CHAPTER
SIXTY-EIGHT
HEDGING TAIL RISK

STEPHEN J. ANTCZAK, CFA

The recent financial crisis has created an increased focus on “tail risk” and ways to minimize exposure to the unexpected. Once the domain of risk managers and fringe thinkers on trading desks, it has become a common phrase among the lexicon on trading floors. For that matter, it is a common phrase even away from trading floors (e.g., Google “tail risk” and one may be surprised at the number of hits received). In fact, a number of hedge funds have recently been created solely to take advantage of tail risk.

In this chapter, we first discuss why tail events seem to occur with such regularity. We find that one or all of three characteristics (leverage, transient funding, and the influence of “noneconomic” objectives and constraints on investment decisions) are associated with many, if not most, tail events. We then provide some background on three specific tail risks that we “hedge” later in the chapter. These are a sharp decline in the equity market, public sector fiscal imbalances, and an economic downturn. It is important to recognize that we define an equity market downturn as a risk for fixed income investors in part because of the high correlation between stocks and segments of the fixed income market. The co-movement between the equity market and the high-yield sector of the credit market from May 2001 to May 2010 is shown in Exhibit 68–1. In addition, many bond investors, and for that matter investors in general, tend to view both opportunities and risks in a cross market context far more now than in years past.

EXHIBIT 68–1
Co-movement of the Equity and High-Yield Credit Markets: May 2001–May 2010

images

With regard to constructing hedges, we next highlight four key challenges that most hedges face: (1) correlation between the portfolio being protected and the hedge vehicle itself, (2) cost, (3) the potential for slippage, and (4) the reliance on historical relationships, as these relationships can be transitory over time. We then consider two very broadly defined hedging strategies—unfunded and funded approaches—and note that both types typically face the challenges highlighted above (Exhibit 68–2). We define unfunded hedges as those for which an investor is willing to dedicate a certain amount of capital to protect the portfolio. In some respects, unfunded strategies are comparable to insurance policies. Funded strategies tend to be utilized by market participants who are unable or unwilling to pay the cost of insurance outright. They nonetheless require a hedge, and therefore want (or need) to go long an asset to pay for insurance. Funded hedges tend to become more popular when the catalyst for a market setback is difficult to predict, as performance can lag if a premium is continuously being paid to protect against an event that does not occur. We assess the performance of various hedging vehicles in the context of a declining stock market tail event.

EXHIBIT 68–2
Select Characteristics of Unfunded and Funded Hedges

images

This chapter was written when the author was the Head of U.S. Credit Strategy at Société Générale.

The author would like to thank Jung Lee and Sandeep Mody for their assistance in developing this chapter.

We then assess the effectiveness of various funded packages in the contexts of the second (sovereign credit event) and third risks (economic downturn). Finally, we discuss trade-specific hedge risks, such as counterparty risk. We find that funded hedges can be more risky than unfunded approaches, in large part because they have more “moving parts,” but they are not necessarily less effective.

STEP-BY-STEP GUIDE TO HEDGING

There is no perfect hedging vehicle or approach, but we do believe that a checklist consisting of the following six steps can be fairly useful when constructing one.

Step One. Decide whether to hedge. A credit portfolio manager sees a high likelihood of a tail event occurring. Does this mean that he should necessarily hedge? Perhaps, but not necessarily, as there are a number of factors that could warrant not hedging. Suppose that this portfolio manager handles 25% of an endowment’s capital. What happens if the endowment also expects a tail event and shifts the 75% of funds that are not handled by this credit manager into cash? If the credit manager also hedges, the endowment may very well be overhedged. Or what if the portfolio manager anticipates a sharp pickup in defaults, but comes to this conclusion after the consensus does? It may already be priced in and therefore not cost effective (Exhibit 68–3).

EXHIBIT 68–3
U.S. Speculative-Grade Default Rate versus High-Yield Bond Index

images

Step Two. Decide what to hedge. Even if an investor decides that it is worthwhile to hedge, it is almost as important to understand exactly what is to be hedged. One type of tail event (e.g., sovereign default) could require a very different type of hedge than another (e.g., BP oil spill).

Step Three. Identify challenges to watch out for. There are a number of challenges that could have some influence on the efficiency of virtually all hedge vehicles. These include the correlation between the hedging vehicle and the asset being hedged, the cost of the hedge, the potential for slippage between the hedged asset and the hedge itself, and the reliance on historical data to anticipate potential future performance.

Step Four. Decide whether to fund or not. Given that hedges are in some ways comparable to insurance policies, an important choice must be made with regard to how to pay the premium. One could simply dedicate a certain amount of capital to pay for insurance and “write off” the premium. The downside, though, is that it is quite possible to under-perform benchmarks or competitors if a tail event does not occur. Conversely, one could fund the hedge by going long an asset that is less sensitive to a tail event than the hedge, but there is a tradeoff as new risk factors can be introduced.

Step Five. Craft an efficient hedge. Finding an efficient hedge to a large extent involves balancing the payoff potential in the event of a tail scenario with challenges such as cost. In addition, one can often use scenario analysis to identify downside risk with which one is comfortable.

Step Six. Identify trade-specific risks. While we identified four generic challenges that can influence the typical hedge, there can be a number of trade-specific risks that are important to consider as well. For example, some hedges may have significant counterparty risk, liquidity can be far more of a factor for some hedges than others, etc.

THE NEED TO HEDGE

In theory, tail risk should happen infrequently—the once-in-a-lifetime storm, so to speak—but reality may be a bit different than theory. In Exhibit 68–4 we present a sample of some catalysts for major downturns from 1990 to 2010. The exhibit shows that we have seen catalysts for major downward moves fairly frequently—essentially every three years or so.

EXHIBIT 68–4
Sample of Some Catalysts for Major Downturns, 1990–2010

images

While there is no single reason that can account for what seems to be relatively frequent tail events, three ingredients do seem to be well represented among most observations—excess leverage (be it financial, operational, or the like) combined with unstable access to funding and potentially noneconomic investment objectives/constraints. Events ranging from the Russian default to the U.S. real estate bubble shared some of these characteristics.

