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A statistical analysis of investor preferences for portfolio selection

Abstract

Is the market portfolio consistent with the investors’ preferences for risk and return in the capital markets? The answer to this question is not so simple: on the one hand, the market portfolio (which is derived from a minimization of a coherent risk measurement) is an efficient portfolio in terms of risk and return and therefore should be consistent with the investor’s preference. On the other hand, since none of the current risk indices are considered to be coherent risk measurements, the market portfolio might not be consistent with the investors’ preference. This research attempts to fill this gap by invoking the Lorenz curve ranking method combined with compatible statistical tests, in order to rank the S&P 500 Index and its components in 2014–2017. We conclude that the S&P 500 Index is not considered to be the market portfolio from the investors’ point of view, but rather seen as another asset. In addition, we conclude that the investors exhibit a decreasing risk aversion behavior in ranking financial assets, which suggests that they are willing to take risks for higher rewards. This methodology presents a unique way to empirically examine the theoretical preference relation of von Neumann and Morgenstern.

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Notes

  1. 1.

    Knight (1921) clarifies the difference between risk and uncertainty conditions. According to him, under risk conditions each possible event has a probability (whether the probability is right or wrong). However, uncertainty conditions mean that it is not possible to know whether the probability exists, because the events are unknown. For example, risk conditions include estimating the values of a stock price, but uncertainty is not knowing whether this stock price even exists (because knowing that the stock exists means that there are possibilities for its price, hence its risk conditions).

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Acknowledgements

The authors share equal contribution in this article. The authors thank Prof. Haim Shalit from Ben-Gurion University of the Negev for his helpful comments on a previous version of this paper. The authors also thank Prof. Ralph Sonenshine from the American University and Prof. Christo Auret from University of the Witwatersrand for their helpful comments during the 26th Eurasia Business and Economics Society (EBES) Conference. Furthermore, the authors are grateful for the two anonymous reviewers’ helpful remarks and comments.

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Correspondence to Doron Nisani.

