exploring systematic hedging strategies for equity portfolios · as risk reversals, put...

Exploring systematic hedging strategies for equity portfolios

Chief Investment Office GWM Vinay Pande Gerald Lucas Tze, Shao Yang Tang Miguel Costa Jason Draho July 2, 2019

This report has been prepared by UBS Financial Services Inc. (UBS FS) and UBS Switzerland AG and UBS AG. Analyst certification and required disclosures begin on page 21.

Chief Investment Office GWM

Summary

Systematic Hedging of Equity portfolios has generally been viewed as a drag on portfolio performance. That is true in the same sense most kinds of insurance are a drag on performance – until they are not.

Systematic Hedging of equity risk should generally not be viewed as an alternative to holding a well-diversified portfolio.

This introductory paper examines a few simple and widely used approaches to systematic hedging such as short and long dated out-of-the-money (OTM) puts and put spreads as well as VIX futures. We find no single strategy is demonstrably superior at all times, but that the effectiveness of a strategy is a function of the market environment it is deployed in. In addition, the degree of risk aversion of the investor, as well as the riskiness of the portfolio being hedged (e.g. idiosyncratic or undiversified risk) is generally difficult and expensive to hedge.

Generally short dated puts suffer from more rapid time decay than long dated puts and benefit less from spikes in implied volatility. On the other hand, they are more responsive to market moves and less likely to suffer from "strike sensitivity" (discussed below). Put Spreads offer protection on a greater proportion of an equity portfolio for a given dollar outlay, but only down to the lower strike of the put spread. VIX futures are usually extremely responsive in market selloffs, but their price declines quickly as the speed of the market decline slows, i.e. VIX requires an investor to be rather nimble. In addition VIX often, but not always, suffers from costly roll-down because the VIX curve is usually positively sloped. On the other hand, VIX is less exposed to "strike sensitivity" than conventional puts.

The discussion in this paper is confined to simple strategies illustrated in the context of the US equity market, specifically the S&P Index. Later instalments will discuss more complex strategies and cover selected non-$ equity markets.

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The US economy may have entered the tenth year of recovery, following the Great Financial Crisis, and the US Equity Market has enjoyed a bull run almost as long. Neither economic cycles, nor equity bull markets, die of old age. In the modern era, the end of the cycle has generally been brought about by the Federal Reserve taking away the proverbial punch bowl by raising interest rates or, more commonly in recent times, by a financial or market accident. Since end Jan 2018, the S&P has basically traded sideways to modestly higher, except for the violent selloff in Q4 '18 and the equally impressive recovery in Q1 this year. Unsurprisingly, the violence of that selloff, the rally in global bond yields, the slowdown in global growth – and their association with the Chinese slowdown, Fed policy tightening and trade and geopolitical conflicts – have unnerved many equity investors. We hear increasing calls for hedging solutions and/or for signposts that suggest an exit from equity positions. The difficulty with timing such an exit is that, as many investors are aware, the period just before the end of the cycle is often marked by large equity appreciation that precedes a violent decline in a recession (Chart 1). Similar spikes are experienced in the volatility of government bond yields (Chart 2) and in credit spreads (Chart 3) during recessions. The difficulty with systematic hedging is that it can be a large drag on performance. And the difficulty with timing a hedge is that it requires the same skill (or luck) that is required to time the market itself. Nevertheless, the declines that equity markets experience in recessions are so impressive that it would be wise to at least consider hedging strategies as an alternative to exiting the market. Indeed, once an investor properly accounts for the cost of not being invested, or holding cash well in excess of actual liquidity needs, the cost of systematic hedging may appear less onerous. (For example setting aside 5% of AUM by investing it in money markets, instead of equities, has "cost" 25 bps p.a. since 2005, and about 60 bps p.a. since 2012, in terms of foregone equity return.) Further, one also needs to factor the cost of opportunities foregone when investors are unable, for psychological or other reasons, to take advantage of investment opportunities after large selloffs in equity markets because losses on unhedged positions begin to exceed their pain thresholds.

