the art of hedging - member | soa...following the financial crisis has driven many institu-tional...

Article from Risk Management Newsletter August 2015 Issue 33

The Art of HedgingBy Boris Lerner and Christopher Metli

INVESTOR HEDGING BEHAVIOR HAS EVOLVED OVER THE LAST FIVE YEARS, FROM AN INTENSE FOCUS ON BUYING TAIL RISK PROTECTION AT ANY PRICE TO A MORE NIMBLE APPROACH IN RECENT YEARS. But in one form or another, hedges continue to be bought as institutional investors remain hesitant about the sustainability of the bull market. While VIX is at the low end of its historical range (although certainly not the lowest on record), that does not necessarily mean hedges are cheap. Implied volatility continues to trade above realized volatility, and downside options are more expensive than ATM volatility would suggest.

For many investors, systematically buying puts month after month is not a viable strategy. This has been par-ticularly true over the last several years, when market pullbacks have been shallow and short, and payouts on hedges have been compressed. But despite the chal-

lenges, hedging and risk management remains critical to an efficient portfolio design.

Institutional investors seeking to hedge have no short-age of choices, and need the right framework to manage the different risks in portfolios as they arise. After studying the performance of over 100 different strategies using S&P 500 options, variance swaps, VIX futures, and VIX options during the last 15 years, we think institutional investors should consider a hedging framework such as Exhibit 1 that takes into account:

1. The type of risk being hedged (systemic large tail versus a fundamental moderate correction).

2. Fundamental views of the balance of risks and like-ly scenarios in the market,

3. Current market pricing of protection.

16 | AUGUST 2015 | Risk management

What risk are you hedging?

Systemic tail

Moderate tail risk is priced in

VIX is low, and op=ons are rich rela=ve to

curve shape

VIX futures cheap to fair value

VIX Futures

VIX futures fair or rich

Variance Swaps

Buy VIX Op=ons

Skew flat / Futures low*

VIX Collars

Skew steep / Futures low*

VIX Call Spread Collars

Skew flat / Futures high*

VIX Calls

Skew steep / Futures high*

VIX Call Spreads

Significant tail risk is priced in

Moderate correc=on

Buy SPX Op=ons

Low / falling vola=lity market

Skew flat

SPX Put Spread Collars

Skew steep

SPX Put Spreads

High vola=lity market

Skew steep

Skew flat

SPX Puts

Note: SPX collars may be useful as beta reducers, as well as in sharply falling markets when momentum is to the downside

Source: Morgan Stanley Quantitative and Derivative Strategies

*Either VIX is low and / or VIX futures curve is flat

Exhibit 1: A Framework for Hedging

Risk management | AUGUST 2015 | 17

While much of the time spent designing a hedging pro-gram ends up being spent on selecting the right option expiry, strike, etc., perhaps the most important decision is a more basic one—what risk are you trying to hedge? We find that if your view is for a large and systemic selloff—greater than what is priced by the market—then a volatility-based hedge can potentially make more sense. For smaller and more-fundamentally driven selloffs, directional hedges via equity options may be the more appropriate choice.

The simple backtest of 1-month 30-delta SPX puts and 30-delta VIX calls in Exhibit 2 highlights the differ-ences between the two strategies (this is scaled using a 1 point change in volatility: 1 percent SPX return assumption). Performance is broadly similar, but VIX calls have a larger—and faster—payoff in tail events such as the 2008 Credit Crisis, 2010 Flash Crash and 2011 US downgrade, while SPX puts outperformed in more recent moderate corrections. This is the key behavior of a volatility based hedge—volatility rises disproportionately more with larger moves down in the S&P 500 than it does for small selloffs.

However, this convexity is not free—it is priced into VIX options. In normal markets, VIX call options expire in-the-money less often than S&P 500 options—see Exhibit 3. VIX calls also do not capture some of the more moderate drawdowns as well as S&P 500 hedges—if an event is not one that precipitates forced liquidation and a rush to buy more hedges, volatility hedges will typically underperform equity options. But the profit on VIX calls when they are in-the-money is typically higher than it is for SPX puts (i.e., VIX can double or triple, while the SPX cannot fall by more than 100 percent).