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Appendices

Appendix 1: Ranking of the S&P 500 Index and its components in 2014

$$ SRCL \succ_{5 - L} RSG \succ_{2 - L} ARE \succ_{2 - L} PG \succ_{4 - L} VNO \succ_{2 - L} PSA \succ_{3 - L} GGP \succ_{4 - L} AVB $$
$$ \succ_{2 - L} CHD \succ_{3 - L} WM \succ_{5 - L} TRV \succ_{3 - L} ESS \succ_{2 - L} ALL \succ_{3 - L} BRK.B \succ_{2 - L} CB $$
$$ \succ_{4 - L} FRT \succ_{2 - L} COST \succ_{4 - L} KIM \succ_{5 - L} UDR \succ_{3 - L} EQR \succ_{2 - L} PEP \succ_{3 - L} MAC $$
$$ \succ_{4 - L} SPG \succ_{3 - L} REG \succ_{2 - L} AWK \succ_{3 - L} SO \succ_{4 - L} MO \succ_{2 - L} HSIC \succ_{3 - L} SLG $$
$$ \succ_{3 - L} HCN \succ_{2 - L} EXR \succ_{3 - L} BXP \succ_{2 - L} AIV \succ_{3 - L} BDX \succ_{3 - L} MAA \succ_{2 - L} WFC $$
$$ \succ_{5 - L} ABC \succ_{3 - L} MAR \succ_{2 - L} CVS \succ_{5 - L} MMM \succ_{2 - L} AMT \succ_{3 - L} KR \succ_{2 - L} SRE $$
$$ \succ_{5 - L} DVA \succ_{2 - L} DRE \succ_{3 - L} DUK \succ_{2 - L} XEL \succ_{3 - L} O \succ_{2 - L} JNJ \succ_{3 - L} LNT $$
$$ \succ_{2 - L} SYK \succ_{4 - L} ORLY \succ_{3 - L} EIX \succ_{2 - L} ED \succ_{3 - L} DTE \succ_{4 - L} DPS \succ_{{2 - {\text{L}}}} ES $$
$$ \succ_{3 - L} GPC \succ_{3 - L} SHW \succ_{2 - L} AZO \succ_{4 - L} CMS \succ_{2 - L} CSCO \succ_{4 - L} BLL \succ_{2 - L} CTAS $$
$$ \succ_{3 - L} LLY \succ_{2 - L} PNW \succ_{3 - L} HD \succ_{2 - L} VTR \succ_{2 - L} HCP \succ_{2 - L} ETR \succ_{3 - L} LOW $$
$$ \succ_{2 - L} GD \succ_{3 - L} NI \succ_{2 - L} APH \succ_{3 - L} STZ \succ_{4 - L} LEG \succ_{2 - L} WEC \succ_{2 - L} UNP $$
$$ \succ_{2 - L} ESRX \succ_{2 - L} CHRW \succ_{2 - L} TDG \succ_{2 - L} EW \succ_{2 - L} SIG \succ_{5 - L} HBI \succ_{2 - L} EA $$
$$ \succ_{5 - L} LUV \succ_{2 - L} CNC \succ_{2 - L} RCL \succ_{2 - L} AVGO \succ_{2 - L} SWKS \succ_{1 - L} {\varvec{GSPC}} \succ_{2 - L} WMT $$
$$ \succ_{3 - L} MCD \succ_{2 - L} CLX \succ_{3 - L} KMB \succ_{2 - L} CL \succ_{5 - L} SYY \succ_{3 - L} MMC \succ_{2 - L} CINF $$
$$ \succ_{2 - L} PLD \succ_{3 - L} GIS \succ_{2 - L} FISV \succ_{4 - L} PDCO \succ_{2 - L} COL \succ_{3 - L} XL \succ_{3 - L} NEE $$
$$ \succ_{2 - L} ABT \succ_{2 - L} KO \succ_{3 - L} HST \succ_{2 - L} DLTR \succ_{5 - L} SCG \succ_{2 - L} EFX \succ_{6 - L} FIS $$
$$ \succ_{3 - L} SWK \succ_{3 - L} PCG \succ_{5 - L} LMT \succ_{2 - L} SBAC \succ_{4 - L} BF.B \succ_{3 - L} SNA \succ_{3 - L} PPL $$
$$ \succ_{6 - L} HRL \succ_{2 - L} ROST \succ_{4 - L} LH \succ_{3 - L} AEP \succ_{6 - L} VFC \succ_{6 - L} IFF \succ_{2 - L} MDT $$
$$ \succ_{5 - L} INTU \succ_{3 - L} DIS \succ_{3 - L} ADP \succ_{3 - L} DLR \succ_{2 - L} PPG \succ_{5 - L} PNC \succ_{3 - L} JWN $$
$$ \succ_{4 - L} IDXX \succ_{2 - L} DGX \succ_{4 - L} BK \succ_{3 - L} AEE \succ_{3 - L} UNH \succ_{2 - L} MSFT \succ_{4 - L} HIG $$
$$ \succ_{3 - L} NWL \succ_{4 - L} CTL \succ_{2 - L} D \succ_{4 - L} FDX \succ_{3 - L} CDNS \succ_{3 - L} NOC \succ_{2 - L} NKE $$
$$ \succ_{3 - L} APD \succ_{3 - L} INTC \succ_{2 - L} MCK \succ_{3 - L} AAPL \succ_{2 - L} ZBH \succ_{3 - L} TGT \succ_{3 - L} ZTS $$
$$ \succ_{2 - L} ORCL \succ_{3 - L} PEG \succ_{2 - L} CBG \succ_{5 - L} MCO \succ_{2 - L} AAP \succ_{3 - L} NDAQ \succ_{4 - L} ADM $$
$$ \succ_{2 - L} RTN \succ_{4 - L} TXN \succ_{2 - L} APTV \succ_{4 - L} EQIX \succ_{3 - L} EXC \succ_{2 - L} TAP \succ_{4 - L} RHI $$
$$ \succ_{4 - L} GLW \succ_{3 - L} CSX \succ_{2 - L} HPQ \succ_{5 - L} GPN \succ_{2 - L} COO \succ_{3 - L} ALLE \succ_{4 - L} LB $$
$$ \succ_{2 - L} ANTM \succ_{4 - L} MTD \succ_{2 - L} AET \succ_{3 - L} M \succ_{2 - L} MS \succ_{3 - L} LLL \succ_{2 - L} WDC $$
$$ \succ_{3 - L} FL \succ_{2 - L} HUM \succ_{3 - L} AMAT \succ_{2 - L} AMGN \succ_{2 - L} CMG \succ_{3 - L} LRCX \succ_{4 - L} UHS $$
$$ \succ_{2 - L} IRM \succ_{3 - L} NCLH \succ_{3 - L} HCA \succ_{2 - L} KMX \succ_{4 - L} COTY \succ_{2 - L} MNST \succ_{4 - L} AYI $$
$$ \succ_{2 - L} AGN \succ_{2 - L} FFIV \succ_{2 - L} ARNC \succ_{5 - L} ALK \succ_{2 - L} DAL \succ_{2 - L} AAL \succ_{2 - L} MU $$
$$ \succ_{2 - L} ILMN \succ_{1 - L} BAX \succ_{3 - L} UPS \succ_{2 - L} MKC \succ_{4 - L} ITW \succ_{2 - L} TMK \succ_{3 - L} XRAY $$
$$ \succ_{3 - L} USB \succ_{2 - L} PAYX \succ_{3 - L} MTB \succ_{2 - L} WY \succ_{2 - L} PBCT \succ_{3 - L} CPB \succ_{3 - L} PX $$
$$ \succ_{2 - L} AJG \succ_{3 - L} T \succ_{3 - L} RE \succ_{2 - L} HSY \succ_{2 - L} VRSK \succ_{3 - L} K \succ_{3 - L} VAR \succ_{2 - L} DE $$