Introduction

Source: Bloomberg, June 7th 2019

Chart 1: S&P 500 Chart 2: MOVE Index (Rate Volatility Index) Chart 3: Credit Spread

In this research report, we review some common approaches to systematic hedging of equity portfolios and point out the pros and cons of each. As is the case when considering any investment strategy, one needs to be forward looking. Data mining exercises do not yield reliable guides to action. Nevertheless, mainly for illustrative purposes, we show simulated historical performance of such hedging strategies for the S&P over the period 2005 - today. The starting point has been chosen to be close to a point in the previous cycle similar to the current time. This period encompasses the pre-crisis boom, the Great Financial Crisis, and the slow recovery from the crisis. However, we wish to caution readers, the sample does not include a period of a sustained rise in interest rates or rising inflation; nor for that matter does it include a period of multi-year stagnation or decline in equities as was seen in the 1970's. This historical study is only as useful as the kind of history it encompasses, and the future may be very different. We would also like to emphasize that we do not recommend that investors hold undiversified equity only portfolios. As we will see later, balanced multi-asset portfolios that benefit from diversification across stocks and bonds, for example, have most often, though not always, provided better risk adjusted returns.

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Moody's Baa Spread to Ave. of 10Y/30Y Govt. Rates

HY spread to government curve (rhs)


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In this report we focus on the US market, specifically investments made in the S&P Index. In subsequent instalments of this report we will look also at selected non-USD equity markets. Since this is an introductory paper we home in first on simple systematic strategies. (In subsequent instalments of this series, we plan to look at more complex strategies such as risk reversals, put butterflies, Variance Swaps, VIX options, etc. Structured Derivatives are yet another alternative that may merit consideration.) The simple systematic strategies evaluated here are of two broad varieties: i) Conventional puts. These have the advantage of hedging the risk asset - equity exposure in this case - directly. The disadvantage is these strategies are "Strike Dependent". That is to say that they are exposed to the risk that the market drifts upwards after the put strategy is executed so that when a downward correction does ensue the put strike is further out-of-the-money than when it was instituted. ii) VIX Strategies. These take advantage of the commonly observed phenomenon that equity volatility (and the VIX Index) generally rises when equity markets fall, and vice versa. The advantages of using these strategies are principally a) their high responsiveness to violent selloffs and b) their relative "Strike Independence", in contrast with conventional puts. The disadvantages include a) the fact the hedge is indirect and that there is no guarantee that volatility will rise in a falling market and b) the very high bleed from roll down on the VIX curve.

Introduction

Source: Bloomberg, June 7th 2019


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1/ 90% OTM puts

We start with a simple strategy of buying 90% strike, 1-year puts every month, spending not more than 2% per annum of AUM on option premium . Since the budget is fixed, as is the strike, the amount of protection will vary over time with implied volatility, which drives option premiums. Hence, the entire portfolio may or may not be protected, though occasionally the nominal size of protection may exceed 100% of AUM. (An alternative way to hedge, while sticking to a budget, is to alter the strikes but this sometimes leads to strikes being selected that are very far from markets levels.) In the pages that follow, the table and charts compare an unhedged position in the S&P 500 with 5 different hedge strategies. For each strategy, we compare two periods: 2005 to the present ( to include the Great Financial Crisis) and 2012 to the present ( to exclude the Great Financial Crisis).

Assume an investment of $100 million in S&P Index on January 4th 2005:

SPTR Index (Jan. 4th 2005 =

100 mil.)

SPTR + 1yr 90% put

strategy

CAGR (Annualized Return) 8.45% 7.61%

Volatility 18.37% 14.88%

Sharpe Ratio 0.38 0.41

Downside Deviation 13.10% 10.66%

Sortino Ratio 0.64 0.71

Max. peak to trough Drawdown -55.25% -46.33%

Max. Drawdown Period: 10/09/07 to 03/09/09 10/09/07 to 03/09/09

Source: Bloomberg, data are up to Feb. 28th 2019

Percentage of equity exposures covered by notional of 1yr 90% put

SPTR (Dec. 30th 2011 = 100

million)

SPTR + 1yr 90% put

strategy

CAGR (Annualized Return) 14.10% 12.53%

Volatility 12.68% 11.64%

Sharpe Ratio 1.06 1.02

Downside Deviation 8.89% 8.18%

Sortino Ratio 1.59 1.53

Max. peak to trough Drawdown -19.36% -17.36%

Max. Drawdown Period: 09/20/18 to 12/24/18 09/20/18 to 12/25/18

The pros and cons of this strategy are as follows: Pros: A strip of one-year options will have less theta bleed (time decay or erosion of time value) relative to 3-Mo options but at the expense of higher implied volatility in general. Cons: The primary problem with one-year options in an upward trending market is that the strike will be further away over time (i.e., below 90%), limiting the protection at expiry.