With regard to noneconomic objectives and constraints, for a variety of reasons the actions of some market participants are at times influenced by somewhat arbitrary factors that are not necessarily related to investment efficiency. For example, the performance of many market participants is measured on a quarterly or annual basis, and as a result they may have limited capacity to “sit on cash.” Cash inflows into the bond markets were robust in 2010, and even while many portfolio managers did not see particularly attractive value, they did not have the option of holding high cash balances. In essence, some investors had to buy. But in our experience, valuations supported by “reluctant participants” can be susceptible should volatility or uncertainty edge higher. These investors can look to re-deploy capital to their respective comfort zones quickly.

The factor detailed above goes hand in hand with the market’s tendency to be lulled by incremental movements, in our view. That is, if one has to put money to work, is investing in a leverage buyout with 4.5 turns of leverage really all that different from one with 4 turns? Are 5 turns really all that different from 4.5 turns? The problem is that over time the investment community can find itself a long, long way from shore, so to speak. Is 8.5 turns really all that different from 8 turns? No, but it is very different from 4 turns. Lastly, the financing of assets is not necessarily done on a matched-maturity basis. If funding becomes more difficult, forced selling can very well ensue and snowball out of control. Mismatched funding can take many paths to influence valuations (hedge fund withdrawals and heightened collateral requirements are two examples).

These characteristics were well exhibited in the housing market crisis that began in 2007. With regard to leverage, Exhibit 68–5 shows that the amount of lower-quality mortgage supply that was originated from 2001 to 2007 grew gradually, but that over time growth became extreme relative to the original starting point. In 2001 and 2002, the supply of Alternative-A loans (Alt-A)—viewed in terms of quality as one notch above subprime—was averaging about $2.0 billion per month. This number continually edged higher in the following years—on average $4.4 billion in 2003 and $6.1 billion in 2004. This was still manageable, but before long the average monthly supply was $15+ billion.

EXHIBIT 68–5
Monthly Alt-A Mortgage Supply, 2001–1007

images

Leverage can come in many forms. The robust amount of low-quality mortgage bonds issued was not the only source of housing market leverage in the 2000s. If we define leverage as more exposure to a change in “underlying” valuations (home prices, in this example), then the structured product market boosted leverage in the system severely as well.

Consider common structures back then as shown in Exhibit 68–6. Essentially, a pool of lower-quality mortgage loans was used to create an asset-backed security (ABS), and the mezzanine bond was used to create another, more levered bond, an ABS collateralized debt obligation (ABS CDO). And then a slice of mezzanine debt from the ABS CDO was used to create another security, a CDO with CDO collateral, popularly referred to as a CDO-squared or CDO2, of which the net effect was an even smaller equity base supporting an even larger debt amount.

EXHIBIT 68–6
Evolution of Leveraged Mortgage-Related Structures

images

So where did we end up? To put the resulting leverage into perspective, in some cases in order to wipe out the entire CDO-squared—all the way through the triple-A tranche—the default rate would only have to hit a 13.4% pace (assuming a 50% recovery and significant overcollateralization). Note that the percentage of seriously delinquent1 subprime loans as of the third quarter of 2010 according to Bloomberg was 27.7%, more than double the amount needed to impact the triple-A tranches. And at the same time, the number of “reluctant market participants” may have been rising as well—by many metrics valuations were quite full—which may have left prices in the mortgage market particularly susceptible to any rise in volatility or uncertainty. Exhibit 68–7 shows total assets in money market funds relative to the total return performance of a broad portfolio of mortgage bonds. When volatility edged higher, investors increasingly looked to “park” in cash, and valuations of mortgage bonds had little support and declined soon after.

EXHIBIT 68–7
Total Assets in Money Market Funds versus the CBOE Volatility Index (VIX) and a Portfolio of Mortgage Bonds

images

The key takeaway here is that there has been an increased focus on tail events, in part because they appear to arise more frequently than expected. We believe that to a large extent this is a function of the following three factors:

1. Market participants’ actions may be influenced by factors not necessarily related to investment efficiency, and can “force” investors to take actions unwillingly. Valuations supported by such “reluctant participants” can be susceptible to any increase in volatility or uncertainty.

2. Investors have a tendency to move incrementally, and over time the risk profile of a particular asset class or market segment can increase dramatically and without being noticed.

3. Financing can often be mismatched relative to the assets being supported.

As such, we believe that it is important for investors to always be mindful of the potential for an unexpected drop in valuations as well as ways to protect against possible declines.

OVERVIEW OF SELECT TAIL RISKS

History suggests there may be an innumerable number of tail risk possibilities. Tulip mania? South Sea? Silver? Internet? Housing? It is very difficult to identify bubbles, much less predict when one may burst. However, this does not mean that potential bubbles cannot be effectively hedged, in our opinion.

The goal of this chapter is to provide a framework for hedging tail risk, and in this regard we model three specific risks to be hedged:

1. A severe stock market downturn

2. A sovereign credit event

3. An economic downturn

Below we provide an overview of these tail events.

Stock Market Downturn

Many investors, whether they are equity market investors or not, are cognizant of the performance of the stock market. Because of the depth and breadth of the investor base in this space and the relative liquidity of the stock market, many believe that the equities are an important barometer of risk appetites across all markets. If valuations in the broader stock market encounter pressure, then valuations may well be pressured in other markets as well.

Meaningful declines in the stock market (as gauged by the S&P 500) are not all that infrequent. Over the 25 years from 1985 to 2010 and based on monthly data, for example, the S&P 500 has experienced two-standard deviation declines 12 times and three-standard deviation declines three times (Exhibit 68–8). Note that we define an equity market downturn as a risk for fixed income investors in part due to the high correlation between stocks and select segments of the fixed income market, as shown, for example, in Exhibit 68–9. In addition, bond investors, and for that matter investors in general, tend to view both opportunities and risks in a cross market context far more today than in years past.

EXHIBIT 68–8
Standard Deviation Movements in the S&P 500, 1985–2010

images

EXHIBIT 68–9
Standard Deviation Movements in the High-Yield Debt Market, 1997–2010

images

The key point here is that hedging potential equity market tail events can be important for investors in virtually all asset classes.