$$ \succ_{5 - L} HON \succ_{5 - L} PM \succ_{2 - L} VZ \succ_{2 - L} ROP \succ_{2 - L} SJM \succ_{3 - L} UTX \succ_{2 - L} JBHT $$
$$ \succ_{3 - L} MDLZ \succ_{2 - L} AFL \succ_{3 - L} CCI \succ_{4 - L} ACN \succ_{2 - L} PGR \succ_{3 - L} SNPS \succ_{3 - L} MSI $$
$$ \succ_{4 - L} NTRS \succ_{2 - L} PFE \succ_{4 - L} AIZ \succ_{4 - L} WLTW \succ_{2 - L} EL \succ_{4 - L} DHR \succ_{5 - L} CAG $$
$$ \succ_{2 - L} MON \succ_{4 - L} BBT \succ_{2 - L} COF \succ_{2 - L} ECL \succ_{5 - L} AON \succ_{2 - L} JCI \succ_{2 - L} IBM $$
$$ \succ_{4 - L} TROW \succ_{2 - L} GS \succ_{5 - L} HAS \succ_{3 - L} CNP \succ_{5 - L} JPM \succ_{4 - L} HRS \succ_{2 - L} MRK $$
$$ \succ_{2 - L} CME \succ_{4 - L} WAT \succ_{3 - L} CAH \succ_{2 - L} SBUX \succ_{5 - L} CMCSA \succ_{2 - L} V \succ_{2 - L} DFS $$
$$ \succ_{2 - L} DXC \succ_{4 - L} TEL \succ_{2 - L} FE \succ_{2 - L} PKG \succ_{5 - L} QCOM \succ_{2 - L} ADI \succ_{2 - L} IPG $$
$$ \succ_{2 - L} RMD \succ_{2 - L} WYN \succ_{2 - L} YUM \succ_{3 - L} NSC \succ_{2 - L} HLT \succ_{2 - L} HOLX \succ_{3 - L} IQV $$
$$ \succ_{4 - L} IT \succ_{2 - L} KMI \succ_{3 - L} CBOE \succ_{2 - L} HII \succ_{2 - L} CI \succ_{3 - L} TWX \succ_{4 - L} CHTR $$
$$ \succ_{2-L}NVDA \succ_{3-L}SEE \succ_{2-L}ADBE \succ_{3-L}RHT \succ_{4-L}KLAC \succ_{2-L}DISH \succ_{3-L}ABBV$$
$$ \succ_{2-L}ULTA \succ_{5-L}WHR \succ_{3-L}ADSK \succ_{3-L}AKAM \succ_{2-L}MYL \succ_{6-L}WBA \succ_{2-L}STX$$
$$ \succ_{2-L}ANDV \succ_{2-L}ISRG \succ_{2-L}CELG \succ_{2-L}UAA \succ_{2-L}FB \succ_{3-L}GILD \succ_{4-L}REGN$$
$$ \succ_{2-L}UAL \succ_{1-L}L \succ_{2-L}GE \succ_{2-L}XOM \succ_{2-L}TSS \succ_{2-L}MOS \succ_{3-L}STI \succ_{2-L}IP$$
$$ \succ_{3-L}SPGI \succ_{2-L}RL \succ_{3-L}OMC \succ_{4-L}GWW \succ_{2-L}AIG \succ_{4-L}EMR \succ_{3-L}PCAR$$
$$ \succ_{2-L}CVX \succ_{4-L}AME \succ_{5-L}AVY \succ_{4-L}HBAN \succ_{2-L}PKI \succ_{3-L}ANSS \succ_{3-L}AXP$$
$$ \succ_{2-L}CAT \succ_{3-L}CA \succ_{4-L}FITB \succ_{2-L}TJX \succ_{3-L}TMO \succ_{3-L}AOS \succ_{4-L}EXPD$$
$$ \succ_{2-L}NLSN \succ_{3-L}UNM \succ_{6-L}BLK \succ_{2-L}RJF \succ_{2-L}FOX \succ_{4-L}BA \succ_{3-L}FAST$$
$$ \succ_{4-L}IR \succ_{2-L}C \succ_{2-L}TIF \succ_{3-L}STT \succ_{2-L}BMY \succ_{4-L}DRI \succ_{4-L}AMP \succ_{2-L}BAC$$
$$ \succ_{3-L}BEN \succ_{3-L}F \succ_{2-L}EBAY \succ_{4-L}CMI \succ_{5-L}IVZ \succ_{2-L}RF \succ_{3-L}DG \succ_{3-L}FOXA$$
$$ \succ_{4-L}PFG \succ_{2-L}ZION \succ_{4-L}KEY \succ_{2-L}CERN \succ_{3-L}ICE \succ_{2-L}COP \succ_{3-L}CMA$$
$$ \succ_{3-L}VRSN \succ_{4-L}TSCO \succ_{6-L}CCL \succ_{2-L}GOOG \succ_{6-L}FLIR \succ_{4-L}MCHP \succ_{2-L}PH$$
$$ \succ_{4-L}MHK \succ_{5-L}CF \succ_{2-L}MET \succ_{2-L}HOG \succ_{4-L}AES \succ_{6-L}WU \succ_{6-L}GPS$$
$$ \succ_{3-L}SYMC \succ_{2-L}HRB \succ_{3-L}ALB \succ_{2-L}XYL \succ_{4-L}SLB \succ_{3-L}WMB \succ_{2-L}NTAP$$
$$ \succ_{3-L}ROK \succ_{3-L}KSS \succ_{2-L}MA \succ_{3-L}ATVI \succ_{4-L}CTXS \succ_{2-L}LEN \succ_{3-L}XRX$$
$$ \succ_{3-L}EMN \succ_{3-L}XLNX \succ_{2-L}BSX \succ_{3-L}VMC \succ_{2-L}CTSH \succ_{5-L}DWDP$$
$$ \succ_{3-L}GRMN \succ_{2-L}MAS \succ_{2-L}DHI \succ_{2-L}EXPE \succ_{3-L}TSN \succ_{2-L}URI \succ_{1-L}NWS$$
$$ \succ_{2-L}NUE \succ_{3-L}VIAB \succ_{2-L}NWSA \succ_{2-L}LUK \succ_{3-L}SNI \succ_{2-L}FMC \succ_{3-L}GOOGL$$
$$ \succ_{2-L}OXY \succ_{3-L}PRU \succ_{2-L}PHM \succ_{3-L}LNC \succ_{2-L}PVH \succ_{2-L}JEC \succ_{3-L}PNR$$
$$ \succ_{3-L}HES \succ_{2-L}TXT \succ_{4-L}BWA \succ_{3-L}DOV \succ_{2-L}AMG \succ_{3-L}ETN \succ_{2-L}ADS$$
$$ \succ_{3-L}NRG \succ_{4L}PSX \succ_{4-L}NOV \succ_{2-L}PRGO \succ_{3-L}GM \succ_{3-L}SCHW \succ_{2-L}FBHS$$
$$ \succ_{2-L}DVN \succ_{3-L}PCLN \succ_{4-L}BHGE \succ_{4-L}KSU \succ_{2-L}PWR \succ_{2-L}GT \succ_{3-L}JNPR$$
$$ \succ_{2-L}FTI \succ_{5-L}MRO \succ_{3-L}MLM \succ_{3-L}LYB \succ_{2-L}MPC \succ_{2-L}APC \succ_{3-L}EOG$$
$$ \succ_{2-L}VLO \succ_{5-L}OKE \succ_{2-L}ETFC \succ_{1-L}CBS \succ_{2-L}FLR \succ_{2-L}APA \succ_{2-L}EQT$$
$$ \succ_{1-L}MAT \succ_{2-L}TPR \succ_{3-L}A \succ_{2-L}LKQ \succ_{3-L}COG \succ_{2-L}ALGN \succ_{3-L}MGM$$
$$ \succ_{2-L}FCX \succ_{3-L}KORS \succ_{2-L}NBL \succ_{3-L}RRC \succ_{4-L}HAL \succ_{2-L}BIIB \succ_{3-L}AMZN$$
$$ \succ_{2-L}ALXN \succ_{2-L}WYNN \succ_{5-L}CRM \succ_{2-L}XEC \succ_{5-L}HP \succ_{2-L}VRTX \succ_{2-L}NEM$$
$$ \succ_{3-L}NFLX \succ_{4-L}PXD \succ_{2-L}CXO \succ_{3-L}BBY \succ_{2-L}CHK \succ_{3-L}TRIP \succ_{3-L}NFX$$
$$ \succ_{2-L}AMD \succ_{2-L}DISCK \succ_{2-L}INCY \succ_{3-L}DISCA$$