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Assume an investment of $100 million in S&P Index on December 30th 2011:


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1/ 90% OTM puts


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Assume an investment of $100 million in S&P Index on January 4th 2005: Assume an investment of $100 million in S&P Index on December 30th 2011:


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2/ 1-, 2- and 3-m 90% OTM puts

An alternative is to own 1-, 2- and 3-month 90% strike puts with a new 3-month put being bought as soon as the aged 1-month put expires. The disadvantage with owning long-dated puts is that in a rallying market, the strikes may end up far away from market levels when the equity correction begins. The advantage is that long dated puts appreciate more when implied volatility rises and have less theta (time decay) over the life of the put, although at the expense of higher implied volatility since the vol curve is generally upward sloping.


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SPTR + 1yr 90% put

strategy

SPTR + 3mo 90% put

strategy

CAGR (Annualized Return) 8.45% 7.61% 7.64%

Volatility 18.37% 14.88% 17.20%

Sharpe Ratio 0.38 0.41 0.36

Downside Deviation 13.10% 10.66% 12.27%

Sortino Ratio 0.64 0.71 0.62

Max. peak to trough Drawdown -55.25% -46.33% -54.39%

Max. Drawdown Period: 10/09/07 to 03/09/09 10/09/07 to 03/09/09 10/09/07 to 03/09/09


Percentage of equity exposures covered by notional of 3-mo 90% put

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SPTR + 1yr 90% put

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SPTR + 3mo 90% put

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Volatility 12.68% 11.64% 11.99%






The pros and cons of this strategy are as follows: Pros: There is a lower probability that a strip of 3-Mo options will become further out-of-the-money over time (relative to 1-Yr puts) in an upward trending market. Cons: At equal implied volatilities, a 3-Mo option will have twice the time decay compared to a one-year option (assuming equal equity percent coverage).




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2/ 1-, 2- and 3-m 90% OTM puts


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3/ 1-, 2- and 3-month 98-93% OTM put spread

A third alternative is to buy 1-, 2- and 3-month 98-93% strike put spreads and replace each expiring 1-month put spread with a new 3-month put spread. As before, the budget is constrained to 2% pa of AUM in option premium.


100 mil.)

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strategy

SPTR + 3mo 90% put

strategy

SPTR + 3mo 98%/93%

put spread strategy

CAGR (Annualized Return) 8.45% 7.61% 7.64% 8.01%

Volatility 18.37% 14.88% 17.20% 17.35%

Sharpe Ratio 0.38 0.41 0.36 0.37

Downside Deviation 13.10% 10.66% 12.27% 12.34%

Sortino Ratio 0.64 0.71 0.62 0.65

Max. peak to trough Drawdown -55.25% -46.33% -54.39% -52.79%

Max. Drawdown Period: 10/09/07 to 03/09/09 10/09/07 to 03/09/09 10/09/07 to 03/09/09 10/09/07 to 03/09/09


Percentage of equity exposures covered by notional of 3-mo 98%/93% put spread

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SPTR + 1yr 90% put

strategy

SPTR + 3mo 90% put

strategy

SPTR + 3mo 98%/93%

put spread strategy

CAGR (Annualized Return) 14.10% 12.53% 12.87% 13.29%

Volatility 12.68% 11.64% 11.99% 11.83%

Sharpe Ratio 1.06 1.02 1.02 1.07

Downside Deviation 8.89% 8.18% 8.36% 8.25%

Sortino Ratio 1.59 1.53 1.54 1.61

Max. peak to trough Drawdown -19.36% -17.36% -17.10% -18.02%

Max. Drawdown Period: 09/20/18 to 12/24/18 09/20/18 to 12/25/18 09/20/18 to 12/25/18 09/20/18 to 12/24/18

