key: cord-0049288-datcpvzb authors: Jackwerth, Jens title: What Do Index Options Teach Us About COVID-19? date: 2020-08-20 journal: Rev Asset Pricing Stud DOI: 10.1093/rapstu/raaa012 sha: 8ef42b6b2666ee9f6859ba14f835fc034355103e doc_id: 49288 cord_uid: datcpvzb Risk-neutral distributions of the S&P 500 are informative about the COVID-19 pandemic beyond what one can learn from index values and the market fear gauge of the VIX alone. We learn that, on February 20, 2020, the index did not yet reflect the impending crisis. Only on March 16, 2020, was the full impact visible, with a pronounced bimodality for longer-maturity options revealing a sizeable crash scenario. The corresponding physical distribution is more symmetric and features a high-volatility crash scenario. Firms bought crash protection ahead of the index crash, whereas retail customers bought it as the index was already recovering. Faced with the rising human and economic toll of the COVID-19 pandemic, society tries to learn about the crisis from limited information. As it became apparent that the pandemic would have major economic consequences, financial markets reacted strongly. For example, the S&P 500 index dropped by 34% from February 19, 2020, through March 23, 2020. Such a decline indicates investors' concerns about negative consequences for the U.S. and global economies, but the information is aggregated so that much detail is lost. In effect, we look at a single value (the index) that is the discounted expectation of uncertain future index values. In a similar vein, the VIX1 acts as a gauge for investor uncertainty about future index values; we again have a single value that provides important, but not detailed, information. This paper goes a major step further and uses the pricing of options on the S&P 500 index to estimate an implicit distribution of future index values, the risk-neutral distribution. Since a large number of market participants are buying and selling these index options, we wind up with an average or "representative investor" risk-neutral distribution. As investors are typically risk averse, the risk-neutral distribution includes both a probabilistic assessment of future index values (formally, their physical probabilities) and a risk adjustment (resulting in larger risk-neutral probabilities for painful outcomes and reduced probabilities for beneficial outcomes). I use the richness of risk-neutral index distributions to address questions about crash expectations during the COVID-19 and other pandemics, including the timing and extent to which those distributions reflect concerns about a potential market crash. I also examine option trade data reflecting how risk-averse investors attempt to protect themselves against adverse index movements. When did markets impound the economic impact of the Covid-19 pandemic? Distributions on dates prior to February 20, 2020, do not display noticeable concerns about economic consequences of the pandemic. Leading up to February 28, 2020, the risk-neutral index distributions indicate the beginnings of concern, even though February 28, 2020, is over a month after the first U.S. case and about 2 months after the outbreak started in Wuhan. A much stronger reaction can be seen in the risk-neutral distribution for March 16, 2020. This finding is consistent with Ramelli and Wagner (2020) , who find that mainly the few stocks with strong exposure to China were affected early during the pandemic. Investors realized only belatedly that many other stocks in the S&P 500 were also affected by the pandemic. What risk-neutral scenarios did the option market view as likely? The March 16, 2020, data imply a bimodal (two-hump) distribution of potential outcomes. That distribution can be replicated by a 40% chance of an outcome from a distribution of very adverse (crash) results coupled with a 60% chance of an outcome from a normal scenario distribution. The midpoint of the crash scenario is located 1,461 index points below that of the normal scenario, while this distance is typically around 600 index points (typical days also have crash scenarios, but only mild ones). How does the physical scenario differ from the risk-neutral one? When I remove the implicit risk adjustment, the physical distribution for the crash scenario morphs into a pervasive high-variance scenario but one that overlaps a rather low-variance normal scenario. The distance between the scenario midpoints shrinks to 300 index points because the physical distribution only accounts for the likelihood of a crash, but not for investor risk aversion. Risk-averse investors find crashes painful, and risk-neutral distributions account for this through higher risk-neutral probabilities of crash outcomes. By examining the physical distribution from longer maturity options, I observe that investors do not seem to expect a full price recovery for the index until sometime beyond December 2020. Which option traders bought crash protection? Firms that are members of the Option Clearing Corporation did so over the 4 weeks leading up to March 16, 2020, in time to protect themselves against the losses in the index during this time. Retail customers tried to protect themselves 1 month later during the 4 weeks leading up to April 16, 2020, but lost out as the market recovered over that period. How did the index react to other virus outbreaks? The index did not react to SARS and H1N1, but did possibly react somewhat to Ebola. The index reacted only to COVID-19 with a strong downward move because the COVID-19 death toll exceeds that of earlier outbreaks by a factor of more than 100, and the resultant economic impacts have been enormous. To provide a cursory background of events, I summarize policy responses and economic reactions. The very first COVID-19 case occurred on November 17, 2019, but it was not immediately recognized as that (Wikipedia 2020a ). The first confirmed case was on December 1, 2019, and more sporadic cases were reported as December wore on. Toward the end of the year, hospitals and infectious