In addition, the equity market tends to be correlated with (or even lead) various economic metrics. For example, in Exhibit 68–10 we overlay historical S&P 500 index levels with corporate profits and we see two very similar trends. As such, one could expect a decline in the equity valuations at times of or in periods leading up to economic downturns, and a softer economic backdrop could very well have implications for other markets.

EXHIBIT 68–10
Spread Levels in the High-Yield Market and the Spillover Impact the S&P 500

images

Sovereign Credit Risk

Public sector fiscal imbalances within many developed countries have increased since the financial crisis in 2008. Some worry that the problem could once again become a market focal point and weigh on valuations.

To illustrate the magnitude of the problem, Exhibit 68–11 shows how drastically the gross debt outstanding for the U.S. and Portugal have risen since 2007. It is worth noting that many public sector entities fit a similar profile. Moreover, history suggests that any public sector credit event could have a meaningful spillover effect on valuations elsewhere. For example, when sovereign fears spiked in the spring of 2010, spread levels for many European financials jumped as investors became worried that their sovereign exposure would require meaningful asset writedowns. Even more distant markets, such as the U.S. high-yield market and the S&P 500, were pressured considerably, as can be seen in Exhibit 68–12.

EXHIBIT 68–11
Portugal and the U.S. Gross Debt Levels

images

EXHIBIT 68–12
Percent Change in Levels of iTraxx SovX WE, iTraxx Subordinated Financials, and S&P 500, April–July 2010

images

Economic Downturn

Most asset classes are, at least to some extent, influenced by the broad economic backdrop. For example, one key metric of the economic environment is consumer confidence, and Exhibit 68–13 shows that there is a fairly high correlation between this economic metric and equity market performance.

EXHIBIT 68–13
S&P 500 versus Consumer Confidence, January 1993 to January 2011

images

But there are many different components of the overall economic background and as a result, hedging an unexpected “downturn” can be challenging. For example, Exhibit 68–14 shows retail sales (ex auto) and corporate profits—two very important components of the broader economy with the potential to significantly influence corporate valuations—have done very different things in 2009 and 2010. Specifically, during the March 2009 to September 2010 period retail sales growth remained essentially flat, while corporate profits growth was up 44%. Is the economic backdrop good or bad?

EXHIBIT 68–14
Changes in Corporate Profits and Retail Sales (ex Auto), Q1 2009 to Q3 2010

images

The key takeaway is that hedging economic tail risk can be important, but can also be very challenging for a variety of reasons. These include the number of different economic metrics as well as the sensitivity of various asset valuations to these economic subcomponents.

GENERIC CHALLENGES FACING HEDGERS

As noted earlier, there is no perfect hedge. Before attempting to craft an “efficient” hedge for the three tail risks identified in the previous section, we must first discuss the following four challenges that one often faces.

1. The correlation between the portfolio being protected and the hedge vehicle

2. The cost of hedging

3. The potential for slippage

4. The reliance on historical relationships because these relationships can be transitory over time

Correlation

The first challenge that we focus on is correlation, or the chance that the portfolio being hedged and the hedging vehicle itself do not move in the same direction and/or by the same magnitude as expected. Said differently, imagine purchasing an insurance policy to protect against some event, but the payment received when (and if) the event actually occurred was meaningfully different than the actual loss incurred.

To better put this risk into perspective, we consider how specific hedging vehicles have performed historically relative to equity market selloffs (we acknowledge the narrow definition of risk). Exhibit 68–16 examines price changes for the S&P 500 and the Russell 2000 stock indexes from 1980 to 2010 relative to a variety of hedging tools, such as the 10-year Treasury and spot gold. Again, the expectation is that a stock market downturn could have a meaningful spillover impact on certain segments of the fixed income markets.

The observations in Exhibit 68–15 represent periods in which either the S&P 500 or Russell 2000 valuations (or both) declined by 20% or more. Movements of the various hedging tools presented in this exhibit are considered to be at least partially successful if their values changed by 10% or more (and move in the right direction).

EXHIBIT 68–15
Performance of Various Hedging Vehicles, 1980–2010

images

This study provides three noteworthy points, in our view:

• Of the 13 times that the stock market declined 20% or more from 1980 to 2010, we see that there are many instances in which various hedging tools did not even move in the “right” direction. For example, while gold can be a beneficiary of a “flight-to-quality” bid during times of turmoil, it nonetheless would not have been an efficient hedge against a decline in equity prices. Spot gold experienced only three observations of “material” movement in the correct direction. And the changes in the value of the dollar was essentially a coin flip during times of significant negative changes in equity valuations—up 46% of the time, down 54%.

• Even if the direction of movements between a portfolio being hedged and the hedge itself is highly connected, differences in the magnitude of movements can limit effectiveness as well. For example, Treasuries tend to benefit from a flight-to-quality during periods of severe stress; Exhibit 68–15 shows that the 10-year Treasury moved in the “right” direction 77% of the time. That said, the rise in price of the 10-year seemed fairly modest in comparison to the fall in stock market valuations (e.g., on average the 10-year Treasury price rose 4% versus a decline in the S&P 500 of 21%). One may have to buy an awful lot of Treasuries to hedge, which can present new problems.

• Solely in the context of correlation, we find the VIX and the CDX.IG indexes to be efficient. In terms of consistency, both vehicles moved in the “right” direction each time the S&P 500 and/or the Russell indexes experienced declines of 20% or more, and in terms of magnitude, on average the VIX and the CDX.IG hedges were “in-the-money” by 113% and 84%, respectively.

What Makes the VIX and CDX.IG Indexes Special?

The VIX and the CDX.IG indexes may have many special features, but two that really stand out are the tendency of these vehicles to gap, and for such gaps to be in the “right” direction (i.e., asymmetric payoff profile). With regard to the tendency to gap, we examined how many times the value of the S&P 500 (for reference), VIX, and CDX.IG indexes rose or fell by more than 25% of their respective one-year rolling averages, as shown in Exhibits 68–16 through 68–18. By this metric, we see that extreme observations for the S&P 500 are fairly infrequent (4%), particularly when compared to the VIX (28%) or CDX.IG (43%). Note that we have a longer time series for the S&P 500 and the VIX than for CDX.IG.