Exhibit 4 shows the rolling average returns of VIX calls and S&P 500 puts, as well as which trade was the most effective hedge for the S&P 500 in a given month (hedge effectiveness = zero cost SPX ATM put less the P/L of the hedge, with a lower number meaning a better hedge)1. In calm mar-kets the costs tend to be similar between the two instruments—2012 happened to favor SPX puts,

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Most Effective Hedge for a Given Month (On Trade Entry)

Exhibit 2: VIX Calls versus SPX Puts, Beta-Neutral (1% Vega)

Note: 1% vega based on a 1 point move in VIX for every 1% change in SPX. Source: Morgan Stanley Quantitative and Derivative Strategies



Exhibit 3: VIX Calls Expire ITM Less Often than SPX Puts

Exhibit 4: VIX Call versus SPX Put Hedge Effectiveness

CONTINUED ON PAGE 18

Art of Hedging | from Page 17


late 2013 VIX calls, but in general the trades are similar. But in selloffs they can diverge—VIX calls outperformed in 2011 and 2010, while the modest declines in 2012 favored SPX puts.

The case studies in Exhibit 5 show in greater detail how large tail and moderate tails could unfold; the first is August 2011, the second is the early 2014 EM-led selloff. In 2011 the VIX calls outperformed as fear persisted in the marketplace. In the early 2014 selloff, however, S&P 500 puts where the better performer—although as markets rallied back both hedges ended up performing similarly.

Key to any effective trading strategy, however, is not just knowing the right product—it is knowing what the market is pricing in. One approach for determining this is to ask the question “What are the options markets saying VIX could do if the SPX sells off?” To tease that information out of market pricing, we use the fact that VIX and SPX typically move very closely together, and make a simplified assumption that changes in the S&P 500 map perfectly to VIX (i.e., ignore the chance that VIX may move in a different direction than the S&P 500). We then take the option implied distribution of future SPX returns and line it up versus the option implied distribution of VIX returns (Exhibit 6).

For example today the market prices that the S&P 500 in one month will be below 95 percent of the current price with a 15 percent probability, while also pricing that the VIX will be more than 129 percent of today’s futures level with a 15 percent probability2. Taken together, we can say the market estimates VIX will move 29 percent—roughly 4 points—for a 5 percent decline in the SPX.

Applying these matches across the full spectrum of possible returns in the S&P 500, we obtain a mar-ket-implied VIX versus SPX relationship (the blue line in Exhibit 7), and compare this to what occurred historically (the red best-fit line). This gets at the key consideration when looking at relative value of VIX versus SPX options: how much does the market expect VIX to rise if the S&P 500 falls?

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VIX 1m 30^ Call SPX 1m 30^ Put SPX, rhs

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VIX 1m 30^ Call SPX 1m 30^ Put SPX, rhs

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1m VIX Changes vs SPX Returns

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Currently implied by options

Exhibit 5: Selloff Performance ($1 Premium Spent on Each Option)

Source: Morgan Stanley Quantitative and Derivative Strategies, Bloomberg



Exhibit 6: Aligning the Distributions

Exhibit 7: Market Pricing of Tail Convexity

Risk management | AUGUST 2015 | 19

Options markets currently imply that VIX futures should rise ~11 points if the S&P 500 is down 10 per-cent over a month, slightly cheap versus the historical average.

We can evaluate the performance of hedges under these VIX vs SPX scenarios—both implied and historical—and compare to fundamental views to determine the best hedge. Exhibit 8 shows the payouts as a percent of S&P 500 notional for a 1-month 30-delta SPX put and a premium-equivalent amount of 1-month 30-delta VIX calls (roughly 0.2x contracts). If the future unfolds as priced by the market today, VIX options are a better hedge for anything greater than a 8 percent decline in the S&P 500 over a month. If the future repeats the historical average, VIX calls would be more efficient if the market drops by more than 6 percent over the next month.

The above scenario focuses on hedges held for a month or longer. But an increased focus on risk management following the financial crisis has driven many institu-tional players, both on the sell side and buy side, to have to protect against overnight or rapid intraday gaps lower—a la 1987 or the Flash Crash. To compare SPX puts to VIX calls in these scenarios we use a combined implied / historical approach—factoring in that in a selloff volatility will roll along the existing skew, and then estimating how the implied volatility surface could shift based on historical relationships (Exhibit 9).

