohibited buying at a price above the last traded price, even though one could argue that it pushes stock prices up.

In some countries, the crusade against short selling has been even more strident. In 1995, for example, the Malaysian Finance Ministry proposed mandatory caning as the punishment for short sellers, and declared that the beating would be “light, similar to the punishment carried out on juveniles” – see Jayasankaran (1995).

These extreme views that regulators seem to have about short selling appear to derive, at least in part, from the relative opacity that surrounds short sales and securities lending. Since securities lending is a private agreement, it is extremely difficult to distinguish a normal sale from a short sale. In addition, a few financial intermediaries (e.g. prime brokers) have information on short positions and stock borrowing figures, while most market participants do not, leaving those with the information in a privileged position. Several jurisdictions and markets have therefore decided to improve the transparency of short selling by publishing aggregated data on short sales. For instance, in April 2003, Hong Kong introduced a disclosure requirement for short economic interests with a view to improving the transparency of the economic interests of substantial shareholders in a company. The major benefit is that investors can then see the extent of aggregate short selling in any particular security and draw their own conclusions from that information. Of course, there must be a limit to the disclosure level as well as to the public transparency, because knowledge of individual market participants’ and market makers’ open short positions could jeopardize their trading strategies and expose them to increased risk of being caught in a short squeeze. Hence, information is usually aggregated per security and published on an anonymous basis. So far, we are not aware of any exchange publishing real-time information. The most frequent disclosure is twice daily, in Hong Kong (see Table 5.2 and Figure 5.12 in Box 5.3).

Note that another approach to disclosure adopted in several jurisdictions, including Spain, Sweden and Brazil, is to publish securities lending figures rather than short sales. In some countries these figures may provide a reasonably precise proxy for short-selling activity. In others, they are less useful because stock lending is also used for other activities, e.g. receiving dividends by parties to whom they offer some particular advantage (exercising voting rights, etc).

Unlike investment banks and financial intermediaries, short sellers have no conflict of interests because they have no ties with the companies they are targeting (see Box 5.4). Their research is independent, and sometimes visionary. In 1989, for example, the House Committee on Government Operations (Commerce, Consumer and Monetary Affairs Subcommittee) held hearings about the alleged evils of short selling, featuring testimony from three supposedly victimized firms. Later, the SEC charged the presidents of two of these three firms with fraud, and their stock prices collapsed.

Repos are frequently used by hedge funds to finance their positions and manage their leverage. On the flip side, reverse repos are often used as short-term investments. Note that while repurchase agreements can be negotiated for any term, the majority of repurchase agreements are for overnight terms and the counterparties often choose to renew the repo by renegotiating the repo rate on a daily basis.

Financial derivatives are not new. They have been around for years and are an integral part of a market economy. Market historians found evidence of derivatives in ancient India, Israel, Greece and Rome, as well as in medieval Europe and Japan (see Box 5.5). More recently, in 1865, the Chicago Board of Trade organized a large-scale agricultural futures market. However, the real development of derivatives started when the United States and other industrial nations abandoned the Bretton Woods system of fixed currency exchange rates. This resulted in extreme fluctuations in currencies and interest rates, and was followed by an inflationary oil price shock. Both elements created a strong demand for new hedging instruments that would facilitate the transfer of various risks to institutions which, because of their greater financial reserves and/or financial talent, were better able to manage them.

In 1973, the Chicago Board Options Exchange (CBOE) opened for business and started trading options. This was the first time that an exchange itself had acted as counterparty rather than being just the venue where the contracts were negotiated. But trading options without a model was like wandering in the desert without a compass. Fortunately, the same year, Fischer Black, Myron Scholes and Robert C. Merton provided the first reasonable mathematical model for the pricing of options. The methodology that they introduced has since been expanded for use in pricing a wide variety of derivative instruments and contingent claims that have changed the face of finance by creating new ways of analysing, managing and transferring risks.

In the 1980s, the growth of derivatives was further facilitated by the shifting geographic pattern of international savings and investment, and the globalization of financial markets. In particular, the transformation of the United States from a net supplier of funds to a major borrower, and the emergence of Germany and Japan as major lenders, encouraged the development of new, low-cost, risk-managing financial instruments that could be traded in international financial markets in order to reduce the costs and risks associated with international borrowing and lending.

Unfortunately, the tremendous growth of the financial derivatives markets and reports of major losses associated with derivative products have also generated a great deal of confusion about those instruments. Derivatives have often been stigmatized by the media as a new pariah, and have acquired an aura previously associated with deficits and drugs. Our goal here is quite modest, namely, to give a brief introduction to the main types of derivatives contracts. We focus primarily on understanding the way they work rather than on their pricing. Readers interested in knowing more about derivatives and their valuation should refer to Hull (2005).