EXHIBIT 68–16
S&P 500 Observations That Are More Than 25% from One-Year Rolling Average from January 1997 to February 2010

images

EXHIBIT 68–17
VIX Observations That Are More Than 25% from One-Year Rolling Average from January 1997 to February 2010

images

With regard to asymmetry, we looked at the percent changes for the VIX index and CDX.IG spread over two-week holding periods. We focused on only those observations that moved by 15% or more (see Exhibit 68–19). For the VIX index we find that the number of times since 1997 that the level increased by 15% or more in a two-week period significantly outnumbers the number of times the level declined by 15% or more (459 versus 337, respectively). We find a similar trend for CDX.IG (71 times for spread tightening by 15% or more versus 156 times spread widening by 15% or more) using data going back to late 2004.

EXHIBIT 68–18
CDX.IG Observations That Are More Than 25% from One-Year Rolling Average from January 1997 to February 2010

images

EXHIBIT 68–19
Number of “Large” Positive and Negative Changes in VIX and CDX.IG

images

The key point is that a tendency to exhibit large and asymmetric movements is an important characteristic of any hedging vehicle.

Cost of Hedging

The second key challenge that hedgers may face is cost; that is, it may not matter how closely a hedge vehicle tracks the portfolio that one is protecting or by how much the hedge could move should a tail event occur if the cost is too expensive. Purely in the context of correlation short-tenor, at-the-money S&P 500 puts may be a compelling way to protect against declines in the S&P 500, but when cost is taken into consideration this hedging vehicle can be far less efficient.

To get a better sense of the relative cost of various hedging tools, we consider seven typical vehicles, such as S&P 500 puts and call options on the VIX index, in the context of equity market tail risk. In Exhibit 68–20 we present the cost2 of each of these tools and we see that the range is very, very dramatic. For example, the cost of options can be fairly high (e.g., S&P 500 put), while the cost of others tends to be more modest (e.g., CDX.IG). Some hedges actually pay investors to hedge (e.g., Treasuries). Note that in terms of hedge ratio, we risk-weight each of the tools in Exhibit 68–20.

EXHIBIT 68–20
Cost of Various Hedging Tools

images

Slippage

The relationship between the S&P 500 and various hedging vehicles may very well exhibit a high correlation most of the time, and the cost may be fairly low as well. But does this mean that it is an efficient hedge? Not necessarily.

Another key factor to consider is the potential for infrequent but meaningful “slippage.” To illustrate, suppose that an investor used the high-yield index to protect against a sharp decline in equities. One reason for this decision was the relative cheapness of the hedge. Suppose an investor implemented this hedge on January 2, 2009. Over the following year the S&P 500 rallied about 20%, so ideally the high-yield market would have rallied by the same amount or less. However, it did not. A “unique” event occurred and the high-yield market benefited from a return of liquidity to the marketplace and many issuers were able to refinance their upcoming maturities. As a result, the probability of default for the typical high-yield company tumbled drastically (see Exhibit 68–21) and the total return of the high-yield space was 56% in 2009. As such, our investor’s portfolio gains would have been wiped out and she would have actually incurred a loss of 36% (S&P +20% − HY +56% = −36%, assuming a notional hedge ratio; see Exhibit 68–22).

EXHIBIT 68–21
U.S. Speculative Grade Default Rates, 1971–2010

images

EXHIBIT 68–22
S&P 500 Price Return versus Short Position in High-Yield Index in 2009

images

Cost, Correlation, and Slippage in the Real World

In 2007 volatility across the marketplace was edging higher, signs of an economic slowdown were emerging, and investors were more and more worried about a potential housing market bubble, among other concerns. By early 2008 many were increasingly worried about the exposure of select banks and brokers to these and other problems. To protect against these risks some investors looked to buy protection in the CDS market on banks and brokers that they viewed as particularly vulnerable (e.g., Bear Stearns). Suppose that an equity investor purchased five-year protection on Bear Stearns in early 2008.

Turns out, there were (at least) two problems with this hedge. First, Bear Stearns protection was fairly expensive—five-year CDS was trading at about 315 bp in the first trading session of March 2008, relative to approximately 165 bp for the typical name in the high-grade market. As such, if challenges in the banking system did not magnify purchasing this “insurance” could have weighed on performance somewhat.

The second and more significant problem was slippage relative to the S&P 500. Irrespective of the historical correlation between Bear CDS and the S&P 500, a unique event rendered correlation somewhat meaningless. Again, suppose that an investor purchased Bear Stearns CDS at 315 bp in early March. On March 24, the Federal Reserve deemed Bear Stearns “too big to fail” and took the unusual approach of encouraging JPMorgan to absorb Bear Stearns. A slight exaggeration, but in effect Exhibit 68–23 shows that Bear’s default risk instantly became JPMorgan default risk (far lower!), and Bear CDS rallied to 186 bp by end of the day. In effect, the hedge would have ended up costing our investor far more than the amount her S&P 500 position had rallied.

EXHIBIT 68–23
Bear Stearns versus JP Morgan Five-Year CDS Spreads

images

Reliance on History

Past performance is not an indicator of future returns, the old saying goes. But history is often used to determine how a potential hedge vehicle is likely to perform relative to a particular portfolio. Unfortunately historical relationships can be transient. To illustrate, in Exhibits 68–24 and 68–25 we present the relationship between the 10-year Treasury and the S&P 500 during two different periods, 1970 to 1979 and 2001 to 2010. Exhibit 68–24 plots these two assets during the 1970s, and we see that the correlation was −19%; based on this data one would certainly not expect the 10-year Treasury to be an effective stock market hedging vehicle. However, the relationship has not been stable over time, and Exhibit 68–25 shows the correlation between these two markets has increased sharply in the 2001–2010 period. Trend reversals occur and can be very dangerous.

EXHIBIT 68–24
Correlation of the S&P 500 and 10-Year Treasury, 1970–1979

images

EXHIBIT 68–25
Correlation of the S&P 500 and 10-Year Treasury, 2001–2010

images

UNFUNDED HEDGES (INSURANCE)

A bond investor utilizing an unfunded hedging strategy is essentially looking to purchase an insurance policy. In this section we consider the effectiveness of various unfunded hedging vehicles in the context of the four challenges introduced in the previous section. We define tail risk as a sharp decline in the S&P 500; as noted earlier, over the 25 years from 1985 to 2010 the S&P 500 has experienced two-standard deviation declines 12 times and three-standard deviation declines three times.

