Mispriced index option portfolios

• Author: George M. Constantinides,Stylianos Perrakis,Michal Czerwonko
• Date: 01 June 2020
• Published date: 01 June 2020
• DOI: http://doi.org/10.1111/fima.12288

DOI: 10.1111/fima.12288

ORIGINAL ARTICLE

Mispriced index option portfolios

George M. Constantinides1Michal Czerwonko2Stylianos Perrakis3

1University of Chicago, Chicago, Illinois

2GraduateSchool of Business, Nazarbayev

University, Nur-Sultan, Republic of Kazakhstan

3John Molson School of Business, Concordia

University, Montreal, Quebec,Canada

Correspondence

GeorgeM. Constantinides, University of Chicago,

5807South Woodlawn Avenue, Chicago, IL

60637.

Email:gmc@chicagobooth.edu

Fundinginformation

Centerfor Research in Security Prices; Social

Sciencesand Humanities Research Council of

Canada

Abstract

In model-free out-of-sample tests, we find that the optimal portfo-

lio of a utility maximizing investor tradingin the S&P500 Index, cash,

and index options bought at ask and written at bid prices stochas-

tically dominates the optimal portfolio without options and yields

returns with higher mean and lower volatility in most months from

1990 to 2013. Unlikeearlier claims of overpriced puts, our portfolios

include mostly short calls and are particularly profitable when matu-

rity is short and volatilityis high. Similar results are obtained with the

CAC and DAX indices. Neither priced factors nor a nonmonotonic

stochastic discount factor explains the excessreturns.

1INTRODUCTION

Index option anomalies are mentioned for the first time in Rubinstein (1994) who documents the existence of the

implied volatility (IV) smile in S&P 500 Indexoptions for the post-1987 crash data. Rubinstein (1994) advances several

conjectures regarding the sources of the smile and points out that out-of-the money (OTM)put options may have been

overpriced after the crash. Several subsequent studies claim overpricingin both OTM puts and at-the-money (ATM)

straddles. A parallelline of research, starting with Jackwerth (2000), argues that the stochastic discount factor derived

from the observed equilibrium prices in both the underlying and option marketsis U-shaped and also leads to put mis-

pricing relative to monotonic stochastic discount factors. The parameters of the asset dynamics of the index yielding

the real distribution of the returns are derived by fitting specific models to the entire time series of index values. Fric-

tions, such as margins and bid–ask spreads, are ignored, put–call parity is assumed, and the prices of the in-the-money

(ITM) options are derived from the midpoint quotes of their OTMcounterparts.1

These assumptions are unrealistic and their empirical impact is major for short-term options, as we discuss further

on in this section. Bates (2003) notes that attempts to relax them in a no-arbitrage model have not been particularly

successful. For this reason, we use a different methodology in this paper where we relax the assumptions of the fric-

tionless economy and apply model-free tests of the mispricing in the S&P 500 Index options. We apply a stochastic

c

2019 Financial Management Association International

1Anexception is Santa Clara and Saretto (2009) in which margins play a central role in explaining the observed mispricing. They also consider option bid–ask

spreadsand find that they reduce, but do not eliminate, put overpricing. Their data, however, do not cover the 2008 financial crisis.

Financial Management. 2020;49:297–330. wileyonlinelibrary.com/journal/fima 297

298 CONSTANTINIDESET AL.

dominance (SD) frameworkintroduced by Constantinides and Perrakis (2002) and tested in sample by Constantinides,

Jackwerth, and Perrakis (2009) and out of sample byConstantinides, Czerwonko, Jackwerth, and Perrakis (2011).

In particular, we consider an investor who holds a risk-free bond and a fund tracking the S&P 500 Index,the lat-

ter subject to proportional transaction costs. The investor maximizes the expectationof their i ncreasing andconcave

utility function of cash wealth at the end of a horizon longer than the maturities of any traded options, which can be

infinite.2We call this portfolio the “IndexTrading” (IT) portfolio. We then consider overlaying a zero-net-cost portfolio

on this portfolio consisting of long and short positions in European-style call and put options of 28-,14-, or 7-day matu-

rities on the index. Wecall the IT portfolio, overlaid with the options portfolio, the “Option Trading” (OT)portfolio. We

account for transaction costs in the trading of options bybuying options at their ask price and selling them at their bid

price. Unlike earlier SD studies, the OTportfolio does not consist of a single option and is not predetermined at port-

folio formation time. This generalization has a major impact on the empirical results, particularly for the shorter term

options.