In addition to estimating how the underliers change, we also estimate how implied vol for both instruments might evolve as the market falls, based on historical changes in fixed strike implied volatility relative to S&P 500 returns / VIX futures changes. Compared to SPX, VIX vol-of-vol is much less reactive to changes in the underlying price. In addition, VIX skew tends to flatten (calls get cheaper) as VIX rises. This occurs because VIX is mean reverting, and implied vol and skew reflect this dynamic.

Applying all of these (admittedly rough) estimations produces the scenario analysis in Exhibit 10, demon-strating that for big moves down in the S&P 500, the

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Estimated P/L of 1m 30^ SPX Puts and VIX Calls (VIX Calls Scaled to Same Premium as SPX Puts)

1x SPX Put

0.2x VIX Calls, based on Implied VIX changes vs SPX

0.2x VIX Calls, based on Historical VIX changes vs SPX

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Exhibit 8: VIX 1m Calls Priced to Outperform at -7 to -8% on the SPX



Exhibit 9: Estimated VIX Change for 1-Day SPX Gap

CONTINUED ON PAGE 20

Boris Lerner is an executive

director and a head of the Americas

Quantitative and Derivative Strategies

team at Morgan Stanley in New York,

N.Y. He can be reached at boris.lerner

@morganstanley.com.

convexity of VIX instruments yields the greatest P/L. This assumes $1 of premium is spent on each option.

Given a steep VIX call skew, and the fact that most of the convexity in VIX comes from convexity in the underlying, not convexity in vol-of-vol for small declines in S&P 500 it is generally cheaper to hedge using OTM SPX puts. For one day gaps down larger than -10 percent, low delta VIX calls would be a more efficient hedge.

The table in Exhibit 11 shows the estimated premium that would need to be spent to generate a $1 million profit in given gap risk scenarios. Within each of the VIX and SPX, moving further OTM is always more efficient for these types of moves, and strike selection should only be limited by liquidity.

Investors need to consider the types of risks they are trying to hedge as well as market pricing. When rel-atively moderate, fundamentally driven corrections are the concern, option based hedges are often the best choice to protect against portfolio drawdowns. But when large systemic tail events are the focus—and market expectations of future volatility are not onerous—volatility based hedges can offer more efficient protection.

Disclaimer: https://www.morganstanley.com/disclaimers/instsec.html


ENDNOTES

1 All 1m term, average of 20, 30, and 40-deltas, scaled to 20-delta on open, scaled so the notional of the VIX calls is 1 percent of the SPX (i.e., one percent vega, consistent with a 1 VIX point move: 1 percent move in SPX)

2 Option implied probabilities and related charts in Exhibits 6 and 7 are based on SPX and VIX option prices from June 26, 2015.

Art of Hedging | from Page 19

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P/L

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$1

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rem

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Sp

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1-Day S&P 500 Return

Estimated P/L for $1 Spent

SPX 1m 15^ Put

SPX 1m 10^ Put

SPX 1m 5^ Put

VIX 1m 15^ Call

VIX 1m 10^ Call

VIX 1m 5^ Call


Exhibit 10: VIX Screens Better for Large Gap Risks on Current Pricing

1-Day Return

SPX 1m 15^ Put

SPX 1m 10^ Put

SPX 1m 5^ Put

VIX 1m 15^ Call

VIX 1m 10^ Call

VIX 1m 5^ Call

-5% 154,986 140,741 125,650 216,567 219,119 239,615-10% 52,068 44,080 35,688 50,047 43,478 37,584-15% 29,136 23,735 18,137 21,954 16,851 11,217-20% 19,964 15,927 11,782 13,196 9,538 5,529-25% 15,134 11,925 8,652 9,352 6,570 3,581-30% 12,170 9,513 6,816 7,336 5,077 2,685


Exhibit 11: Current Premium Spent to Hedge $1,000,000: Cheapest for a Given Decline Highlighted

Christopher Metli, CFA, is an

executive director and a senior

derivative strategist at Morgan

Stanley in Boston, Mass. He can

be reached at Christopher.metli@

morganstanley.com.

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