The pros and cons of this strategy are as follows: Pros: There will be a higher probability that this put spread will be in-the-money than a 90% put. This structure is ideal for a market with minor corrections. Cons: A 98-93% put spread will not provide as effective a hedge as a 90% put in a significant correction (> 15% decline with equal equity coverage)




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3/ 1-, 2- and 3-month 98-93% OTM put spread


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4/ 1- and 2-month VIX futures

A fourth alternative to consider is buying 1- and 2-month VIX futures contracts and replacing the front contract, when close to expiry, with a new 2-month VIX Futures Contract. Since buying VIX futures does not involve an up-front cost, unlike an option premium, we approximate the 2% pa of AUM budget by calculating the "roll down" from the 2-month VIX contract futures price to the spot VIX level. If the VIX futures curve is inverted on the transaction day (2-month VIX future level lower than spot VIX), twenty 2-month VIX future contracts were purchased for 1 million USD S&P 500 exposure. (See details in Appendix pages)



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SPTR + 1yr 90% put

strategy

SPTR + 3mo 90% put

strategy

SPTR + 3mo 98%/93%

put spread strategy

SPTR +VIX future

strategy

CAGR (Annualized Return) 8.45% 7.61% 7.64% 8.01% 6.99%

Volatility 18.37% 14.88% 17.20% 17.35% 14.27%

Sharpe Ratio 0.38 0.41 0.36 0.37 0.38

Downside Deviation 13.10% 10.66% 12.27% 12.34% 9.73%

Sortino Ratio 0.64 0.71 0.62 0.65 0.72

Max. peak to trough Drawdown -55.25% -46.33% -54.39% -52.79% -38.37%

Max. Drawdown Period: 10/09/07 to 03/09/09 10/09/07 to 03/09/09 10/09/07 to 03/09/09 10/09/07 to 03/09/09 07/19/07 to 10/09/08

SPTR (Dec. 30th 2011 = 100

million)

SPTR + 1yr 90% put

strategy

SPTR + 3mo 90% put

strategy

SPTR + 3mo 98%/93%

put spread strategy

SPTR +VIX future

strategy

CAGR (Annualized Return) 14.10% 12.53% 12.87% 13.29% 10.00%

Volatility 12.68% 11.64% 11.99% 11.83% 11.24%

Sharpe Ratio 1.06 1.02 1.02 1.07 0.83

Downside Deviation 8.89% 8.18% 8.36% 8.25% 7.69%

Sortino Ratio 1.59 1.53 1.54 1.61 1.30

Max. peak to trough Drawdown -19.36% -17.36% -17.10% -18.02% -15.49%

Max. Drawdown Period: 09/20/18 to 12/24/18 09/20/18 to 12/25/18 09/20/18 to 12/25/18 09/20/18 to 12/24/18 02/09/15 to 08/25/15

The pros and cons of this strategy are as follows: Pros: Due to the payoff convexity in VIX futures, they will generally provide greater protection than puts in a major correction. Investors should also hedged in minor corrections Cons: In an upwardly sloping volatility curve, the roll-down in VIX futures make it a very expensive hedge. Plus investors need excellent timing in exiting VIX due to extreme volatility.




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SPTR +VIX futurestrategy

4/ 1- and 2-month VIX futures




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5/ 1- and 2-month VIX futures (half size)

Given the effectiveness of VIX in episodes of violent selloffs and the equally impressive bleed the strategy suffers in quiet times, we show below the result of doing half the size of the hedge in the example above.


SPTR (Dec. 30th 2011 = 100

million)

SPTR + 1yr 90% put

strategy

SPTR + 3mo 90% put

strategy

SPTR + 3mo 98%/93%

put spread strategy

SPTR +VIX future

strategy

SPTR + half size of VIX

future strategy

CAGR (Annualized Return) 14.10% 12.53% 12.87% 13.29% 10.00% 12.17%

Volatility 12.68% 11.64% 11.99% 11.83% 11.24% 10.84%

Sharpe Ratio 1.06 1.02 1.02 1.07 0.83 1.06

Downside Deviation 8.89% 8.18% 8.36% 8.25% 7.69% 7.48%

Sortino Ratio 1.59 1.53 1.54 1.61 1.30 1.63

Max. peak to trough Drawdown -19.36% -17.36% -17.10% -18.02% -15.49% -13.78%

Max. Drawdown Period: 09/20/18 to 12/24/18 09/20/18 to 12/25/18 09/20/18 to 12/25/18 09/20/18 to 12/24/18 02/09/15 to 08/25/15 09/20/18 to 12/25/18