By contrast, exchange-traded contracts are transacted through a regulated exchange. They are standardized and cannot be specially tailored to specific situations. However, they also have several advantages:

Of course, there are many variations and combinations of the three contracts described above. For instance, forward rate agreements (FRA) are OTC agreements to exchange an amount of money based on a reference interest rate and a reference principal amount, referred to as the notional amount, over a specified period of time. FRAs differ from other forwards in that only an amount based on interest rate differentials, and not the principal, are transferred between parties. Consider, for example, a three-month FRA between a hedge fund and a bank with a $10 million notional principal amount. Then the bank would pay the hedge fund according to the following formula:

Credit derivative products have evolved over time to suit the various needs of buyers and sellers of credit risk, but the most highly utilized credit derivative remains the credit default swap (CDS – see Figure 5.14). The CDS is the simplest, most liquid and most efficient way to hedge concentrations of single-name credit risk. In a sense, it is similar to an insurance contract, providing the buyer with protection against the risk of default or significant credit deterioration of an asset issued by a specified issuer.

A credit default swap is an OTC bilateral agreement between a “protection seller” and a “protection buyer”. The protection seller promises to compensate the protection buyer against an economic loss in a “reference asset” if a “credit event” occurs. In return, the protection buyer pays a fee, either upfront (for short-dated contracts, the transaction then being called a credit default option) or on a regular basis (for long-dated swaps). In practice, there are several important features that need to be agreed between the counterparties and clearly defined in the contract documentation before a trade can be executed. These include:

CDS contracts can efficiently mitigate risks in bond investing by transferring a given risk from one party to another without transferring the underlying bond or other credit asset. Prior to creation of the CDS, there was no vehicle to transfer the risk of a default or other credit event, such as a downgrade, from one investor to another. CDSs can also be used as a way to gain exposure to credit risk with no requirement of an initial funding, which allows leveraged positions. Moreover, a CDS transaction can be entered into where a cash bond of the reference entity of a particular maturity is not available. Further, by entering a CDS as protection buyer, one can easily create a “short” position in the reference credit. With all these attributes, CDSs can be a great tool for diversifying or hedging one’s portfolio.

In the early days of the CDS market, pricing of contracts was more an art than a science. Today, however, pricing is more quantitatively based, using parameters such as (i) the default probability of the underlying, established on the basis of credit data, (ii) the floating leg of the swap, i.e. the expected payoff in case of default and (iii) the fixed leg, i.e. the initial swap spread which is valued on the assumption that the protection buyer stops paying after the default takes place. In theory, CDS spreads should be closely related to bond yield spreads, or excess yields to risk-free government bonds. In practice, as we shall see, there may be some tiny differences, and therefore some arbitrage situations.

An equity default swap (EDS – see Figure 5.15) is a hybrid of a credit derivative and an equity derivative. As with a CDS, an EDS is a vehicle for one party to provide another party with some protection against a possible event relating to some reference asset. With a CDS, the reference asset is a debt instrument and the protection is provided against a possible default or other credit event. With an EDS, the reference asset is some company’s stock and the protection is provided against a dramatic decline in the price of that stock. For example, the EDS might provide protection against a 70% decline in the stock price from its value when the equity default swap was initiated. The event being protected against is called the trigger event or knock-in event.

The EDS has several advantages over the CDS:

The EDS valuation is therefore based on (i) the level of the trigger event for equity default, (ii) the probability of the equity default, and (iii) the expected recovery rate, which is fixed at the beginning of the contract (Box 5.6). From a pricing perspective, an EDS is similar to a deep out-of-the-money long-dated American digital put. A key difference is that the option premium is paid in a series of instalments that cease when the option is triggered.

Leverage can be measured in a number of ways. The traditional measure is the balance sheet leverage, i.e., the ratio of the fund’s balance sheet assets to equity. Although it is widely used in the hedge fund world as a risk measure, balance sheet leverage has several weaknesses. In particular, it fails to take into account market, credit and liquidity risks in a portfolio, as well as the use of off-balance sheet products such as derivatives. A better measure is therefore the “economic leverage”, which captures the degree of risk taken on by the fund in relation to its ability to bear that risk, i.e. the ratio of potential gains and losses to net worth. Not surprisingly, measuring economic leverage precisely is far from straightforward.

It is important to realize that leverage is not a feature restricted to hedge funds. An investor buying a new home and financing it by a mortgage is in fact doing a leveraged investment. His equity capital is represented by his personal contribution (say 20% of the total amount), while the rest is financed by external funds. In this case, we would say that the leverage ratio is 5 to 1, i.e. $5 invested for any $1 of capital. Similarly, an industrial company issuing debt and using the proceeds to build a new plant is also leveraging its balance sheet.