Appendix 2: Ranking of the S&P 500 Index and its components in 2015

$$CLX \succ_{3-L}KO \succ_{2-L}PEP \succ_{3-L}WLTW \succ_{3-L}RE \succ_{2-L}CCI \succ_{3-L}CHD \succ_{3-L}WM$$
$$ \succ_{3-L}RSG \succ_{3-L}ABC \succ_{2-L}VZ \succ_{4-L}MCD \succ_{4-L}XL \succ_{3-L}T \succ_{3-L}PSA \succ_{2-L}SYY$$
$$ \succ_{4-L}CPB \succ_{3-L}K \succ_{3-L}HRL \succ_{2-L}GIS \succ_{3-L}INFO \succ_{5-L}PAYX \succ_{2-L}DPS$$
$$ \succ_{2-L}SJM \succ_{5-L}COST \succ_{3-L}AZO \succ_{5-L}EFX \succ_{2-L}PGR \succ_{4-L}CINF \succ_{3-L}SNA$$
$$ \succ_{3-L}STZ \succ_{2-L}NOC \succ_{3-L}AWK \succ_{3-L}EXR \succ_{2-L}CTAS \succ_{3-L}FISV \succ_{3-L}VRSN$$
$$ \succ_{2-L}HSIC \succ_{2-L}BF.B \succ_{3-L}BDX \succ_{3-L}ROP \succ_{2-L}DHR \succ_{4-L}MO \succ_{2-L}WAT$$
$$ \succ_{3-L}HD \succ_{3-L}GE \succ_{3-L}PKI \succ_{3-L}KR \succ_{2-L}NKE \succ_{3-L}AIZ \succ_{2-L}ALLE$$
$$ \succ_{3-L}ORLY \succ_{3-L}ULTA \succ_{5-L}SNPS \succ_{2-L}LH \succ_{3-L}ECL \succ_{3-L}AYI \succ_{3-L}GPN$$
$$ \succ_{4-L}TSS \succ_{2-L}TDG \succ_{3-L}ATVI \succ_{2-L}VRSK \succ_{3-L}ICE \succ_{2-L}DIS \succ_{2-L}GOOGL$$
$$ \succ_{3-L}AMZN \succ_{3-L}EQIX \succ_{3-L}HOLX \succ_{2-L}GOOG \succ_{3-L}ADBE \succ_{3-L}AOS \succ_{2-L}CI$$
$$ \succ_{2-L}NVDA \succ_{1-L}{\varvec{G}}{\varvec{S}}{\varvec{P}}{\varvec{C}} \succ_{2-L}LMT \succ_{2-L}MKC \succ_{2-L}AJG \succ_{3-L}KMB \succ_{4-L}DVA$$
$$ \succ_{2-L}JNJ \succ_{2-L}CB \succ_{3-L}TMK \succ_{2-L}PM \succ_{3-L}OMC \succ_{5-L}TRV \succ_{2-L}MMC$$
$$ \succ_{5-L}SWK \succ_{2-L}RTN \succ_{2-L}COL \succ_{3-L}GD \succ_{4-L}SO \succ_{2-L}PBCT \succ_{4-L}ACN \succ_{2-L}D$$
$$ \succ_{3-L}XRAY \succ_{4-L}IT \succ_{3-L}ANSS \succ_{3-L}MAA \succ_{2-L}MMM \succ_{3-L}NEE \succ_{3-L}FRT$$
$$ \succ_{4-L}ADP \succ_{3-L}DLR \succ_{3-L}UDR \succ_{2-L}HON \succ_{3-L}CBOE \succ_{3-L}ESS \succ_{5-L}AVB$$
$$ \succ_{2-L}PFE \succ_{4-L}CAH \succ_{3-L}HRS \succ_{5-L}MDLZ \succ_{3-L}XEL \succ_{3-L}IFF \succ_{2-L}PDCO$$
$$ \succ_{4-L}ED \succ_{2-L}AIG \succ_{2-L}AVY \succ_{4-L}NDAQ \succ_{2-L}MDT \succ_{4-L}MA \succ_{3-L}MSI$$
$$ \succ_{4-L}EL \succ_{5-L}SPG \succ_{2-L}TMO \succ_{3-L}ISRG \succ_{5-L}REG \succ_{6-L}EQR \succ_{2-L}TAP$$
$$ \succ_{4-L}ARE \succ_{2-L}V \succ_{4-L}DTE \succ_{3-L}NLSN \succ_{4-L}CMS \succ_{2-L}TJX \succ_{4-L}LOW$$
$$ \succ_{4-L}CAG \succ_{2-L}ESRX \succ_{3-L}MTD \succ_{2-L}LB \succ_{6-L}MCO \succ_{3-L}ES \succ_{3-L}IQV \succ_{2-L}O$$
$$ \succ_{2-L}NWL \succ_{3-L}SPGI \succ_{4-L}SPCL \succ_{2-L}RHT \succ_{2-L}CDNS \succ_{2-L}LKQ \succ_{2-L}BSX$$
$$ \succ_{5-L}HAS \succ_{2-L}MHK \succ_{2-L}CCL \succ_{3-L}JNPR \succ_{3-L}TSN \succ_{2-L}FBHS \succ_{4-L}ROST$$
$$ \succ_{3-L}LLY \succ_{4-L}INTU \succ_{2-L}FB \succ_{2-L}VMC \succ_{3-L}HUM \succ_{2-L}EW \succ_{2-L}MNST$$
$$ \succ_{3-L}CRM \succ_{2-L}EA \succ_{2-L}EXPE \succ_{4-L}ALK \succ_{3-L}VLO \succ_{2-L}REGN \succ_{2-L}ANDV$$
$$ \succ_{2-L}NFLX \succ_{1-L}PG \succ_{3-L}BRK.B \succ_{2-L}L \succ_{5-L}CL \succ_{2-L}UPS \succ_{3-L}AON$$
$$ \succ_{3-L}AFL \succ_{2-L}ITW \succ_{2-L}PX \succ_{3-L}CVS \succ_{2-L}TROW \succ_{4-L}WFC \succ_{2-L}ZBH$$
$$ \succ_{3-L}ALL \succ_{3-L}BA \succ_{4-L}PNW \succ_{6-L}SYK \succ_{2-L}USB \succ_{3-L}LLL \succ_{3-L}SLG$$
$$ \succ_{4-L}AEP \succ_{2-L}EXPD \succ_{3-L}PCG \succ_{2-L}AMT \succ_{3-L}HSY \succ_{2-L}SRE \succ_{4-L}TEL$$
$$ \succ_{3-L}LNT \succ_{3-L}VAR \succ_{2-L}AEE \succ_{2-L}BXP \succ_{3-L}XYL \succ_{5-L}LEG \succ_{3-L}JBHT$$
$$ \succ_{2-L}DUK \succ_{3-L}AME \succ_{3-L}PLD \succ_{2-L}PNC \succ_{3-L}HIG \succ_{3-L}WEC \succ_{2-L}APH$$
$$ \succ_{5-L}EIX \succ_{3-L}CMCSA \succ_{4-L}DRE \succ_{5-L}DG \succ_{2-L}APD \succ_{6-L}MON \succ_{4-L}IR$$
$$ \succ_{5-L}SCG \succ_{3-L}BBT \succ_{4-L}CA \succ_{2-L}ABT \succ_{4-L}TGT \succ_{3-L}AIV \succ_{2-L}MCK$$
$$ \succ_{3-L}PPL \succ_{3-L}KIM \succ_{2-L}JPM \succ_{2-L}MRK \succ_{3-L}ADS \succ_{3-L}CME \succ_{2-L}CSCO$$
$$ \succ_{3-L}IPG \succ_{2-L}SHW \succ_{3-L}VNO \succ_{3-L}BMY \succ_{2-L}SBAC \succ_{3-L}NTRS \succ_{3-L}FIS$$
$$ \succ_{2-L}A \succ_{3-L}XLNX \succ_{3-L}SYF \succ_{2-L}SIG \succ_{4-L}BLL \succ_{4-L}SEE \succ_{5-L}DGX$$
$$ \succ_{2-L}HBAN \succ_{3-L}MCHP \succ_{2-L}MSFT \succ_{3-L}CFG \succ_{2-L}ANTM \succ_{4-L}FL \succ_{2-L}HRB$$
$$ \succ_{3-L}DRI \succ_{2-L}CTSH \succ_{3-L}WBA \succ_{2-L}PCLN \succ_{2-L}UNH \succ_{2-L}TSCO \succ_{3-L}MAC$$
$$ \succ_{2-L}ZTS \succ_{3-L}CHTR \succ_{4-L}APTV \succ_{4-L}RMD \succ_{2-L}MAS \succ_{3-L}HII \succ_{4-L}DLTR$$
$$ \succ_{2-L}ALGN \succ_{3-L}DWDP \succ_{4-L}AAP \succ_{2-L}NCLH \succ_{4-L}HBI \succ_{3-L}CTXS \succ_{3-L}GT$$
$$ \succ_{2-L}RCL \succ_{3-L}AGN \succ_{4-L}AET \succ_{2-L}PSX \succ_{2-L}MLM \succ_{3-L}DHI \succ_{5-L}UAA$$
$$ \succ_{2-L}ETFC \succ_{2-L}COTY \succ_{3-L}CNC \succ_{2-L}AVGO \succ_{2-L}INCY \succ_{1-L}UTX \succ_{4-L}GPC$$
$$ \succ_{2-L}WY \succ_{3-L}JCI \succ_{4-L}FLIR \succ_{2-L}WMT \succ_{3-L}RJF \succ_{2-L}FDX \succ_{3-L}HCN$$
$$ \succ_{2-L}PPG \succ_{3-L}DE \succ_{4-L}IBM \succ_{2-L}BLK \succ_{3-L}F \succ_{2-L}WYN \succ_{4-L}UNM$$
$$ \succ_{4-L}GWW \succ_{3-L}BK \succ_{2-L}ETR \succ_{4-L}AXP \succ_{3-L}MTB \succ_{3-L}GS \succ_{4-L}GGP$$
$$ \succ_{2-L}ORCL \succ_{3-L}PEG \succ_{3-L}HCP \succ_{2-L}XOM \succ_{4-L}DFS \succ_{3-L}GM \succ_{2-L}ROK$$
$$ \succ_{3-L}WU \succ_{2-L}EMR \succ_{4-L}TXT \succ_{3-L}FE \succ_{3-L}STI \succ_{2-L}FAST \succ_{3-L}CERN$$
$$ \succ_{-3L}LUK \succ_{4-L}COO \succ_{2-L}INTC \succ_{4-L}COF \succ_{5-L}VFC \succ_{2-L}AMP \succ_{4-L}C$$
$$ \succ_{3-L}RHI \succ_{4-L}CBG \succ_{2-L}CBS \succ_{4-L}CNP \succ_{4-L}TXN \succ_{3-L}PH \succ_{4-L}FITB$$
$$ \succ_{4-L}TWX \succ_{2-L}SYMC \succ_{3-L}CHRW \succ_{4-L}FOX \succ_{2-L}MET \succ_{2-L}MAR \succ_{4-L}FOXA$$
$$ \succ_{3-L}SNI \succ_{4-L}NWS \succ_{4-L}VTR \succ_{2-L}DOV \succ_{4-L}STT \succ_{3-L}ADSK \succ_{4-L}DXC$$
$$ \succ_{2-L}EMN \succ_{4-L}AAPL \succ_{3-L}GILD \succ_{2-L}EXC \succ_{4-L}KLAC \succ_{2-L}JEC \succ_{3-L}FFIV$$
$$ \succ_{2-L}IRM \succ_{3-L}AMGN \succ_{2-L}CMG \succ_{3-L}LRCX \succ_{4-L}AKAM \succ_{3-L}PKG \succ_{5-L}YUM$$
$$ \succ_{2-L}ADI \succ_{3-L}SCHW \succ_{5-L}IDXX \succ_{2-L}LEN \succ_{2-L}GRMN \succ_{3-L}UHS \succ_{2-L}HCA$$
$$ \succ_{3-L}PRGO \succ_{2-L}TRIP \succ_{6-L}QCOM \succ_{2-L}LUV \succ_{4-L}KSS \succ_{2-L}LYB \succ_{3-L}ABBV$$
$$ \succ_{4-L}CELG \succ_{2-L}MPC \succ_{1-L}BEN \succ_{2-L}DISH \succ_{3-L}ETN \succ_{3-L}BAC \succ_{2-L}IP$$
$$ \succ_{4-L}IVZ \succ_{2-L}GLW \succ_{3-L}ADM \succ_{2-L}HLT \succ_{3-L}KMX \succ_{3-L}PFG \succ_{2-L}NSC$$
$$ \succ_{3-L}MS \succ_{3-L}PRU \succ_{2-L}SLB \succ_{3-L}CMI \succ_{3-L}PCAR \succ_{3-L}KEY \succ_{2-L}UNP$$
$$ \succ_{4-L}CAT \succ_{2-L}GPS \succ_{4-L}JWN \succ_{3-L}OXY \succ_{3-L}CVX \succ_{4-L}NWSA \succ_{2-L}AMG$$
$$ \succ_{3-L}ZION \succ_{3-L}FLS \succ_{5-L}LNC \succ_{2-L}RF \succ_{2-L}CTL \succ_{4-L}NTAP \succ_{3-L}CMA$$
$$ \succ_{2-L}NUE \succ_{2-L}BWA \succ_{3-L}CSX \succ_{4-L}HST \succ_{4-L}AMAT \succ_{2-L}TIF \succ_{4-L}HOG$$
$$ \succ_{2-L}PNR \succ_{3-L}XRX \succ_{2-L}MAT \succ_{5-L}TPR \succ_{2-L}FMC \succ_{4-L}FLR \succ_{3-L}AES$$
$$ \succ_{4-L}DAL \succ_{2-L}WHR \succ_{2-L}DISCK \succ_{4-L}BBY \succ_{2-L}DISCA \succ_{3-L}PHM \succ_{3-L}ALB$$
$$ \succ_{2-L}ALXN \succ_{3-L}HPQ \succ_{2-L}ILMN \succ_{3-L}MGM \succ_{2-L}SWKS \succ_{6-L}BIIB \succ_{2-L}VRTX$$
$$ \succ_{2-L}NFX \succ_{1-L}RL \succ_{4-L}M \succ_{2-L}COP \succ_{4-L}KSU \succ_{3-L}MOS \succ_{2-L}EQT \succ_{2-L}EOG$$
$$ \succ_{4-L}PVH \succ_{2-L}HAL \succ_{2-L}BHGE \succ_{3-L}WDC \succ_{4-L}NAVI \succ_{2-L}VIAB \succ_{3-L}HES$$
$$ \succ_{4-L}CF \succ_{2-L}UAL \succ_{2-L}MYL \succ_{2-L}AAL \succ_{3-L}FTI \succ_{2-L}XEC \succ_{2-L}COG$$
$$ \succ_{3-L}ARNC \succ_{4-L}PXD \succ_{2-L}STX \succ_{2-L}URI \succ_{2-L}CXO \succ_{2-L}NEM \succ_{2-L}AMD$$
$$ \succ_{1-L}NOV \succ_{2-L}KMI \succ_{3-L}APC \succ_{2-L}APA \succ_{3-L}NBL \succ_{2-L}HP \succ_{3-L}DVN$$
$$ \succ_{2 - L} WMB \succ_{2 - L} OKE \succ_{2 - L} NRG \succ_{1 - L} MRO \succ_{2 - L} MU \succ_{2 - L} WYNN \succ_{3 - L} RRC $$
$$ \succ_{1 - L} BAX \succ_{3 - L} KORS \succ_{2 - L} PWR \succ_{2 - L} EBAY \succ_{2 - L} FCX \succ_{2 - L} NI \succ_{3 - L} CHK $$