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SPTR + 1yr 90% put

strategy

SPTR + 3mo 90% put

strategy

SPTR + 3mo 98%/93%

put spread strategy

SPTR +VIX future

strategy


future strategy

CAGR (Annualized Return) 8.45% 7.61% 7.64% 8.01% 6.99% 7.75%

Volatility 18.37% 14.88% 17.20% 17.35% 14.27% 13.69%

Sharpe Ratio 0.38 0.41 0.36 0.37 0.38 0.46

Downside Deviation 13.10% 10.66% 12.27% 12.34% 9.73% 9.71%

Sortino Ratio 0.64 0.71 0.62 0.65 0.72 0.80

Max. peak to trough Drawdown -55.25% -46.33% -54.39% -52.79% -38.37% -39.49%

Max. Drawdown Period: 10/09/07 to 03/09/09 10/09/07 to 03/09/09 10/09/07 to 03/09/09 10/09/07 to 03/09/09 07/19/07 to 10/09/08 07/19/07 to 10/10/08

The pros and cons of this strategy are as follows: Pros: In an upwardly sloping volatility curve, there will be less bleed or roll-down when using half the size. Cons: In a major correction, investors will probably not be fully hedged but should still have reasonable protection. Again, timing is critical when exiting VIX due to high volatility.




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Half size VIX futurecontribution

5/ 1- and 2-month VIX futures (half size)



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SPTR + 3mo98%/93% put spreadstrategySPTR +VIX futurestrategy

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SPTR + 3mo98%/93% put spreadstrategySPTR +VIX futurestrategy

SPTR + half size of VIXfuture strategy


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6/ 50:50 Stock and Long Bond Portfolio

Finally, we compare the results with a 50:50 Stock and Long Bond portfolio which has no option protection. As is clear, the total returns and volatilities for both the S&P 500 and long duration bonds are similar, as they should be for equal risk securities. But since returns between equities and bonds can diverge significantly at times, the balanced 50:50 portfolio not only has slightly higher returns but a much lower volatility, resulting in a higher Sharpe ratio.

Source: Bloomberg, Feb. 28th 2019

Long Duration Bond Total

ReturnS&P 500 Total Return

50% SPTR and 50% Long

Duration U.S. Govt. Bond

Index


Volatility 17.41% 18.37% 9.64%






Worst Calendar Year Return -25.34% -37.00% -4.52%

Worst Calendar Year: 2009 2008 2008

The pros and cons of this strategy are as follows: Pros: A balanced S&P 500 and long-duration bonds provided the best risk adjusted returns over the long run e.g. since 2005, but not since 2012. This is because long maturity bonds were generally inversely correlated with equities and rallied by 300 bps. Cons: With long-term yields so low now, it is uncertain how much protection bonds can offer in a selloff. Plus, there is the risk of both bonds and equities selling off simultaneously.

Period: January 4th 2005 to February 28th 2019 Period: December 30th 2011 to February 28th 2019

Long Duration Bond Total

ReturnS&P 500 Total Return



Index


Volatility 14.21% 12.68% 7.48%






Worst Calendar Year Return -17.25% -4.38% -2.43%

Worst Calendar Year: 2013 2018 2018

0

50

100

150

200

250

300

350

400

Long Duration Bond Total Return

S&P 500 Total Return

50% SPTR and 50% Long Duration U.S. Govt. Bond Index

0

50

100

150

200

250

300

Dec-11 Dec-12 Dec-13 Dec-14 Dec-15 Dec-16 Dec-17 Dec-18

Long Duration Bond Total Return

S&P 500 Total Return

50% SPTR and 50% Long Duration U.S. Govt. Bond Index


15

Summary





100 mil.)