In essence, given that stock and credit market performance can be fairly highly correlated, this bond investor is worried about protecting his portfolio from the spillover impact of an equity market selloff. To illustrate, Exhibit 68–26 shows that that from 1997 to 2010 the high-yield market, for example, has experienced eight declines of two standard deviations or more (compared to eight declines in the S&P 500 during the same period as shown in Exhibit 68–27). During the periods that the S&P 500 had declined by two or more standard deviations, the spread in the high-yield market widened by about 19% on average and there were three overlapping periods between the sharp downturns in the equity space and the high-yield market.

EXHIBIT 68–26
Standard Deviation Movements in the High-Yield Debt Market, 1997–2010

images

EXHIBIT 68–27
Standard Deviation Movements in the S&P 500, 1997–2010

images

Assessing the Effectiveness of Various Hedging Vehicles

The seven common hedging vehicles that we evaluate are Treasury, Treasury future, HY index, CDX.IG, CDX.HY, SPX put, and VIX call hedges. We find that there is no “perfect” hedge, and a tradeoff is required based on a particular investor’s preferences, objectives, and constraints. Note that we consider a fairly wide variety of hedging tools in the section, ranging from cash market instruments to derivatives in both the debt and equity markets, because in practice investors have increasingly looked to have as many “tools in the tool box” when identifying potential hedges for debt market downturns.

Before beginning, there are four calculation details to note. First, the performance of each hedging vehicle is based on a base case expectation. In particular, we assume that the most likely market environment is that the S&P 500 is range-bound (70% chance that returns are stuck in the −2% to +2% range), but with a meaningful chance (30%) that the S&P 500 falls by up to 15%. Hedge performance is based on these probabilities and magnitudes, and as we will show later alternative scenarios can change results meaningfully.

Second, in terms of the weighting of each hedge vehicle, notional sizes are determined in a risk equivalent context. That is, in dollar terms we calculate the P&L range for a $10 million investment in the Treasury market in each scenario that we evaluate. We then back out notional weightings for the other hedge vehicles to generate the same risk profile (P&L range).

Third, the expected P&L for each hedge is based on their betas relative to the S&P 500 since 2005 (daily observations). We calculate four separate betas for each hedging tool—fairly modest bullish moves in the SPX (gains of less than 7.5%), more extreme bullish moves (SPX gains of 7.5% or more), and we use the same approach to determine betas in bear markets (SPX declines of up to 7.5% and more than 7.5%). Finally, the horizon is 30 days.

We discuss four findings in particular:

1. Dramatic differences in payoff profiles

2. Variation of success

3. Possibility of our base case being wrong

4. Slippage

Payoff Profiles Can Vary Dramatically

In Exhibit 68–28 we present the P&L for the seven hedges. We find that in absolute dollar terms the effectiveness of the various hedges varies dramatically—the range of P&Ls was $40,000 as of January 2011.

EXHIBIT 68–28
P&L for Various Hedge Vehicles in Our Base Case Scenario (70% Chance of Being Range-Bound, 30% Chance of S&P 500 Falling by Up to 15%)

images

By this measure of effectiveness the Treasury market hedge (long cash or futures) was the best performer, as it earned money in a status quo scenario (coupon clip), but also benefited from a flight-to-quality in more bearish scenarios. Interestingly, the S&P put comes in the sixth place, in part because it is fairly expensive. The cash high-yield cash market came in the last place, in part because it is a fairly expensive hedge and can be driven by factors that can have less of an impact on equities (e.g., defaults).

There Are Many Variation of Success

But this does not mean that Treasuries are the best hedge per se. That is, a P&L of $42,000 may go a long way to offsetting any loss we may incur due to falling equity prices, but remember that the notional exposure required to generate this return is $10 million! In comparison, the put position only requires a notional exposure of $43,000. In the context of return on notional exposure, the put position would outperform dramatically, 33.8% versus 0.4% (Exhibit 68–29).

EXHIBIT 68–29
Return on Notional Exposure

images

Some investors may not have any constraints in terms of how much notional exposure they can have to a particular position, or how much balance sheet that they can tie up with any particular trade, etc., but many do face some of these constraints and the best hedge for these market participants may be something less “capital-intensive.”3

Possibility of an Incorrect Base Case

Another important consideration is performance should our base case scenario be incorrect. Recall that our base case was that a range-bound market was most likely (70%), but that there was a 30% chance that the S&P declines by up to 15%. How would performance look if the chance of improved valuations was much higher and stocks rallied instead of falling sharply?

In Exhibit 68–30 we present P&L for our various hedges in an environment in which stocks rally by 5%. Perhaps the most important point here is that the susceptibility to an incorrect market call is limited for some vehicles, but not for others. For example, the most that the S&P put can lose is the option premium ($43,000; note that this is different from the option cost shown in the exhibit which reflects the cost for only the one-month holding period). Conversely, the high-yield hedge (cash) loses $64,000, in part due to the coupon paid ($22,000) but also due to a mark-to-market loss of $42,000. Treasury hedges do well in this scenario, primarily because there is no upfront cost for the hedge—a coupon is earned with this hedge, not paid.

EXHIBIT 68–30
P&L for Various Hedge Vehicles in a Moderately Bullish Scenario (S&P 500 up 5%)

images

What about Slippage?

In the context of some risks the Treasury hedge appears to be particularly effective, but the tool can be especially vulnerable to others, such as slippage. That is, the historic relationship between stocks and Treasuries might be fairly strong, but the Treasury market can be far more sensitive to factors such as monetary policy and inflation expectations than the equity market. As a result slippage can be dramatic at some points in time.

To illustrate, suppose that an investor bought a 30-year Treasury position to protect against a potential stock market setback on January 15, 2009. Over the next several months, equities performed well, but Treasuries sold off far more than their beta (versus the S&P 500) would suggest primarily because the bond market began anticipating and pricing in more inflation. As a result, the hedge would have lost 25% over the next few months, which is significantly more than the stock market gain of 9.6% (Exhibit 68–31).