Appendix 3: Ranking of the S&P 500 Index and its components in 2016

$$ JNJ \succ_{5 - L} WM \succ_{3 - L} UPS \succ_{2 - L} {\varvec{GSPC}} \succ_{3 - L} RSG \succ_{2 - L} ALL \succ_{2 - L} MMM \succ_{4 - L} SYY $$
$$ \succ_{2 - L} MMC \succ_{2 - L} BRK.B \succ_{2 - L} PG \succ_{6 - L} T \succ_{2 - L} LMT \succ_{3 - L} NOC \succ_{2 - L} RE $$
$$ \succ_{2 - L} CMCSA \succ_{4 - L} CINF \succ_{4 - L} ITW \succ_{3 - L} AFL \succ_{4 - L} APH \succ_{2 - L} AON \succ_{3 - L} MCD $$
$$ \succ_{4 - L} ADP \succ_{4 - L} MO \succ_{2 - L} UNH \succ_{3 - L} UTX \succ_{3 - L} RTN \succ_{3 - L} AJG \succ_{2 - L} HON $$
$$ \succ_{5 - L} TRV \succ_{3 - L} CTAS \succ_{2 - L} SNPS \succ_{3 - L} GD \succ_{3 - L} EXPD \succ_{3 - L} CHRW \succ_{2 - L} SO $$
$$ \succ_{2 - L} LLL \succ_{2 - L} PM \succ_{3 - L} DGX \succ_{3 - L} SYK \succ_{2 - L} TMK \succ_{3 - L} ES \succ_{2 - L} DHR \succ_{2 - L} HII $$
$$ \succ_{2 - L} TWX \succ_{3 - L} PH \succ_{5 - L} IDXX \succ_{2 - L} FFIV \succ_{2 - L} MCHP \succ_{3 - L} IP \succ_{3 - L} PWR $$
$$ \succ_{3 - L} CHTR \succ_{2 - L} CMI \succ_{2 - L} DXC \succ_{2 - L} AMAT \succ_{4 - L} MLM \succ_{5L} ALGN \succ_{2 - L} ALB $$
$$ \succ_{4 - L} NVDA \succ_{2 - L} CMA \succ_{2 - L} OKE \succ_{2 - L} NEM \succ_{2 - L} AMD \succ_{1 - L} PEP \succ_{2 - L} PGR $$
$$ \succ_{5 - L} KO \succ_{3 - L} CL \succ_{2 - L} CB \succ_{3 - L} VZ \succ_{2 - L} VRSK \succ_{3 - L} L \succ_{3 - L} DTE \succ_{2 - L} GE $$
$$ \succ_{4 - L} GIS \succ_{3 - L} MKC \succ_{3 - L} XYL \succ_{3 - L} PCG \succ_{2 - L} DIS \succ_{3 - L} FISV \succ_{3 - L} D $$
$$ \succ_{3 - L} PNW \succ_{2 - L} PAYX \succ_{3 - L} WMT \succ_{3 - L} CLX \succ_{4 - L} EIX \succ_{2 - L} CBOE \succ_{4 - L} NEE $$
$$ \succ_{3 - L} PX \succ_{3 - L} FRT \succ_{5 - L} CMS \succ_{2 - L} K \succ_{3 - L} MSI \succ_{4 - L} XEL \succ_{3 - L} CME \succ_{3 - L} SCG $$
$$ \succ_{2 - L} NDAQ \succ_{4 - L} XOM \succ_{4 - L} AEE \succ_{2 - L} PFE \succ_{3 - L} AZO \succ_{3 - L} HSY \succ_{5 - L} DUK $$
$$ \succ_{2 - L} MRK \succ_{4 - L} IBM \succ_{3 - L} AEP \succ_{4 - L} INFO \succ_{5 - L} ED \succ_{2 - L} WEC \succ_{3 - L} IT \succ_{5 - L} SJM $$
$$ \succ_{2 - L} ORCL \succ_{5 - L} APD \succ_{3 - L} TXN \succ_{2 - L} TJX \succ_{4 - L} OMC \succ_{3 - L} AWK \succ_{2 - L} FIS $$
$$ \succ_{3 - L} CPB \succ_{3 - L} PEG \succ_{3 - L} CNP \succ_{2 - L} HD \succ_{4 - L} LEG \succ_{3 - L} INTU \succ_{4 - L} USB $$
$$ \succ_{2 - L} COO \succ_{3 - L} GPC \succ_{4 - L} KHC \succ_{4 - L} SWK \succ_{3 - L} DRE \succ_{2 - L} VAR \succ_{3 - L} ROST $$
$$ \succ_{3 - L} JBHT \succ_{3 - L} DWDP \succ_{4 - L} KLAC \succ_{5 - L} HRS \succ_{2 - L} CSCO \succ_{4 - L} ISRG \succ_{3L} ACN $$
$$ \succ_{3 - L} NI \succ_{4 - L} GLW \succ_{2 - L} CDNS \succ_{3 - L} DE \succ_{4 - L} FDX \succ_{2 - L} MTD \succ_{3 - L} CA \succ_{3 - L} DRI $$
$$ \succ_{4 - L} BAX \succ_{2 - L} ICE \succ_{4 - L} AMT \succ_{3 - L} AIG \succ_{3 - L} GWW \succ_{4 - L} ROK \succ_{4 - L} XLNX $$
$$ \succ_{2 - L} COL \succ_{3 - L} PNC \succ_{3 - L} RMD \succ_{3 - L} BSX \succ_{4 - L} ARE \succ_{2 - L} ORLY \succ_{3 - L} AVY $$
$$ \succ_{3 - L} WU \succ_{4 - L} FLIR \succ_{4 - L} DFS \succ_{2 - L} MSFT \succ_{4 - L} JPM \succ_{3 - L} ZTS \succ_{5 - L} ADI $$
$$ \succ_{2 - L} ANSS \succ_{3 - L} PLD \succ_{2 - L} CVX \succ_{4 - L} HAS \succ_{3 - L} EXC \succ_{2 - L} AXP \succ_{4 - L} AIZ $$
$$ \succ_{3 - L} FAST \succ_{4 - L} AAPL \succ_{4 - L} IR \succ_{2 - L} UNP \succ_{3 - L} O \succ_{4 - L} ZBH \succ_{2 - L} CBS $$
$$ \succ_{5 - L} NLSN \succ_{2 - L} JCI \succ_{3 - L} GRMN \succ_{3 - L} MTB \succ_{2 - L} ULTA \succ_{4 - L} DLR \succ_{2 - L} NUE $$
$$ \succ_{6 - L} CAG \succ_{2 - L} QCOM \succ_{2 - L} SYMC \succ_{2 - L} YUM \succ_{2 - L} FMC \succ_{3 - L} ZION \succ_{2 - L} HPE $$
$$ \succ_{2 - L} HAL \succ_{2 - L} RF \succ_{2 - L} XEC \succ_{1 - L} COST \succ_{5 - L} KMB \succ_{2 - L} DPS \succ_{3 - L} ETR $$
$$ \succ_{2 - L} PPL \succ_{3 - L} REG \succ_{5 - L} BDX \succ_{5 - L} CHD \succ_{2 - L} CCI \succ_{3 - L} BF.B \succ_{2 - L} MDT $$
$$ \succ_{2 - L} ECL \succ_{3 - L} SBUX \succ_{5 - L} GOOG \succ_{2 - L} EL \succ_{3 - L} ROP \succ_{3 - L} GOOGL \succ_{3 - L} SRE $$
$$ \succ_{2 - L} SPG \succ_{3 - L} AVB \succ_{4 - L} LH \succ_{2 - L} MA \succ_{3 - L} BXP \succ_{2 - L} MAC \succ_{3 - L} HSIC $$
$$ \succ_{3 - L} BLL \succ_{3 - L} PBCT \succ_{2 - L} WBA \succ_{5 - L} VNO \succ_{2 - L} DVA \succ_{4 - L} V \succ_{3 - L} KIM $$
$$ \succ_{3 - L} EFX \succ_{2 - L} XL \succ_{4 - L} TMO \succ_{3 - L} TEL \succ_{2 - L} XRAY \succ_{3 - L} IPG \succ_{3 - L} BBT $$
$$ \succ_{2 - L} SNA \succ_{3 - L} EMR \succ_{3 - L} WAT \succ_{2 - L} TAP \succ_{5 - L} AME \succ_{3 - L} ESS \succ_{4 - L} CVS $$
$$ \succ_{3 - L} HIG \succ_{4 - L} INTC \succ_{2 - L} TROW \succ_{3 - L} LOW \succ_{3 - L} TGT \succ_{3 - L} AIV \succ_{2 - L} SPGI $$