SPTR + 1yr 90% put

strategy

SPTR + 3mo 90% put

strategy

SPTR + 3mo 98%/93%

put spread strategy

SPTR +VIX future

strategy


future strategy



Index

CAGR (Annualized Return) 8.45% 7.61% 7.64% 8.01% 6.99% 7.75% 8.86%

Volatility 18.37% 14.88% 17.20% 17.35% 14.27% 13.69% 9.64%

Sharpe Ratio 0.38 0.41 0.36 0.37 0.38 0.46 0.76

Downside Deviation 13.10% 10.66% 12.27% 12.34% 9.73% 9.71% 6.64%

Sortino Ratio 0.64 0.71 0.62 0.65 0.72 0.80 1.33

Max. peak to trough Drawdown -55.25% -46.33% -54.39% -52.79% -38.37% -39.49% -24.32%

Max. Drawdown Period: 10/09/07 to 03/09/09 10/09/07 to 03/09/09 10/09/07 to 03/09/09 10/09/07 to 03/09/09 07/19/07 to 10/09/08 07/19/07 to 10/10/08 12/03/07 to 03/09/09

SPTR (Dec. 30th 2011 = 100

million)

SPTR + 1yr 90% put

strategy

SPTR + 3mo 90% put

strategy

SPTR + 3mo 98%/93%

put spread strategy

SPTR +VIX future

strategy


future strategy



Index

CAGR (Annualized Return) 14.10% 12.53% 12.87% 13.29% 10.00% 12.17% 9.27%

Volatility 12.68% 11.64% 11.99% 11.83% 11.24% 10.84% 7.48%

Sharpe Ratio 1.06 1.02 1.02 1.07 0.83 1.06 1.15

Downside Deviation 8.89% 8.18% 8.36% 8.25% 7.69% 7.48% 5.30%

Sortino Ratio 1.59 1.53 1.54 1.61 1.30 1.63 1.75

Max. peak to trough Drawdown -19.36% -17.36% -17.10% -18.02% -15.49% -13.78% -8.85%

Max. Drawdown Period: 09/20/18 to 12/24/18 09/20/18 to 12/25/18 09/20/18 to 12/25/18 09/20/18 to 12/24/18 02/09/15 to 08/25/15 09/20/18 to 12/25/18 05/02/13 to 08/21/13


16

Summary


1/ There is no right or wrong hedge as it depends upon the market environment, as evident in the bar chart below, where different strategies outperform in different years. In violent selloffs, like Q4 2008 and Q4 2018, VIX hedges perform markedly better, but at the expense of excessive "bleed" or roll-down in quieter markets. We see that both of the 90% put strategies reduced annualized returns by slightly more than 0.8% since 2005 while costs were 2% per annum, resulting in net hedge costs of 1.2% per annum. Since there have only been four selloffs greater than 10%, the 98-93% put spread has been a better hedge (i.e., it lost less money) than the other option strategies. But this comes at the expense of less protection in bear markets (>15% selloff if equal equity percent coverage). 2/ Is diversifying into government bonds the best solution? While a balanced 50:50 S&P 500 and long-duration bonds has provided the best risk adjusted returns since 2005, long maturity bonds rallied by 300 bps over this period. With long-term yields so low now (2.6% for 30-year Treasuries), it is uncertain how much protection bonds can offer in a selloff. Plus investors run the risk of both bonds and equities selling off due to inflation or geo-political concerns, though this is not our base case. 3/ Conclusion: Net, we recommend that investors have a well diversified portfolio. The choice to hedge should be based on investors' risk tolerances, and their expectations of what the future will bring. While being hedged 100% of the time has not proved economical in the bull market over the past decade, the risk of not being in the market versus a partially hedged position can also weigh on returns.

-60%

-40%

-20%

0%

20%

40%

2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 2015 2016 2017 2018 2019SPTR Index (Jan. 4th 2005 = 100 mil.) SPTR + 1yr 90% put strategySPTR + 3mo 90% put strategy SPTR + 3mo 98%/93% put spread strategySPTR +VIX future strategy SPTR + half size of VIX future strategy50% SPTR and 50% Long Duration U.S. Govt. Bond Index

-20%

0%

20%

40%

2012 2013 2014 2015 2016 2017 2018 2019SPTR (Dec. 30th 2011 = 100 million) SPTR + 1yr 90% put strategySPTR + 3mo 90% put strategy SPTR + 3mo 98%/93% put spread strategySPTR +VIX future strategy SPTR + half size of VIX future strategy50% SPTR and 50% Long Duration U.S. Govt. Bond Index




17

Appendix

How do we decide how many VIX future contracts to purchase to hedge 1 million USD S&P 500 exposure, with budget of 2% p.a. of equity AUM?

