The opinions expressed in this article are those of the author and do not represent those of APG Investments.

1. Introduction

Financial leverage (leverage) is at the heart of the current financial crisis, and now is as good a time as any to shed light on this elusive topic. Many people think it is effective to control risk by limiting leverage, but that is a trap to be avoided. It is well known that leverage has the potential to introduce new risks, as well as magnifying returns and existing risks. What is less well known, however, are the practical considerations and limitations. Here, the devil is in the detail.

Leverage is useful to get a desired level of risk in a portfolio, but it demands improvements to reporting and risk measurement. Leverage introduces new risks: liquidity risk and additional counter party risk. These new risks require new measures. You have to improve the measurement of risk, liquidity and counter party exposure. If leverage in the portfolio is high it may increase very fast at times of stress.

In extreme cases with large leverage (such as in the current crisis) leverage was used to achieve target returns from very small spreads. This way leverage becomes a very cyclical and dangerous investment tool. This has led both to very low spreads on credit (such as mortgages) and to the current crisis. I will review the concepts first and then go on to the limitations and practical problems.

2. Definition(s)

We speak of leverage when: (a) an institution’s financial assets are larger than its capital; (b) an institution is exposed to the change in value of a position more than the amount that it paid for the position; or (c) an institution owns a position with embedded leverage. A position with embedded leverage is a position with an exposure larger than the underlying market factor. (Institution in this text may also be read as bank, company or investor.)

As an extension of the balance sheet, leverage can have impact on two aspects of the investment position:

• Exposure: due to the extra investment, extra exposure is created to a market, region, investment style or factor. The institution now holds more of the underlying investment and is more exposed to any movement in price.

• Risk: as a result of the extra investment, returns and also risks (or better: volatility) are magnified. Whether the total portfolio is more risky depends on the total portfolio and the liabilities.

Leverage increases the exposure to the underlying investment. For example when investor A borrows money to buy more stock of a company, he gets more exposure to that company and he may also increase risk. That increase in risk is not necessary however. In the example investor A's risk would increase. Suppose however that investor A had also promised to sell that equity in the future to someone else. Now investor A's total risk may be lower after leveraging and buying the extra equity, than before. The key is to look at the total position. The distinction between the effect of leverage on exposure and on risk is critical. This distinction helps you to understand why leverage is not a desirable or undesirable outcome of the portfolios construction. It is the risk that is the interesting portfolio characteristic.

Financial leverage is considered a balance sheet effect and is usually defined as a balance sheet ratio. The definition is:

where a is the ratio of money borrowed to the ratio of money owned (or equity capital in the balance sheet). This definition is useful even for off-balance sheet leverage, but the concept then needs to be extended.

We can distinguish between balance sheet leverage, economic leverage and embedded leverage. Balance sheet leverage relates only to the visible leverage. This is the leverage which shows on the balance-sheet as borrowed money. Economic leverage relates to all leverage of an institution. Economic leverage also shows the leverage due to off-balance sheet items. This is done by creating a replicating balance sheet for the purpose of calculating leverage and risk. In this replicating balance sheet, off balance-sheet items are also included. These off-balance sheet items are usually conditional obligation that do not need to be shown. An example is a guarantee for a loan from someone else to a subsidiary. Although that guarantee obviously has a lot of value if that subsidiary fails, it may not show on the balance sheet. Derivative products are other examples of off-balance sheet items. Embedded leverage can be found in products that in themselves are leveraged, but whose leverage is not represented in reporting. This leverage would never show on the balance sheet, not even on the replicating balance sheet. An example of embedded leverage is the leverage in a non-listed private real estate funds with loan financing, where the institution holds a minority. This means all leverage in titles that are not consolidated is embedded. This includes indirect real estate investments and hedge funds (or would include tranches of leveraged CDOs) that are minority owned. To get a complete perspective on leverage you should consider all leverage. That includes embedded leverage that is not in the economic leverage because it is not owned directly. All leverage should be analyze in a replicating portfolio. This replicating portfolio is then broader than even the replicating balance sheet and includes all leverage whether on-balance, off-balance or embedded.

Clearly then leverage does not only occur from borrowing money, but has many sources. Some of the most important are borrowed stock, swaps, options and other derivatives. Obviously it now becomes less simple to use the definition of leverage in terms of the balance sheet that was given. The general approach is to analyze all positions as the replicating portfolio. For this replicating portfolio the leverage can be calculated with the definition of leverage in Formula I. This is not standard practice because: the transparency of the embedded leverage is frequently insufficient, the amount of effort involved in such reporting is huge. An approximation of the embedded leverage however is already a good step forward.