$$ \succ_{4 - L} IFF \succ_{3 - L} ALLE \succ_{3 - L} MAA \succ_{3 - L} ETN \succ_{3 - L} AAP \succ_{4 - L} SHW \succ_{2 - L} STZ $$
$$ \succ_{3 - L} MON \succ_{3 - L} ADBE \succ_{2 - L} PCAR \succ_{3 - L} PPG \succ_{2 - L} IQV \succ_{3 - L} JEC \succ_{3 - L} AOS $$
$$ \succ_{2 - L} FOX \succ_{3 - L} UDR \succ_{3 - L} FOXA \succ_{4 - L} MAR \succ_{6 - L} BA \succ_{2 - L} SLB \succ_{3 - L} CSX $$
$$ \succ_{4 - L} WLTW \succ_{3 - L} EQIX \succ_{3 - L} A \succ_{2 - L} WFC \succ_{3 - L} BLK \succ_{3 - L} FB \succ_{4 - L} IRM $$
$$ \succ_{2 - L} PSX \succ_{3 - L} MHK \succ_{3 - L} NSC \succ_{2 - L} AET \succ_{3 - L} BK \succ_{2 - L} TXT \succ_{3 - L} FL $$
$$ \succ_{4 - L} VMC \succ_{2 - L} CAT \succ_{3 - L} HCA \succ_{3 - L} TDG \succ_{2 - L} PKI \succ_{4 - L} FBHS \succ_{3 - L} NTRSS $$
$$ \succ_{3 - L} SNI \succ_{2 - L} HUM \succ_{3 - L} CTXS \succ_{3 - L} GS \succ_{2 - L} EMN \succ_{4 - L} DOV \succ_{3 - L} WHR $$
$$ \succ_{2 - L} DG \succ_{3 - L} LKQ \succ_{3 - L} PCLN \succ_{2 - L} HLT \succ_{3 - L} DLTR \succ_{4 - L} PKG \succ_{4 - L} TSN $$
$$ \succ_{2 - L} PDCO \succ_{3 - L} HOLX \succ_{3 - L} TSCO \succ_{4 - L} LRCX \succ_{2 - L} LUK \succ_{3 - L} UNM \succ_{6 - L} WYN $$
$$ \succ_{2 - L} ABBV \succ_{3 - L} KSU \succ_{4 - L} MAS \succ_{3 - L} PFG \succ_{2 - L} EA \succ_{4 - L} PRU \succ_{2 - L} KEY $$
$$ \succ_{4 - L} BMY \succ_{3 - L} STI \succ_{3 - L} TSS \succ_{3 - L} EBAY \succ_{2 - L} AMZN \succ_{3 - L} ADM \succ_{2 - L} AVGO $$
$$ \succ_{6 - L} SYF \succ_{2 - L} JNPR \succ_{3 - L} FITB \succ_{2 - L} NTAP \succ_{2 - L} LUV \succ_{4 - L} HOG \succ_{2 - L} EW $$
$$ \succ_{2 - L} BBY \succ_{2 - L} AKAM \succ_{2 - L} MU \succ_{1 - L} LLY \succ_{2 - L} PSA \succ_{2 - L} NKE \succ_{5 - L} AMGN $$
$$ \succ_{4 - L} GGP \succ_{3 - L} VTR \succ_{2 - L} EQR \succ_{2 - L} HRL \succ_{4 - L} ABT \succ_{3 - L} MCO \succ_{2 - L} OXY $$
$$ \succ_{5 - L} FE \succ_{2 - L} PYPL \succ_{3 - L} GM \succ_{2 - L} VRSN \succ_{3 - L} SEE \succ_{2 - L} ANTM \succ_{3 - L} ESRX $$
$$ \succ_{2 - L} KR \succ_{4 - L} MNST \succ_{3 - L} CI \succ_{4 - L} TIF \succ_{3 - L} MDLZ \succ_{3 - L} COF \succ_{3 - L} HCN $$
$$ \succ_{2 - L} CAH \succ_{2 - L} PNR \succ_{3 - L} NWL \succ_{2 - L} LEN \succ_{4 - L} WY \succ_{3 - L} SLG \succ_{2 - L} VFC $$
$$ \succ_{3 - L} MAT \succ_{4 - L} SBAC \succ_{2 - L} EXR \succ_{5 - L} CERN \succ_{3 - L} STT \succ_{2 - L} F \succ_{2 - L} PHM $$
$$ \succ_{4 - L} TPR \succ_{2 - L} AES \succ_{6 - L} GILD \succ_{3 - L} CCL \succ_{4 - L} CTSH \succ_{2 - L} DISCK \succ_{4 - L} GPN $$
$$ \succ_{3 - L} RHT \succ_{2 - L} DHI \succ_{4 - L} HST \succ_{3 - L} FLR \succ_{3 - L} ALK \succ_{3 - L} HBAN \succ_{3 - L} UHS $$
$$ \succ_{3 - L} BEN \succ_{4 - L} RJF \succ_{2 - L} XRX \succ_{3 - L} C \succ_{3 - L} NWS \succ_{4 - L} MS \succ_{2 - L} NWSA $$
$$ \succ_{4 - L} BAC \succ_{2 - L} CFG \succ_{3 - L} RHI \succ_{2 - L} CTL \succ_{4 - L} MGM \succ_{2 - L} FLS \succ_{3 - L} HPQ $$
$$ \succ_{2 - L} EXPE \succ_{4 - L} AYI \succ_{3 - L} MET \succ_{2 - L} LYB \succ_{3 - L} AMP \succ_{3 - L} PVH \succ_{2 - L} CRM $$
$$ \succ_{3 - L} ETFC \succ_{2 - L} CELG \succ_{3 - L} ATVI \succ_{3 - L} PXD \succ_{7 - L} SCHW \succ_{2 - L} GT \succ_{2 - L} EOG $$
$$ \succ_{2 - L} DISH \succ_{4 - L} ADSK \succ_{2 - L} M \succ_{3 - L} MCK \succ_{2 - L} EQT \succ_{5 - L} KORS \succ_{3 - L} LNC $$
$$ \succ_{2 - L} KMX \succ_{2 - L} FTI \succ_{2 - L} AAL \succ_{3 - L} CXO \succ_{4 - L} WRK \succ_{2 - L} NAVI \succ_{2 - L} BHGE $$
$$ \succ_{2 - L} HP \succ_{3 - L} KSS \succ_{2 - L} COG \succ_{2 - L} KMI \succ_{2 - L} URI \succ_{1 - L} ABC \succ_{2 - L} DISCA $$
$$ \succ_{3 - L} SRCL \succ_{2 - L} LB \succ_{3 - L} IVZ \succ_{3 - L} HBI \succ_{4 - L} DAL \succ_{2 - L} BIIB \succ_{3 - L} VLO $$
$$ \succ_{4 - L} HCP \succ_{2 - L} COTY \succ_{3 - L} CBG \succ_{3 - L} UAL \succ_{2 - L} CMG \succ_{4 - L} APTV \succ_{2 - L} AMG $$
$$ \succ_{2 - L} JWN \succ_{3 - L} BWA \succ_{3 - L} SWKS \succ_{2 - L} CNC \succ_{4 - L} SIG \succ_{2 - L} NBL \succ_{5 - L} NFLX $$
$$ \succ_{2 - L} APA \succ_{2 - L} HES \succ_{4 - L} APC \succ_{2 - L} RRC \succ_{1 - L} QRVO \succ_{2 - L} DVN \succ_{2 - L} MRO $$
$$ \succ_{1 - L} RL \succ_{3 - L} AGN \succ_{4 - L} LNT \succ_{2 - L} HRB \succ_{3 - L} REGN \succ_{2 - L} ADS \succ_{2 - L} UAA $$
$$ \succ_{2 - L} RCL \succ_{3 - L} MYL \succ_{2 - L} VIAB \succ_{3 - L} PRGO \succ_{2 - L} ANDV \succ_{5 - L} COP \succ_{2 - L} TRIP $$
$$ \succ_{3 - L} MPC \succ_{4 - L} WYNN \succ_{4 - L} GPS \succ_{2 - L} NFX \succ_{5 - L} NOV \succ_{2 - L} NCLH \succ_{3 - L} INCY $$
$$ \succ_{2 - L} ILMN \succ_{2 - L} MOS \succ_{2 - L} VRTX \succ_{3 - L} ALXN \succ_{3 - L} WDC \succ_{2 - L} CF \succ_{6 - L} STX $$
$$ \succ_{2 - L} NRG \succ_{2 - L} ARNC \succ_{2 - L} WMB \succ_{3 - L} FCX \succ_{2 - L} CHK $$