disease centers around Wuhan, China, knew about a pneumonia of unknown cause. On January 3, 2020, the genetic sequence of the virus was first decoded, and U.S. officials had first knowledge of the virus. Online discussion about the virus was suppressed in China on January 7, 2020. The U.S. Centers for Disease Control and Prevention (CDC) issued a travel warning that same day. On January 8, 2020, Chinese scientists publicly announced the new virus, and the World Health Organization (WHO) and the European Centre for Disease Prevention and Control posted their first risk assessments. On that same day came the first public notice on the Chinese state broadcaster CCTV about a new viral outbreak. By the end of January 2020, the WHO had issued several reports, cases spread to countries other than China, and the first confirmed U.S. case occurs on January 20, 2020 (Wikipedia 2020b) . February 2020 saw a steady flow of information about new cases, detailed in daily WHO updates (Wikipedia 2020c) . The spread of new infections increased into the hundreds in Italy, Iran, and South Korea (China had already exceeded those numbers) beginning on February 21, 2020. March 2020 saw a steady worsening of the crisis, and the WHO finally declared it a pandemic on (2,247 cumulative deaths recorded by that time2). The VIX then increased at first slowly, then considerably starting on February 27, 2020, and continued until the middle of March 2020. With the WHO's declaration of the pandemic on March 12, 2020, the VIX broke 75, and the S&P 500 dropped from 2,741 to 2,481, for a 9.51% daily loss. In the risk-neutral distributions, we see a fullblown reaction on March 16, 2020 (7,180 cumulative deaths). Thereafter, the VIX moves down to about 40 on April 16, 2020 (147,789 cumulative deaths), and the S&P 500 recovers to around 2,800. By May 26, 2020 (351,979 cumulative deaths), the VIX fell further, to below 30, and the S&P 500 stabilized at around 3,000. This paper contributes to an understanding of the impact of the coronavirus on the economy. A growing number of papers tackle the subject. Nguyen (2020), Ramelli and Wagner (2020) , and Yan et al. (2020) document the impact of the crisis on different industries. Yilmazkuday (2020) investigates the reaction of the S&P 500 index to COVID-19-related deaths. Croce, Farroni, and Wolfskeil (2020) determine the price of pandemic-infection risk. Cheng (2020) I collect midpoint implied volatilities for call options on the S&P 500 index from January 2, 2020, . (1) The grid is given by Δ = 50, which defines the distance between two consecutive strike prices from 0 to 6,500; ′′ denotes the numerical approximation to the second derivative of the implied volatility curve. Equation (1) Δ 4 ) works well empirically. Finally, the smooth implied volatilities curve is translated into a call option price curve, whose second derivative is the risk-neutral distribution (see Breeden and Litzenberger 1978) : where Rf is the gross interest rate. I pose five questions and answer them using the forward-looking information embedded in option prices. But why the long wait? Ramelli and Wagner (2020) document that sectors more exposed to China were affected earlier, less exposed sectors later. The S&P 500 index contains some sectors with large exposure to China and many domestic sectors with small exposure. Thus, the initial reaction of the index was small. Only when investors realized that the crisis was not solely confined to stocks with large exposure to China but affected most U.S. stocks did the index react strongly. Incidentally, on March 12, 2020, the WHO declared a pandemic, clearly marking that the whole world was affected by then. The next two distributions of Figure 3 on April 16, 2020, (purple) and May 26, 2020, (brown) reflect the subsiding fear of a market crash as volatility decreases and the index recovers to 2,800 and 2,992. The brown distribution has less than 1 month left to maturity and is thus very concentrated and peaked. Lengthening the maturities to almost 1 year (December 18, 2020), Figure 4 paints a similar picture. Interestingly, the distribution on March 16, 2020, now hints at a bimodal distribution.3 I explore the two components of this distribution next. The figure graphs risk-neutral distributions on January 2, 2020, February 20, 2020, February 28, 2020, March 16, 2020, April 16, 2020, and May 26, 2020. In Figure 5 , I fit a mixture of two normal distributions to the risk-neutral distribution from Figure 4 on March 16, 2020, with a maturity date on December 18, 2020.4 At the height of the crisis, the market views two scenarios as likely. In 42% of cases, a severe crash scenario over the next 9 months is centered on a fairly catastrophic expected future index value of 1,505 with a standard deviation of 597. In the other 58% of cases, the index recovers to almost precrisis values (2,966) with a standard deviation of 376. The crash scenario mean is located 1,461 index points below that of the normal scenario, whereas the distance was only around 600 on January 2, 2020, and February 20, 2020, whence I fit mixtures to those risk-neutral distributions. Next, I study the time series of decompositions of the risk-neutral distribution into crash and normal scenarios. Figure 6 graphs the means of the crash and the normal scenarios (both scaled by the underlying) and the probability of the crash scenario from January 2, 2020, through May 26, 2020. The maturity date is always December 18, 2020. The decomposition of the risk-neutral distribution follows the evolution of the moments of the riskneutral distribution. The crash scenario becomes more probable (close to 50%, up from about a third) after February 20, 2020, when the VIX starts to increase from around 16. The mean of the crash scenario remains unchanged at about 90% of the index value, and the mean of the normal scenario remains unchanged at about 110%. During this time leading up to the height of the crisis, only the probability of the crash scenario increased. A novel insight is the