Another important concept in leverage is the level of netting. Netting occurs when two offsetting positions are reported as the net position they represent. This occurs frequently in investment portfolios. Currency contracts for example are never actually closed. They are unwound by entering into an offsetting contract. When they mature both the original and offsetting contract terminate and the net position is settled. It makes no sense to report these offsetting position separately, and canceling them out in the reporting and in the calculation of leverage and risk is called netting. Netting can however occur on different levels. On one end of the spectrum you could net on the asset category level. On the other end two positions could only be netted if they have matching settlement dates, counter parties and underlying titles, such as is the case with currency contracts. Which netting to use, depends on the purpose. Netting on a high level is useful for asset category exposure, on a low level it is useful for counter party exposure. This means that the counter party risk is usually several times the net investment of an institution. This is why financial institutions are so interconnected.

3. Uses

Leverage is often associated with hedge funds, who typically apply leverage in their investment strategies. However many investment strategies make use of leverage. In the context of securities lending, repos and long/short strategies a kind of leverage is introduced. The activity of security lending itself could be considered leverage, because cash collateral, in time to be returned to the borrower, is usually re-invested. The investment risk may be limited even though the size of the lending may be large. Long/Short equity strategies are an example where leverage is used in a controlled manner to enhance the effectiveness of investment strategies. The portfolio is leveraged by borrowing equities instead of cash. The same can be done in Fixed income management. Fixed Income managers frequently use repos to create extra value to the portfolios. The cash proceeds from the repo are re-invested.

Derivative instruments are part of the standard investment tool-kits of many institutions for their asset allocation and management of interest rate, currency and credit risks. Different instruments are used: futures/forwards, swaps and options. These instruments create leverage effects, though how is impossible to tell out of the context of the strategy. The management of the risks associated with these instruments takes place at different levels in the organization: allocation, fund- and portfolio level. Derivatives are also used for active strategies in assets such as commodities and alpha return strategies.

Besides the explicit leverage from the instruments described above, there can also be embedded leverage. By investing in hedge funds or non-listed investment funds an investor also creates leverage in the portfolio as these hedge funds or private funds also create financial leverage on their balance sheets. In a context of low interest rates, many real estate companies routinely use financial constructions to improve the returns on their real estate investments. Usually the Private equity market is subdivided into two sub-sectors: Venture Capital and Buyouts. If the buyout is funded with a relatively small amount in equity and lots of debt, it is called a leveraged buyout (LBO). A typical LBO capital structure consists of 30% equity and 70% debt.

In the overall implementation of many strategies leverage is introduced, often through derivatives. GTAA strategies and absolute return funds (hedge funds) typically employ leverage in various ways. With derivatives it is possible to create an exposure without having cash. This could cause a leverage position. To counter this a cash position (´committed cash´) is usually held to de-leverage the exposures created by derivatives used for asset management. For tactical duration management of a Fixed Income portfolio, interest rate futures positions and swaps cannot be hedged with cash. The cash position would partly eliminate the duration-effect of the swap or future position. In short leverage is now everywhere in institutions' investment portfolios.

The Counterparty Risk Management Policy Group¹ wrote (some lines omitted):

It is common wisdom that leverage has the potential to increase market risk. As a result, the general public associates high levels of leverage with high levels of market risk. Yet in a world of active portfolio management an increase in leverage may be associated with a decrease in market risk. For example, it is common for financial intermediaries to manage the market risks they assume from their customers by taking offsetting market risk positions. By the same token, a reduction in leverage (as traditionally measured) can be associated with a rise in market risks. Therefore, in the context of market risk, leverage is best viewed as a tool to achieve a desired risk profile relative to capital, and its impact is best assessed by measures of market risk, such as VAR and stress testing.

Options can be replicated by buying or selling the underlying and holding a position in cash. This insight is in fact fundamental to the pricing of options. The ratio of underlying (stock) to hold can be calculated from the option pricing formula and is referred to as the delta of the option. This delta is not constant. It depends on the market level (the price of the underlying to be exact) and on the interest rate, among other things.

When you replicate balance sheets with derivatives (and any other conditional asset or obligation), to represent the same exposure, the replication is not constant. Every time there is a market move the replicating portfolio has to be rebalanced, to look like the original portfolio again. The distribution of returns from the balance sheet and the replicated balance sheet is quite different even if the overall exposure is not. This means that in circumstances leverage can be used to create portfolios that would not be possible otherwise. Where to apply leverage will be decided on a case by case basis.

5. Leverage and risk

Under some limiting condition, the relation between leverage and risk is simple. If we assume a portfolio is levered by borrowing a truly risk-free asset then using leverage only magnifies and shifts the distribution of returns. The distribution of returns shifts to the right if the return on the portfolio is larger than the return of the risk-free asset, it shifts left otherwise. You can see this if the formula used in the definition is rewritten to represent the sensitivity of a leveraged portfolio with respect to the return on the underlying asset. This rewritten formula is:

where R_p is the return on the portfolio, R_f the return on the risk-free asset and R_a the return on the underlying asset.