Appendix 4: Ranking of the S&P 500 Index and its components in 2017

$$ {\varvec{GSPC}} \succ_{2 - L} MON \succ_{2 - L} HON \succ_{2 - L} WM \succ_{3 - L} ALL \succ_{3 - L} BRK.B \succ_{2 - L} AFL $$
$$ \succ_{4 - L} MCD \succ_{2 - L} TMK \succ_{3 - L} MMM \succ_{3 - L} CBOE \succ_{3 - L} V \succ_{2 - L} LMT \succ_{3 - L} MCO $$
$$ \succ_{3 - L} PGR \succ_{2 - L} AME \succ_{3 - L} NOC \succ_{2 - L} AXP \succ_{3 - L} ROP \succ_{3 - L} BAX \succ_{2 - L} YUM $$
$$ \succ_{4 - L} NEE \succ_{3 - L} AVY \succ_{3 - L} SPGI \succ_{2 - L} FTV \succ_{4 - L} RTN \succ_{3 - L} HD \succ_{3 - L} VRSN $$
$$ \succ_{3 - L} BA \succ_{2 - L} SWK \succ_{3 - L} MA \succ_{2 - L} EL \succ_{3 - L} ITW \succ_{2 - L} ABT \succ_{3 - L} ACN \succ_{2 - L} UNH $$
$$ \succ_{3 - L} MHK \succ_{3 - L} HRS \succ_{2 - L} ZTS \succ_{3 - L} SNPS \succ_{2 - L} MSFT \succ_{4 - L} SHW \succ_{2 - L} BLK $$
$$ \succ_{3 - L} MAR \succ_{2 - L} INTU \succ_{3 - L} BDX \succ_{3 - L} TSS \succ_{3 - L} STZ \succ_{2 - L} WMT \succ_{3 - L} CRM $$
$$ \succ_{2 - L} TEL \succ_{4 - L} PKI \succ_{3 - L} AMT \succ_{5 - L} DE \succ_{2 - L} MTD \succ_{3 - L} TMO \succ_{2 - L} WAT $$
$$ \succ_{3 - L} CI \succ_{3 - L} HLT \succ_{4 - L} ABBV \succ_{4 - L} ANSS \succ_{2 - L} CCI \succ_{4 - L} CDNS \succ_{2 - L} DHI $$
$$ \succ_{3 - L} ISRG \succ_{2 - L} A \succ_{3 - L} FB \succ_{3 - L} AET \succ_{4 - L} PHM \succ_{2 - L} SBAC \succ_{3 - L} BF.B \succ_{4 - L} TXN $$
$$ \succ_{2 - L} XYL \succ_{3 - L} AAPL \succ_{3 - L} ANTM \succ_{4 - L} WYN \succ_{2 - L} COL \succ_{4 - L} ADBE $$
$$ \succ_{3 - L} AMZN \succ_{4 - L} RHT \succ_{2 - L} CAT \succ_{2 - L} TROW \succ_{2 - L} PYPL \succ_{2 - L} FMC \succ_{2 - L} WYNN $$
$$ \succ_{3 - L} VRTX \succ_{2 - L} ALGN \succ_{3 - L} NRG \succ_{1 - L} KO \succ_{2 - L} PEP \succ_{2 - L} PG \succ_{3 - L} JNJ $$
$$ \succ_{3 - L} PFE \succ_{3 - L} DUK \succ_{2 - L} ECL \succ_{2 - L} RSG \succ_{4 - L} AEP \succ_{2 - L} XEL \succ_{4 - L} APH $$
$$ \succ_{2 - L} L \succ_{4 - L} AJG \succ_{6 - L} FISV \succ_{2 - L} ED \succ_{3 - L} CMS \succ_{5 - L} FIS \succ_{2 - L} WLTW \succ_{3 - L} MMC $$
$$ \succ_{3 - L} AON \succ_{2 - L} DTE \succ_{2 - L} UTX \succ_{2 - L} SYK \succ_{4 - L} WEC \succ_{3 - L} AWK \succ_{2 - L} APD $$
$$ \succ_{3 - L} PX \succ_{2 - L} NDAQ \succ_{2 - L} PEG \succ_{2 - L} CB \succ_{3 - L} HSY \succ_{3 - L} TRV \succ_{3 - L} CLX $$
$$ \succ_{3 - L} INFO \succ_{2 - L} DPS \succ_{3 - L} CSCO \succ_{2 - L} CNP \succ_{3 - L} GOOG \succ_{2 - L} CTAS \succ_{3 - L} FBHS $$
$$ \succ_{4 - L} ORCL \succ_{3 - L} GOOGL \succ_{2 - L} ARE \succ_{3 - L} HIG \succ_{2 - L} GD \succ_{6 - L} DGX \succ_{3 - L} PPG $$
$$ \succ_{2 - L} LLL \succ_{4 - L} CL \succ_{3 - L} VRSK \succ_{2 - L} CME \succ_{3 - L} IFF \succ_{2 - L} CHD \succ_{3 - L} CTSH $$
$$ \succ_{2 - L} MDT \succ_{3 - L} AOS \succ_{2 - L} BK \succ_{4 - L} EXPD \succ_{2 - L} JPM \succ_{4 - L} LLY \succ_{2 - L} PSX $$
$$ \succ_{4 - L} INTC \succ_{2 - L} MO \succ_{3 - L} MAS \succ_{6 - L} PH \succ_{2 - L} ROK \succ_{4 - L} LKQ \succ_{2 - L} MNST $$
$$ \succ_{3 - L} FDX \succ_{2 - L} PFG \succ_{3 - L} UNM \succ_{3 - L} EMR \succ_{4 - L} UNP \succ_{5 - L} LH \succ_{2 - L} EQIX $$
$$ \succ_{2 - L} ALLE \succ_{3 - L} FLIR \succ_{5 - L} GLW \succ_{2 - L} CCL \succ_{2 - L} PKG \succ_{6 - L} GPN \succ_{2 - L} AMG $$
$$ \succ_{4 - L} NWSA \succ_{5 - L} CMI \succ_{2 - L} HPQ \succ_{3 - L} VLO \succ_{5 - L} DOV \succ_{4 - L} PCLN \succ_{2 - L} TSN $$
$$ \succ_{3 - L} IT \succ_{4 - L} RMD \succ_{2 - L} LEN \succ_{5 - L} AMP \succ_{2 - L} NWS \succ_{4 - L} VFC \succ_{2 - L} CBG $$
$$ \succ_{5 - L} NTAP \succ_{4 - L} VAR \succ_{2 - L} CERN \succ_{3 - L} DXC \succ_{3 - L} RCL \succ_{4 - L} APTV \succ_{2 - L} PVH $$
$$ \succ_{3 - L} ILMN \succ_{2 - L} DLTR \succ_{4 - L} ETFC \succ_{2 - L} AVGO \succ_{5 - L} ALB \succ_{2 - L} NFLX \succ_{4 - L} ATVI $$
$$ \succ_{2 - L} CSX \succ_{4 - L} CNC \succ_{2 - L} LRCX \succ_{2 - L} AMAT \succ_{2 - L} URI \succ_{2 - L} BBY \succ_{2 - L} MU $$
$$ \succ_{2 - L} NVDA \succ_{1 - L} TWX \succ_{3 - L} AEE \succ_{2 - L} PNW \succ_{2 - L} LNT \succ_{2 - L} XOM \succ_{3 - L} D $$
$$ \succ_{2 - L} EQR \succ_{3 - L} ETR \succ_{2 - L} AVB \succ_{3 - L} UDR \succ_{2 - L} DHR \succ_{3 - L} SRE \succ_{2 - L} PM $$
$$ \succ_{2 - L} NI \succ_{2 - L} KMB \succ_{3 - L} MAA \succ_{2 - L} IBM \succ_{3 - L} PAYX \succ_{4 - L} ESS \succ_{5 - L} USB $$
$$ \succ_{2 - L} EXC \succ_{5 - L} CVX \succ_{2 - L} DIS \succ_{3 - L} SYY \succ_{3 - L} PLD \succ_{3 - L} DRE \succ_{4 - L} EMN $$
$$ \succ_{2 - L} WY \succ_{3 - L} ETN \succ_{2 - L} UPS \succ_{2 - L} DWDP \succ_{3 - L} IQV \succ_{2 - L} SNI \succ_{4 - L} STT $$
$$ \succ_{3 - L} BXP \succ_{4 - L} BSX \succ_{2 - L} MDLZ \succ_{4 - L} AMGN \succ_{2 - L} HCN \succ_{3 - L} BLL \succ_{4 - L} SBUX $$
$$ \succ_{2 - L} MSI \succ_{3 - L} CINF \succ_{4 - L} IR \succ_{2 - L} C \succ_{3 - L} MKC \succ_{5 - L} CA \succ_{2 - L} GRMN \succ_{3 - L} ADP $$
$$ \succ_{2 - L} PRU \succ_{4 - L} WFC \succ_{5 - L} HII \succ_{5 - L} PNC \succ_{2 - L} BEN \succ_{3 - L} PNR \succ_{4 - L} CHRW $$