We select the zero-net-cost option portfolio at the start of each 28-,14-, or 7-day maturity from the entire universe

of available options filtered by limits on moneyness and liquidity.In all cases, the options are kept until maturity and

the OT investoris not allowed to close positions. We develop a linear programming (LP) algorithm that identifies all of

the option portfolios such that the OT portfolio stochastically dominates (SD) the ITportfolio in the second degree if

both are liquidated at the options’ maturity. The SD conditions built into the LP indicate that the total excesspayoff

of the OT portfolio overthe IT portfolio is nonnegative at low values of the index support, intersects the support at a

single value, becomes nonpositive at high values, and has a positive expected payoff.We use only observables at the

time the portfolios are formed in order to ensure that our strategies can be executedby any option end user and that

any excessprofits are anomalous. We find these portfolios for almost every month of our data for all three maturities

from 1990 to the end of 2012.

Once we identify the set of SD portfolios at each date, we select one from the set by optimizing a given criterion,

either the Sharpe ratio or a similar criterion.3The resulting portfolios are of variable composition and contain both call

and put options with 28, 14, or 7 days to maturity.Their realized excess returns over the IT holdings are very similar for

all of the optimization criteria. Using these realized returns, we then confirm with out-of-sample tests that irrespec-

tive of the selection criterion, the options portfolios would have increased, onaverage, the utility of any risk-averse IT

investor.The results are stronger for shorter maturity options than for their longer term counterparts in terms of both

profitability and the significance of the SD tests. Our results also hold in even stronger form if we assume that there is

no bid–ask spread and execute the OToption trades at the midpoint of the spread, but without distorting the data by

imposing put–call parity and eliminating ITM options. As a robustness check, we repeat our tests using options on the

CAC and DAXindices, as well as weekly options of the S&P 500 Index, and obtain similar results.

It is important to note that the out-of-sample SD test does not depend upon the portfolio selection criteria that

establish SD. The SD test compares two time series drawn from two different distributions and examines the null of

nondominance. The only requirement is that the observations be serially uncorrelated, a requirement that is verified

for all of the series used in our tests. Because the portfolios are chosen using only observables at every point of the

resulting time series, the out-of-sample test results identify a tradable anomaly insofar as an investorholding an index-

tracking tradable fund, such as SPDR, can increase their returns without incurring additional volatility risk or costs. In

fact, in all of the cases, the total volatility of the OT portfolios is lower than that of the volatility of the IT portfolios,

thereby precluding the possibility that the excess return is compensation for volatility risk. It is in this sense that we

claim that there exist mispriced indexoptions.

Although most options in the OT portfolios are OTM,more than 37% of the portfolios contain ITM calls and more

than 32% contain ITM puts. The portfolios include more than double the number of calls than puts and the call positions

are overwhelminglyshort positions, consistent with the practice of writing covered calls and contradicting the common

2Foran infinite horizon under transaction costs, the IT investor maximizes the utility of the flow of consumption (Constantinides, 1986).

3Specificportfolio selection criteria are imposed as we have many portfolios that satisfy our SD conditions.

CONSTANTINIDESET AL.299

1990 1995 2000 2005 2010

0

10

20

30

40

50

60

70

Year

Spread(%)

FIGURE 1 Median of proportional spreads around the midpoint price for ATM(K∕St=1)and OTM (K∕St=0.93)

puts with 28 and 7 days to maturity [Color figure can be viewed at wileyonlinelibrary.com]

Note: Solid darker(lighter) lines correspond to 28-day ATM(OTM) options. Dashed darker (lighter) lines correspond to

7-day ATM(OTM) options.

belief that puts rather than calls are overvalued.4An exception is the 2008–2009 period of the financial crisis when

there appears to be investor overreactionin the form of inflated put prices.

The potential errors implied by assuming away frictions are large. In Figure 1, we illustrate the observed bid–ask

spread, as a percentage of its midpoint, for selected put options for each yearof our dataset. The data for this important

variable, widely used as an indicator of option market illiquidity, clearly show two effects, a moneyness effect and a

maturity effect, with OTM and 7-day maturity options as the least liquid. Forthe least liquid 7-day OTM options, the

spread rarely dips below 30% and can be as high as 60% of its midpoint. Furthermore, there are clear indications that

the spread has increased over time for all maturities and degrees of moneyness, as shown by the regressions of all

spreads data (not just the annual medians) for the four time series in Figure 1 against a constant and a time trend.

Inthe absence of friction and market segmentation, put–call parity implies that if OTM puts are overpriced and short

positions are profitable after adjusting for risk, then ITM calls are also overpriced. Yet, Bondarenko (2014, table 1)

reports that long positions in ATM puts yield a negative and highly significant average monthly return of –0.39%,

whereas long positions in ATM calls yield a positive, but insignificant averagemonthly return of 0.04%. Many studies

present evidence that the option market is at least partially segmented. Chen, Joslin, and Ni (2019, figure 2) find that

calls and puts with the same moneyness are not substitutes for each other.Constantinides and Lian (2018) report that

4In unreported results, we allow the OT portfolios to short an optimally chosen quantity of the underlying. Short puts appear in very few dates, while the

preponderanceof short calls is maintained.