Nevertheless, leveraging as applied to investing is often considered an aggressive strategy comparable to gambling. The reason is that it magnifies both profits and losses. For instance, say a hedge fund invests $1000 of its equity capital in a stock that rises by 10%. The fund earns $100, that is, a 10% return. By contrast, if the fund had borrowed $10 000 and invested it along with its original $1000, it could have earned $1100, that is, a 110% return, before factoring in the borrowing costs. Now, what if the same stock had dropped by 10%? If the fund had invested only $1000, it would have lost $100, that is, 10%, and its shares would be worth $900. But if the fund had borrowed another $10 000 and invested it in the stock, the total investment of $11 000 would have fallen to $9900. Instead of losing $100, the fund would have lost $1100 plus the borrowing costs, that is, more than its initial equity capital. Clearly, although leverage opens the door to increased income and gain if the market moves on expected lines, it also creates certain risks if the market trend is contrary to expectations.

With hedge funds, leverage can take several forms. It may, for instance, involve explicitly borrowing external funds via a loan, or implicitly borrowing through a margin brokerage account. Last but not least, hedge funds can also use financial instruments (such as repurchase agreements, futures and forward contracts and other derivative products) to establish positions by posting margins rather than the full face value of the position. In all cases, when calculating the real exposure, the amount borrowed should be treated as a negative allocation. It actually becomes a liability of the portfolio as opposed to an asset. For instance, when a hedge fund with $100 capital borrows an additional $25 against its portfolio holdings, it has a $25 liability that must be paid for, but it also has $125 to invest. Of course, the operation only makes sense when the return on investment is higher than the cost of borrowing.

As mentioned already, leveraged investing is often dismissed as gambling. We personally disagree with this assertion. In our opinion, leverage, as long as it stays reasonable, plays a positive role in the financial system. It improves market liquidity, lowers credit costs, and results in a more efficient allocation of resources in the economy. It allows younger people to invest more in equities rather than having to wait until they are older and have sufficient resources to do so. And why, one might ask, is borrowing to buy a new home a perfectly natural thing to do, while funding one’s future through an investment loan is apparently another story?

The unpopularity of leverage can be traced back to a few disasters encountered by over-leveraged speculators, most of the time because of pyramidal schemes. Once an investment is financed by leverage, the new asset (e.g. the stock) can be used as collateral for obtaining another loan. The only leverage constraint is therefore the degree to which banks and broker-dealers will finance additional trades and allow leverage on leverage. In a sense, over-collateralization may become an eventual constraint in the same way that a reserve requirement on deposits limits the creation of new money.

The best illustration of over-leveraging is arguably provided by the fund called Long Term Capital Management (LTCM). For several reasons, LTCM’s counterparties did not take risks properly into account (see Box 5.7). They granted LTCM huge trading lines in a variety of products, and LTCM took advantage of those lines to achieve its exceptional degree of leverage. When the fund almost went bankrupt in 1998, the whole financial system was at risk, and the Federal Reserve had to step in and organize a rescue.

The primary lesson to be learned from the LTCM debacle is that the combination of tremendous leverage and illiquid markets is similar to a vodka party. It often starts well, but ends up badly. Before the Russian collapse, the level of leverage used by LTCM was comparable to the leverage used by banks and securities firms – see Table 5.3. However, two factors distinguish banks and securities firms from hedge funds: (i) they have more diverse sources of income and of funding and (2) they are subject to government oversight that monitors risk management systems, public disclosure and capital requirements. LTCM, by contrast, had very few sources of income and was completely opaque and largely unregulated.

Fortunately, hedge funds have learned from the disaster and most of them have dramatically reduced their leverage. Moreover, their counterparties (banks, brokers, etc.) are now imposing higher margin requirements when lending to hedge funds and put in place stricter rules to control their exposure. It seems that Wall Street can sometimes learn from its losses.

The second lesson is also related to the use of leverage. Market participants often fail to consider leverage in their comparisons. As an illustration, let us look at the annual return of three investment strategies (Figure 5.17), namely, investing in LTCM, investing in an index fund mimicking the S&P 500, and buying the same index fund on margin using a 2 to 1 leverage. In the last-mentioned case, we assume that interest is paid on debit balances at the rate of 10% p.a.

As can be seen, while LTCM averaged a 29.62% return p.a. between 1994 and 1997, the plain vanilla indexed fund achieved an average return of 20.17% p.a., and the leveraged strategy 28.67% p.a., net of financing costs. If we include the year 1998 (which is obviously unfair), the average return drops to −22.35% p.a. for LTCM, but rises to 21.44% p.a. for the index fund and 31.47% p.a. for the leveraged strategy. Had we taken the risk of leveraging our index fund 50 to 1 as did LTCM, our returns would have been nothing short of spectacular.