EXHIBIT 68–31
S&P 500 versus 30-Year Treasury Price

images

The key takeaway is that unfortunately, there does not seem to be a perfect hedging vehicle to minimize exposure to tail risk. Four key challenges tend to impact the effectiveness of most hedges—cost, correlation, slippage, and reliance on historical relationship. In effect, investors must weigh these challenges (and others) with their own market expectations, objectives, and constraints.

That said, we examined a variety of hedging vehicles in several different scenarios, and found that in the context of these challenges the CDX.IG and the VIX indexes can be particularly effective. Vehicles such as Treasuries can do well in most scenarios, but do have significant slippage risk, and the performance of some options (e.g., short-tenor, at-the-money S&P puts) can be constrained by cost.

FUNDED HEDGES (ALPHA TRADES)

In the previous section we examined unfunded hedges, which in some respects are comparable to the outright purchase of an insurance policy. The cost of the policy is obviously a concern, but not necessarily an investor’s primary concern. In this section we introduce funded hedges, or package trades in which some long exposure is used to pay for the cost of insurance. As a result the net hedge cost declines, but there is a tradeoff as other challenges can become more intense and new ones introduced. For example, counterparty risk can be an important consideration when employing a funded hedge strategy.

The reason why many market participants use funded hedges tends to result from two factors. First is the impossibility of being able to accurately predict the timing of a tail event. In practice, at best one may be able to do is anticipate a higher (lower) probability of an event occurring over a given time frame. Second, the performance of many investors is measured against a benchmark index or relative to the performance of competitors over a fairly short time. As such, if a tail event does not occur fairly quickly, the relative performance of an investor using an unfunded strategy will likely be negative, at least by some metrics.

Suppose that back in early 1995 an equity investor that was benchmarked against the S&P 500 on an annual basis was worried about “irrational exuberance.” She shorted the segment of the stock market that she believed was most irrational—the NASDAQ. Unfortunately for this investor, while the equity market may very well have been irrational, such irrationality lasted for five more years. By early 2000 the NASDAQ had rallied 500% from early 1995 levels, and this investor would have lagged her benchmark by over 300%, as seen in Exhibit 68–32.

EXHIBIT 68–32
Nasdaq vs. S&P 500, 1995–2000

images

In this section, we evaluate funded hedges in the context of two specific risks (sovereign risk, economic downturn), but before proceeding there are three important points to make:

1. Focus, focus, focus: As a rule of thumb, unfunded hedges tend to protect portfolios against a wider variety of events than funded hedges, and this is primarily because funded hedge packages have both long and short elements (as opposed to an unfunded hedge with just short exposure). Essentially, the goal of a funded package is to short an asset that is particularly sensitive to a specific problem, and go long an asset that is fairly immune.

2. Use scenarios more than history: In the previous section our analysis of hedge efficiency was to a large extent based on history—if the S&P 500 moves by X amount, then hedge XYZ can be expected to move by Y amount. But funded hedges rely more heavily on scenario analysis than historical relationships. In essence, the goal is to construct a package that provides an asymmetric payoff profile across a wide variety of potential scenarios with a tolerable amount of downside risk. In this regard, more qualitative analysis may be needed.

3. Additional risk factors introduced: Funded packages also have more “moving parts” than unfunded packages and as a result additional risks can come into play. For example, counterparty, mark-to-market, and liquidity risks, to name a few, can all be found in abundance in funded hedges.

Again, in this section we provide two examples of funded hedges. We first focus on a sovereign risk hedge, and then a hedging vehicle to protect against an economic downturn. We find that while funded hedges have more “moving parts” and potential risks than unfunded hedges do, these risks can often be managed and results very effective.

Sovereign Fiscal Imbalances

While for many decades the focus of fiscal solvency has been in the emerging markets, sovereign default has become a risk factor in many developed economies as well. Public debt levels have spiked since 2007 (Exhibit 68–33) and some do not believe that all governments have the political wherewithal to solve the challenge.

EXHIBIT 68–33
Portugal and the U.S. Gross Debt Levels, 1996–2010

images

One lower cost strategy to protect against a potential sovereign credit event is to go long names with little direct risk to public sector fiscal imbalances and fairly limited near-term risk in general. The income from this portfolio could be used to pay for short exposure to issuers with significant direct exposure to the sovereign problem and/or other near-term challenges.

Consider the package presented in Exhibit 68–34. The names of the companies and countries in the long and short positions of the package cannot be disclosed, but the levels presented in the exhibit reflect the real life values as of September 2010. The short side of this package is composed of names that had at least some of the following characteristics as of late 2010:

EXHIBIT 68–34
Example of a First to Default Hedge for Sovereign Risk

images

1. A direct link to the weak credit profile of the public sector

2. Meaningful maturities coming due in the near term (total of $295 billion through 2012). Refinancing could be a significant challenge should sovereign fears rise further and market participants begin to worry about a spillover into the banking system.

3. More cyclical names that (as of September 2010) could be particularly vulnerable to an economic slowdown caused by sovereign concerns.

The cost of this portfolio at a time when sovereign fears were particularly intense (mid-September 2010) was 1170 bp, based on one-year CDS (as of September 14, 2010). To overcome this fairly prohibitive cost one could use a one-year first-to-default structure (FTD); FTD packages pay those with short exposure in the event that any one of the names in the structure defaults, but only one. There is no additional payment should two, three, or more names experience a credit event.

The benefit of using this structure is that it costs relatively little to establish a short position. As of mid-September 2010 the cost was approximately 70% of the portfolio’s sum-of-spreads (1,170 bp). So an investor only would have to pay 819 bp to short exposure to the basket of vulnerable names (1,170 bp × 70% = 819 bp).

This short position can be funded with long exposure to select names that appear to have little near-term default risk. Part of the reason is simply because the names in the long position in Exhibit 68–34 have little or no debt coming due in the period 2010–2012. Three of the five names have no upcoming maturities through 2012, and in aggregate only about $240 million will mature during this period.

In addition, the average implied default rate is far lower for the long positions than for the short positions (0.7% versus 3.0% average implied default rates, assuming 40% recovery for corporates and 70% recovery for sovereign names as of September 14, 2010). The market did not perceive all that much near-term risk for the long candidates (again, as of September 2010).

The key point is that short exposures appear to be more vulnerable to spread-widening catalysts, and the position is positive carry (151 bp, as of September 2010).