When leverage is large it may not be clear just how large the risk really is, and it may increase very fast at times of stress. The value of the assets drops but the value of the loan does not, the owned capital is reduced much faster than the total asset value. When leverage is very large the risk measurements become very sensitive to misspecification of the underlying distributions, simply because the difference between profit and loss becomes extremely small. Most risk models, including those produced by commercially available systems, are trend following. After periods with low risk, the estimate is low; after periods with high risk the estimate is high. Combined with a tendency to increase leverage in a boom, when measured risk tends to be low, a leverage strategy can become very pro-cyclical. Security brokers and dealers have a tendency to do this as a company strategy. They increase leverage in boom times (i.e., when spreads are low on credit) and reduce it in bad times, see Adrian, 2008².

6. Leverage introduces new risks

The most important additional risk is that liquidity becomes much more of an issue. Leverage enhances funding liquidity and asset liquidity risk (think of the current crisis). The liquidity of the assets and of the risk-free asset is not constant through time, how it behaves is not very well described, understood or modeled. In difficult times (stress in the financial markets) it becomes difficult to trade, even on otherwise liquid products. On leveraged positions liquidity is much more of an issue as you may want to exit, or you may be forced to exit, possibly as a result of regulatory restrictions. Also, now you have to exit on two position, the long and the short. Such exit may then be costly, or worse impossible.

Whatever you borrow you will have to return at some point in time, it can be called. It should be obvious that this can be a process occurring at multiple market parties at the same time. Additionally as this happens liquidity tends to dry up, meaning you will not get the replacement position anywhere else. What to do about this? First of all you need to know what you have borrowed and what the position and status of events is on these titles. To maintain a good overview of rights to collateral and obligation to borrowed issues it is critical to maintain insight in the economic (corporate) events. If the position is not on your books, as may be the case when you us a prime broker for the borrowing, you have an obligation to reconcile. Reconciliation should be set up prior to entering in to issue borrowing, and maintained at good quality all the time. Then of course you need to monitor the liquidity of whatever you borrow and whoever you borrowed it from, to ascertain at any time where they stand with respect to recall.

Leverage on a portfolio is not constant through time. When the return on the risk-free asset becomes high in relation to that on the assets (but still less than that on the assets) leverage rises fast. The portfolio returns then become highly sensitive to changes in the return on the asset. You therefore need to monitor your leverage and set some limits in advance even if you have appropriate risk limits.

Most of the time the risk-free assumption does not hold. In the description above on the use of leverage it can be seen that most of the time the borrowed asset is not risk-free at all and in fact can be rather risky. Risk-free should be understood as being certain in value at the investment horizon for the investor. Most leverage is from derivative positions and swaps. Therefore the simple formulas above break down and the borrowed asset should be fully modeled jointly with the invested assets to get a good perspective on risk. Embedded leverage is usually your worst nightmare. By definition, it is not transparent and not tractable from data series. The reason why it is not tractable from data series is because it is managed. Laddered loans, swaps and swaptions are commonly used to manage these risks. You should only enter embedded leverage if you have good faith in whoever manages this risk for you, and you have very good reason to have such good faith. The key to managing embedded leverage is reporting and transparency of the investment entity, but this may be hard to achieve.

Additional counter party risk does also result from the use of leverage, but most of the time this is mitigated very well by the exchange of collateral or the use of a clearing house. However if this is not well set up it is certainly a barrier to the use of leverage by an institution.

7. Conclusion

Leverage in investment portfolios is a common result of portfolio construction techniques, with or without derivatives. It has the potential to enhance risk and exposure. It is a useful tool to achieve the desired level of risk in a portfolio. But containing the amount of leverage is not a good way to control risk, because leverage is a tool that can be used to increase and reduce risk. Leverage has to be monitored well to have an accurate view of it's impact on risk. All leverage has to be monitored even leverage embedded in products and funds, but this is hard to achieve.

Using leverage introduces (or magnifies) risks, most of all liquidity risks, that you have to control. These controls are operational measures needed to monitor and modify aspects of liquidity, leverage and counter party risk. Using leverage in a portfolio requires understanding of the limitations of risk models and the limited knowledge and modeling of liquidity. It is wise to maintain a margin error for both these limitations.

Footnotes:

¹Improving Counterparty Risk Management Practices, Counterparty Risk Management Policy Group, June 1999

²Tobias Adrian and Hyun Song Shin, 2008. Liquidity and Leverage. Federal Reserve Bank of New York Staff Reports nº. 328.