For example, on February 12th 2019, we rolled the February 2019 contract (UXG9 index), which had 1-day to expiry, to a new 2-month VIX future contract (April 2019 contract, UXJ9 index). The spot VIX on Feb. 12th 2019 was 15.43; the April 2019 VIX contract was 16.875; and the roll down was 1.445 vol points. (Levels can be found in "VIX Index CT" screen in Bloomberg. To hedge 1 million S&P 500 exposure with budget of 2% p.a., the budget on February 12th 2019 in USD term was 1,000,000 * 2% / 12 = $1,667. Taking VIX roll down into consideration, the April 2019 VIX contracts to buy for each 1 million USD S&P 500 exposure was 1,667 / (1.445 * 1000) = 1.15 contracts.

What is VIX Index?

VIX is an estimate of 1-month S&P 500 implied volatility, based on interpolated 1- and 2-month options. The level of VIX is based on the implied volatilities over a wide range of strikes to incorporate volatility skew (put volatility is higher than call volatility). In general, VIX increases when equites decline and vice versa. However, there have been periods where VIX increases as equities rally.

What is Sharpe Ratio?

Sharpe Ratio is the annualized excess return divided by the annualized standard deviation of the excess returns. Excess return, in this case, is the S&P 500 total return minus money market rate return.

What is Sortino Ratio?

Sortino Ratio is the annualized return divided by the annualized downside deviation of the returns, with minimum acceptable return (MAR) set as zero. The higher the Sortino ratio, the better are the risk adjusted returns. Downside deviation is similar to standard deviation, but only counts negative daily returns into the calculation.


18

y = -0.0114x + 5E-05R² = 0.6168

-20%

-15%

-10%

-5%

0%

5%

10%

15%

-10 0 10 20

SPTR

2nd VIX Future

y = -54.191x - 0.0085R² = 0.6168

-10

-5

0

5

10

15

-20% -10% 0% 10% 20%2n

d V

IX f

utu

re

SPTR

Appendix

Regression (2005 to 2019) X = 2nd VIX future daily movements Y = S&P daily returns

Beta = 1.14% ( 1 Vol point movement corresponds to 1.14% S&P movement)

Regression (2005 to 2019) X = S&P daily returns Y = 2nd VIX future daily movements

Beta = 54 ( 1% S&P movement corresponds to 0.54 Vol point movement) Or 1 Vol point movement corresponds to 1.85% S&P movement

Based on historical regression, on average, 1 Vol point movement corresponds to 1.5% (average of 1.14% and 1.85%) S&P movement. Or 1 % S&P movement corresponds to 0.67 Vol point movement. For each VIX future contract, 1 Vol point movement results in 1,000 USD PnL. Hence, in order to hedge 1 million S&P 500 exposure, historical regression indicates to use approximately 15 2nd VIX future contracts. ( 1,000,000 * 1% / 0.67 / 1000 = 14.9 contracts). This is the reason that we choose to cap the VIX future contracts at 20 contracts per 1 million S&P exposure if the VIX curve is inverted or very flat.

How to decide the "VIX to S&P 500" hedge ratio?

0%

20%

40%

60%

80%

100%

120%

140%

160%

How many percent of "15 VIX contracts to hedge 1 million S&P 500 exposure" we achieved on a rolling basis with 2% p.a. budget?


19

Appendix

Options and futures are not suitable for all investors, and trading in these instruments is considered risky and may be appropriate only for sophisticated investors. Past performance is not necessarily indicative of future results. Various theoretical explanations of the risks associated with these instruments have been published. Prior to buying or selling an option, and for the complete risks relating to options, you must receive a copy of "The Characteristics and Risks of Standardized Options." You may read the document at http://www.optionsclearing.com/about/publications/character-risks.jsp or by writing to UBS Financial Services, Inc., 1200 Harbor Boulevard, Weehawken, NJ, 07086.