Potential Risks

This trade package can benefit in the event of a sovereign credit event, but it does have risks that should be considered. For example, an FTD is an over-the-counter derivative product and is subject to non-standard prices that a bank or other dealer may provide upon unwinding, and as such the package is vulnerable to illiquidity. This risk is tempered, however, because of the fairly short tenor of the package—worst case, an investor can hold to maturity (one-year).

The aggregate delta mismatch is also a risk, but there are several factors that help to offset it. Specifically, the short tenor of the package limits the impact in absolute dollar terms, and the range-bound spread environment that the market was in can help to limit the severity of mismatch as well. Exhibit 68–35 shows that the high-grade market had been trading in a very tight range from mid to late 2010. If spreads do not move, delta mismatches do not matter.

EXHIBIT 68–35
CDX.IG S14 One-Year Index Spread Level

images

And the notional mismatch—$50 million versus $10 million—is also a potential challenge. But let’s take a step back from the FTD package itself and consider the riskiness of the underlying constituents. From a credit perspective, which is more risky—a $100 million Treasury position or $10 million exposure to First Data (rated B3/B/B) paper? Large exposure to a low probability event or small exposure to a higher probability event? In a risk-adjusted context, one could argue that the Treasury position is less risky.

Marking-to-Market: The FTD Hedge

While there are more moving parts with these relatively complicated packages, they can be very efficient hedging vehicles. For example, we marked-to-market the FTD trade package three months after it was initiated (i.e., December 15, 2010). Exhibit 68–36 shows that this package was deeply in-the-money, the long portion of the portfolio being 429 bp tighter and the short portion being 109 wider. In dollar terms this translates into a gain of $2.3 million, which could go a long way to offsetting any sovereign-induced decline in a portfolio.

EXHIBIT 68–36
FTD Hedge Marked-to-Market

images

Economic Downturn

One of the biggest risks that portfolio managers in virtually all asset classes face is exposure to severe economic downturn. That said, we believe that “cheap” and effective economic downturn hedges can be found. In this section we present an example of a positive carry package with an asymmetric payoff profile that existed in the credit space when heading into the 2007 recession. The favorable payoff profile resulted in large part from a unique combination of sector specific characteristics and the shape of select CDS curves.

With regard to sector characteristics, in the credit market all sectors tend to suffer heading into and during the early portion of recessions, but the extent of suffering can vary sharply. To illustrate, Exhibit 68–37 highlights the total returns of cyclical and noncyclical sectors in the high-yield market in 2008. On average the cyclical sectors generated a total return of –32% in 2008, while the non-cyclicals were far more resilient (−16%). So from this perspective shorting select cyclical sectors may have been the most effective trade.

EXHIBIT 68–37
Total Returns of Cyclical and Non-Cyclical Sectors in the High-Yield Market, 2008

images

But which one should be shorted? For unique reasons at any given point in time some sectors may be even more vulnerable than others heading into an economic downturn. As noted above, there were numerous challenges in the economic backdrop back in early 2007, but many of the challenges centered around a potential bubble in the housing market. So ideally, back in 2008 shorting cyclical companies with exposure to the housing market, such as the home-building space, might have been a good hedge.

But what about the cost? Turns out, the cost of shorting the typical home-builder heading into the last recession was not prohibitive either. Despite appearing to be more vulnerable to a slowdown, on average spreads in the homebuilder space were about the same as those in most other sectors. Exhibit 68–38 shows that the typical homebuilder (292 bp) was essentially trading at the same level as the typical cyclical (298 bp) and the typical non-cyclical (273 bp).

EXHIBIT 68–38
Spreads of Cyclical and Non-Cyclical Sectors in the High-Yield Market, 2007

images

The key point is that homebuilders appeared to be particularly vulnerable to an economic downturn yet spread levels were very much in-line with the typical names in the market. Affordability is a good starting point for an effective hedge.

But the challenge is to craft a trade package that does not cost much, if anything, and has an asymmetric payoff profile. In this regard we can take advantage of the fact that many homebuilders had very steep credit curves prior to the 2008 recession. For example, KB Homes, a benchmark issuer in the homebuilding space, had a three-year/five-year spread slope of 111 bp heading into the 2008 recession (Exhibit 68–39), relative to about 100 bp for the typical high-yield name.

EXHIBIT 68–39
KBH CDS Curve on March 15, 2007

images

The steep curve enabled a potential investor to duration-weight a curve flattener and still earn positive carry. In effect, one could buy (go short) $15 million of three-year KBH protection and sell (go long) $10 million protection in the five-year tenor, and be duration-neutral and still earn 49 bp in carry (Exhibit 68–40). The curve flattener, when combined with the potential susceptibility of this name to an economic downturn and its fairly tight spread levels, resulted in a package with an asymmetric payoff profile.

EXHIBIT 68–40
KBH 3Y/5Y Curve Flattener

images

Consider the following four scenarios:

1. Status quo: Again, the steep slope of the KBH credit curve enabled a potential hedger to implement a duration-weighted 3s/5s curve flattener (hedge ratio of about 1.5×) and still earn 49 bp (Exhibit 68–40). And such, results are modestly favorable in a status quo scenario, particularly in a ROE context (as the position requires little collateral).

2. Coin flip: If the economy did not slow down and valuations simply “bounce around” the position should be fairly immune because it is duration matched.

3. Bullish: The package would likely be susceptible if an economic downturn did not occur and spreads tightened, but this risk is mitigated in part by positive carry and already tight spread levels. How much tighter can the front-end get?

4. Bearish: As a rule of thumb, credit curves typically flatten sharply when default risk increases, and default risk rises when the economy slows as shown in Exhibits 68–41 and 68–42. This package is well positioned to benefit, not only due to the disproportionate change in CDS spreads (short-tenor spreads under more pressure than longer-tenor ones), but also because of the disproportionate amount of protection bought and sold ($15 million versus $10 million).

We price the KBH trade package after a one-year holding period (as of March 14, 2008). Exhibit 68–43 shows that the KBH curve inverted sharply—three-year protection widened 407 bp, while five-year protection increased 251 bp—and Exhibit 68–44 shows that this package generated a positive P&L of $0.3 million (ROE of 122%).