$$ \succ_{2 - L} BBT \succ_{3 - L} MTB \succ_{4 - L} TXT \succ_{3 - L} NTRS \succ_{5 - L} COST \succ_{2 - L} TJX \succ_{4 - L} EBAY $$
$$ \succ_{2 - L} F \succ_{4 - L} DRI \succ_{2 - L} DFS \succ_{4 - L} XRAY \succ_{4 - L} ZBH \succ_{3 - L} RJF \succ_{3 - L} COO $$
$$ \succ_{2 - L} SJM \succ_{4 - L} LYB \succ_{2 - L} OXY \succ_{4 - L} AIZ \succ_{3 - L} HUM \succ_{3 - L} SEE \succ_{2 - L} NKE $$
$$ \succ_{3 - L} EIX \succ_{3 - L} LOW \succ_{2 - L} IP \succ_{5 - L} IVZ \succ_{2 - L} RE \succ_{4 - L} STI \succ_{3 - L} MRK \succ_{3 - L} LUK $$
$$ \succ_{4 - L} HOLX \succ_{2 - L} ROST \succ_{3 - L} JBHT \succ_{4 - L} ADI \succ_{2 - L} HCA \succ_{4 - L} DLR \succ_{2 - L} SNA $$
$$ \succ_{4 - L} WRK \succ_{5 - L} GPC \succ_{3 - L} TIF \succ_{2 - L} BAC \succ_{3 - L} KSU \succ_{3 - L} MCHP \succ_{2 - L} ANDV $$
$$ \succ_{4 - L} EW \succ_{3 - L} GM \succ_{4 - L} EA \succ_{2 - L} IDXX \succ_{3 - L} NSC \succ_{2 - L} SCHW \succ_{2 - L} CMA $$
$$ \succ_{2 - L} HAS \succ_{3 - L} BWA \succ_{2 - L} LUV \succ_{4 - L} TPR \succ_{2 - L} DG \succ_{3 - L} FOXA \succ_{2 - L} ICE $$
$$ \succ_{3 - L} ADSK \succ_{4 - L} KLAC \succ_{2 - L} CTXS \succ_{2 - L} MPC \succ_{2 - L} KORS \succ_{2 - L} EFX \succ_{2 - L} GPS $$
$$ \succ_{4 - L} ARNC \succ_{1 - L} SO \succ_{2 - L} PPL \succ_{2 - L} AIV \succ_{2 - L} KHC \succ_{2 - L} AIG \succ_{3 - L} VZ \succ_{2 - L} FE $$
$$ \succ_{4 - L} VTR \succ_{2 - L} CAG \succ_{2 - L} T \succ_{3 - L} LEG \succ_{3 - L} IRM \succ_{2 - L} TAP \succ_{3 - L} PSA \succ_{3 - L} GIS $$
$$ \succ_{3 - L} HRL \succ_{3 - L} CMCSA \succ_{2 - L} PBCT \succ_{3 - L} WU \succ_{2 - L} K \succ_{3 - L} ADM \succ_{3 - L} EXR $$
$$ \succ_{2 - L} OMC \succ_{3 - L} MS \succ_{2 - L} GS \succ_{3 - L} WBA \succ_{2 - L} REG \succ_{6 - L} PCAR \succ_{3 - L} LNC $$
$$ \succ_{2 - L} GILD \succ_{5 - L} JEC \succ_{2 - L} COF \succ_{2 - L} UHS \succ_{5 - L} HST \succ_{5 - L} XLNX \succ_{2 - L} MET $$
$$ \succ_{2 - L} FITB \succ_{3 - L} EOG \succ_{2 - L} VNO \succ_{3 - L} RF \succ_{4 - L} BMY \succ_{2 - L} PWR \succ_{3 - L} FAST $$
$$ \succ_{3 - L} RHI \succ_{2 - L} HBAN \succ_{3 - L} GT \succ_{2 - L} FOX \succ_{5 - L} KEY \succ_{4 - L} ESRX \succ_{4 - L} WHR $$
$$ \succ_{2 - L} FFIV \succ_{2 - L} ZION \succ_{2 - L} CHTR \succ_{3 - L} ADS \succ_{3L} SYMC \succ_{2 - L} DAL \succ_{4 - L} BIIB $$
$$ \succ_{3 - L} O \succ_{3 - L} EXPE \succ_{2 - L} CFG \succ_{3 - L} NEM \succ_{5 - L} QCOM \succ_{2 - L} NCLH \succ_{5 - L} HPE $$
$$ \succ_{2 - L} ABC \succ_{3 - L} COP \succ_{5 - L} MCK \succ_{2 - L} XRX \succ_{4 - L} SWKS \succ_{2 - L} MGM \succ_{2 - L} SYF $$
$$ \succ_{4 - L} TDG \succ_{2 - L} CXO \succ_{2 - L} NUE \succ_{3 - L} RL \succ_{4 - L} DVA \succ_{2 - L} QRVO \succ_{2 - L} HRB $$
$$ \succ_{4 - L} AKAM \succ_{2 - L} CF \succ_{2 - L} STX \succ_{3 - L} FCX \succ_{1 - L} SLG \succ_{2 - L} FRT \succ_{2 - L} KMI $$
$$ \succ_{3 - L} HCP \succ_{2 - L} SLB \succ_{3 - L} JCI \succ_{2 - L} AES \succ_{5 - L} XL \succ_{2 - L} HSIC \succ_{2 - L} PCG $$
$$ \succ_{2 - L} SPG \succ_{3 - L} WMB \succ_{2 - L} SRCL \succ_{3 - L} CVS \succ_{4 - L} JNPR \succ_{2 - L} KMX \succ_{5 - L} AGN $$
$$ \succ_{2 - L} NLSN \succ_{3 - L} CBS \succ_{2 - L} CPB \succ_{3 - L} CAH \succ_{2 - L} HOG \succ_{2 - L} VMC \succ_{4 - L} OKE $$
$$ \succ_{2 - L} PDCO \succ_{3 - L} IPG \succ_{2 - L} TSCO \succ_{3 - L} GWW \succ_{3 - L} CELG \succ_{2 - L} HAL \succ_{4 - L} AZO $$
$$ \succ_{2 - L} COG \succ_{4 - L} MLM \succ_{2 - L} DISH \succ_{3 - L} FLR \succ_{2 - L} FLS \succ_{2 - L} ORLY \succ_{3 - L} TGT $$
$$ \succ_{2 - L} REGN \succ_{5 - L} AAL \succ_{2 - L} MYL \succ_{2 - L} PRGO \succ_{4 - L} COTY \succ_{2 - L} WDC \succ_{2 - L} KSS $$
$$ \succ_{1 - L} GE \succ_{2 - L} MAC \succ_{2 - L} GGP \succ_{3 - L} XEC \succ_{2 - L} NOV \succ_{2 - L} FTI \succ_{5 - L} APC $$
$$ \succ_{4 - L} ALK \succ_{5 - L} ULTA \succ_{2 - L} KIM \succ_{3 - L} PXD \succ_{2 - L} MOS \succ_{4 - L} UAL \succ_{3 - L} HBI $$
$$ \succ_{2 - L} DISCA \succ_{3 - L} DISCK \succ_{2 - L} ALXN \succ_{4 - L} SCG \succ_{2 - L} NBL \succ_{3 - L} DVN \succ_{6 - L} CMG $$
$$ \succ_{2 - L} EQT \succ_{4 - L} HP \succ_{2 - L} VIAB \succ_{2 - L} JWN \succ_{2 - L} NAVI \succ_{2 - L} KR \succ_{3 - L} CTL \succ_{1 - L} HES $$
$$ \succ_{2 - L} APA \succ_{2 - L} NFX \succ_{1 - L} AYI \succ_{3 - L} INCY \succ_{2 - L} BHGE \succ_{3 - L} NWL \succ_{2 - L} AAP $$
$$ \succ_{2 - L} TRIP \succ_{3 - L} RRC \succ_{2 - L} LB \succ_{2 - L} MRO \succ_{6 - L} FL \succ_{2 - L} M \succ_{2 - L} MAT \succ_{2 - L} UAA $$
$$ \succ_{4 - L} SIG \succ_{2 - L} UA \succ_{2 - L} ES \succ_{3 - L} CHK \succ_{3 - L} AMD \succ_{1 - L} $$

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Nisani, D., Shelef, A. A statistical analysis of investor preferences for portfolio selection. Empir Econ 61, 1883–1915 (2021). https://doi.org/10.1007/s00181-020-01947-8

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Keywords

  • Investment management
  • Expected utility model
  • Stochastic dominance rules
  • Marginal conditions for stochastic dominance
  • Lorenz curves

JEL Classification

  • D81
  • G11
  • G32