divergence of crash and normal scenarios during the height of the crisis from March 3, 2020, through March 24, 2020. The crash scenario is now somewhat less likely (40%) but it is located at only 65% of the index value while the normal scenario is located at about 125%. The increased uncertainty about the pandemic manifests itself in a widened bimodal distribution. With the start of April 2020, the risk-neutral distribution signals less uncertainty. The crash scenario rises from 70% to 85% of the index value while the normal scenario falls from 115% to 110%, and the crash scenario keeps a probability of about 40%. All risk-neutral values are somewhat difficult to interpret as the drift under the risk-neutral distribution is the risk-free rate, not the sum of risk-free rate and market risk premium. Thus, I momentarily turn to the physical distribution. The pricing kernel (accounting for the risk aversion of investors) relates physical probabilities p to risk-neutral probabilities q. I assume a particularly simple power utility specification for the pricing kernel of a representative investor, and the relation becomes where r is the gross return cum dividends on the index, Rf the gross interest rate, and marginal power utility ′( ) = − . Bliss and Panigirtzoglou (2004) suggest a value for the risk aversion coefficient of  = 4, while Jackwerth and Menner (2020) suggest a value of  = 3 for their more recent sample from April 1986 through December 2017. The latter paper shows in statistical tests that future index returns are compatible with such a physical distribution. Thus, I use  = 3 for computing physical distributions.5 Since I am looking at the distribution on a day with very high volatility,6 a fact that might make a representative investor more risk averse than normal, I alternatively use  = 5. Note that the mixture completely obscures the physical distribution. Looking at the overall expected future index value of 3,009, the market on March 16, 2020, expects index values to need more than 9 months to recover to precrisis levels (3,386 on February 19, 2020). Increasing the risk aversion coefficient to  = 5 deemphasizes the crash scenario somewhat (35%), while the boom scenario gains further in importance. The corresponding unreported figure is similar to that in Figure 7 . For each option trader category (Option Clearing Corporation member firms "Firm"; broker/dealers "BD"; professional customers, such as hedge funds and large banks, "Procust"; retail customers "Cust"; and market makers "MM"), I collect for each call strike price the daily net demand on the Chicago Board Options Exchange.7 I add demand at nearby strike prices up to the midpoint between neighboring strike prices (and widening the intervals toward the ends of the range). As positive call option demand implies a positive delta (sensitivity of the option with respect to the index), I subtract the corresponding put option demand (which implies negative delta) to arrive at an aggregate demand for buying delta. Because option demand fluctuates daily, I aggregate the demand through the 4 weeks leading up to a particular date. The resultant (4-week) buying delta demand measures total exposure to the index due to option positions (at a particular strike price) of a particular trader category. Positive buying delta demand of customers means that customers stand to gain from their option position if the index goes up. Negative buying delta demand of firms means that firms hedge long exposure to the index through a (partially) offsetting position in options. I start with the short maturity (June 19, 2020). My first date is February 20, 2020, and during the 4 weeks leading up to it, firms, professional customers, retail customers, and market makers buy and sell options at different strikes in moderate amounts without any discernable pattern. Broker/dealers always trade very little. I skip February 28, 2020, as the 4-week sample heavily overlaps with the previous sample. On March 16, 2020, for options maturing on June 19, 2020, Figure 8 shows some moderate selling of delta by firms (strike 2,600) as retail customers and market makers demand that delta. These firms gained over those weeks during the index's downturn. Professional customers even demanded delta (strike 2,000), while retail customers sold some smaller amount of delta (strike 2,200). Overall, customers were exposed to the falling market during those weeks. The picture changes on April 16, 2020, (see Figure 9 ), when retail customers massively sell delta (strikes 2,400 and 2,800) over the preceding 4 weeks, and market makers absorb large quantities of delta. Interestingly, the retail customer demand for selling delta arises only after the index losses in mid-March 2020. Customers were concerned about aftershocks but bought (no longer needed) protection in a recovering market. Index option prices translate into risk-neutral distributions, which contain richer information than index and VIX values. The risk-neutral distributions of the S&P 500 index show the full impact of the COVID-19 pandemic on the index only on March 16, 2020, almost 2 months after the first news about the pandemic. The 9-month risk-neutral distribution on that day is bimodal, showing a 40% chance of a severe crash scenario. The physical distribution of the crash scenario becomes a more moderate high-volatility scenario moving much closer to the actual index level. The expected future index value on March 16, 2020, is 3009, suggesting that by the end of 2020, the index will not have recovered its previous high of 3,386. Firms managed to sell exposure to the falling market through option positions during the 4 weeks leading up to March 16, 2020. Retail customers only established such positions 1 month later as the market was already recovering. Other viral outbreaks, such as SARS and H1N1, do not show up in the index, the VIX, or the risk-neutral distributions, whereas some evidence of the Ebola outbreak seems to appear. 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