EXHIBIT 68–43
KBH CDS Curve on March 14, 2008

images

EXHIBIT 68–44
Return on KBH Curve Flattener

images

The key takeaway is that as a rule of thumb funded hedges have more “moving parts” and potential risks than do unfunded hedges. That said, the risks can often be managed, in our experience. In this section we examined using funded hedges to manage two specific risks—public sector fiscal imbalances and an economic downturn—and found positive carry hedges that in theory offered an asymmetric payoff profile. We then marked-to-market these packages, and found that theory was consistent with reality.

EXHIBIT 68–41
GS 3Y/7Y Curve vs. U.S. Speculative-Grade Default Rate

images

EXHIBIT 68–42
JCP 3Y/7Y Curve vs. GDP

images

Trade-Specific Risks

As discussed, most hedges face, at least to some extent, four generic challenges. In addition, many packages also have trade-specific challenges/risks as well. For example, if an investor purchases protection via the CDX.IG index he/she may be exposed to mark-to-market risk. Investors that mark portfolios to market are subject to potentially large movements in P&L that may cause a position to trigger a stop/loss. As we discussed in an earlier section, in 2007 market volatility was increasing and investors sought to buy protection in the CDS market on banks and brokers that they viewed as particularly vulnerable. But ensuing spread widening was certainly not one directional, and some investors could have been forced out of positions (stop loss) even if they ultimately finished in-the-money.

The sovereign hedge described previously most certainly has liquidity risk (i.e., bid/ask spread could widen sharply if the package holder tried to unwind the position) as well as counterparty risk. With regard to liquidity risk, an investor seeking to capture the P&L of a particular trade that is in-the-money should consider the sizing and appropriate execution costs upon entering and exiting a position in a normal versus a stressed scenario. As a subset of liquidity risk, positions that are purchased on margin are particularly susceptible, as changes in margin or collateral requirements during stressful market periods can be dramatic.

The important point is that there are a large number of trade-specific risks for which one must account. We do not attempt to identify or analyze all potential risks within various hedges, but we do walk through one specific example in this section. In particular, we calculate a potential cost of counterparty risk for the Bear Stearns hedge described earlier.

The Cost of Counterparty Risk

It may be possible to control counterparty risk via regular reviews of trading partners, collateral requirements, etc., but however controlled it can be, it probably cannot be completely eliminated. Earlier we walked through an example in which an investor bought CDS protection on Bear Stearns as a hedge. Using the same example, assume again that the investor bought five-year CDS protection on Bear in early March 2008 at 315 bp, but add the wrinkle that the position was purchased from Lehman. The key question is whether or not Lehman will be around to provide compensation should Bear default. Note that Lehman CDS was trading at 228 bp at the time.

Counterparty risk is to a large extent a function of two factors:

1. The joint probability of default (i.e., Bear and Lehman both experience a default);

2. The size of a loss in the event of a default, which depends on recoveries for both Bear and Lehman; that is, if Bear defaults our investor would be owed a certain amount by Lehman, but if Lehman also defaults this claim probably would not be paid in full.

We rely on the following equation to calculate how much this counterparty risk costs in terms of basis points:

Counterparty risk
= Joint default probability × [100 × (1 – Recovery BSC)
× (1 – Recovery LEH]/Duration BSC

If we assume recovery rates of 40% for both Bear and Lehman, and that five-year CDS spread levels are entirely compensation for credit risk, the implied default rate is 23.1% for Bear Stearns and 17.3% for Lehman. As such, the extra compensation that investors should receive for counterparty risk is about 36 bp as shown below:

Joint default probability = Default probabilityBSC × Defaulty probabilityLEH
= 23.1% × 17.3% = 4.0%
Counterparty cost = 4.0 % × [100 × (1 – 40%) × (1 – 40%)]/ 4.0 = 36 bp

The key point is that the cost of Bear protection was probably higher than the nominal spread of 315 bp. By some metrics the cost of counterparty risk alone is 36 bp, pushing the true cost to 351 bp (315 bp + 36 bp).

KEY POINTS

• Tail events tend to occur more often than one might expect, in large part because (1) the actions of investors can be influenced by factors that are not necessarily related to investment efficiency, (2) market participants tend to move incrementally and over time risk profiles can increase dramatically, and (3) the financing of risk assets and/or operations tends to be transitory and the lack of stable access to financing can cause any modest change in valuations to snowball.

• If and when an investor decides to hedge, it is important to understand exactly what is to be hedged. One type of tail event (e.g., sovereign default) could require a very different type of hedge than another (e.g., BP oil spill).

• There is no perfect hedge. Four challenges that should be considered for most hedge vehicles are (1) correlation (i.e., the likelihood that a hedged asset and the hedging vehicle do not move in the same direction and magnitude), (2) cost, (3) potential slippage that can be induced by the sensitivity of the hedge or the hedged asset to a unique development, and (4) the reliance on history, since the relationship can be transitory over time. In addition, there can be a number of trade-specific risks that are important to consider as well (e.g., counterparty risk, liquidity, etc.). In effect, investors must weigh these challenges with their own market expectations, objectives, and constraints.

• Unfunded hedges are defined as those for which an investor is willing to dedicate a certain amount of capital to protect the portfolio. In some respects, unfunded strategies are comparable to insurance policies. The cost of the policy is obviously a concern, but it is not necessarily an investor’s primary concern.

• An evaluation of seven unfunded hedges in the setting of declining equity prices finds that while there is no perfect hedge for all investors, various VIX and CDX.IG strategies can be efficient in a fairly wide range of scenarios. A tendency to exhibit large and asymmetric movements is an important characteristic of any hedging vehicle.

• Funded hedges are defined as packages in which some long exposure is used to pay for the cost of insurance. As a result, the net hedge cost declines, but there is a tradeoff as other challenges can become more intense and new ones introduced.

• Funded hedges typically become more popular when the timing of any potential negative catalyst is difficult to ascertain and when performance of investors is measured over a fairly short period of time. We find that while funded hedges have more “moving parts” and potential risks than unfunded hedges do, these risks can often be managed and hedge results can be effective.

..................Content has been hidden....................

You can't read the all page of ebook, please click here login for view all page.
Reset
3.238.57.9