20

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Appendix

Risks and definitions

Bonds are subject to interest rate risks. Bond prices generally fall when interest rates rise.Investments in commodities may have greater volatility than investments in traditional securities, particularlyif the instruments involve leverage. The value of commodity-linked derivative instruments may be affected bychanges in overall market movements, commodity index volatility, changes in interest rates, or factors affectinga particular industry or commodity, such as drought, floods, weather, livestock disease, embargoes, tariffs andinternational economic, political and regulatory developments. Use of leveraged commodity-linked derivatives createsan opportunity for increased return but, at the same time, creates the possibility for greater loss.Duration—The percentage price change of a bond for a 1% change in the yield of the underlying bond, normallyexpressed in years. That is, a bond with a10-Year duration would increase in price by 10% for a 1% decline in yield.Futures and Options trading is not suitable for every investor as there is a substantial risk of loss, and losses inexcess of an initial investment may occur.Global macro strategies trade a broad range of strategies in which the investment process is predicated onmovements in underlying economic variables and the impact these have on equity, fixed income, hard currency andcommodity markets.There is no guarantee that the use of long and short positions will succeed in limiting an investor‘s exposure todomestic stock market movements, capitalization, sector swings or other risk factors. Using long and short sellingstrategies may have higher portfolio turnover rates. Short selling involves certain risks, including additional costsassociated with covering short positions and a possibility of unlimited loss on certain short sale positions.Equity Risk Premium (ERP) equals the spread above the government curve that equates the present value ofexpected dividend cash flows with the current price of the equity index, when these cash flows are discounted bythe government zero-curve plus ERP. Based on this definition, ERP represents expected long-term excess returns ofcommon stock indices over long-term risk-free zero coupon rates. Calculation of ERP depends on consensus forecastsfor earnings and GDP as well as certain assumptions about forward dividend growth, which may or may not proveto be accurate.Relative value trade: A trade comprising a long position in a financial instrument together with a short positionin another financial instrument, where overall trade performance depends on the performance of the long positionrelative to the performance of the short position.Relative value strategies maintain positions in which the investment thesis is predicated on realization of a valuationdiscrepancy in the relationship between multiple securities.Our Return Target is based upon index returns and market prices (e.g., futures contract prices if the traderecommends a specific future), and is not a projection of the potential profit or loss that an investor should expectto receive when following the recommendation. Additionally, the Return Target does not account for any transactioncosts that an investor would incur by implementing the recommendations made herein, such as commissions, fees,margin interest, and interest charges. Actual transactions adjusted for such transaction costs will result in reducedtotal returns, and returns may be further reduced depending on the specific financial instruments available to betraded by the investor.Spread: The difference between the yields of two securities.VIX/VSTOXX Vega: The profit/loss impact of a one point change in VIX/VSTOXX.


21

Appendix

Disclaimer

UBS Chief Investment Office's ("CIO") investment views are prepared and published by the Global Wealth Management business of UBS Switzerland AG (regulated by FINMA inSwitzerland) or its affiliates ("UBS").The investment views have been prepared in accordance with legal requirements designed to promote the independence of investment research.Instrument/issuer-specific investment research – Risk information:This publication is for your information only and is not intended as an offer, or a solicitation of an offer, to buy or sell any investment or other specific product. The analysiscontained herein does not constitute a personal recommendation or take into account the particular investment objectives, investment strategies, financial situation and needs of anyspecific recipient. It is based on numerous assumptions. Different assumptions could result in materially different results. Certain services and products are subject to legal restrictionsand cannot be offered worldwide on an unrestricted basis and/or may not be eligible for sale to all investors. All information and opinions expressed in this document were obtainedfrom sources believed to be reliable and in good faith, but no representation or warranty, express or implied, is made as to its accuracy or completeness (other than disclosuresrelating to UBS). All information and opinions as well as any forecasts, estimates and market prices indicated are current as of the date of this report, and are subject to changewithout notice. This publication is not intended to be a complete statement or summary of the securities, markets or developments referred to in the report. 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