Context

The S&P 500,[2] or simply the S&P,[4] is a stock market index that measures the stock performance of 500 large companies listed on stock exchanges in the United States. It is one of the most commonly followed equity indices.[5] The average annual total return and compound annual growth rate of the index, including dividends, since inception in 1926 has been approximately 9.8%, or 6% after inflation; however, there were several years where the index declined over 30%.[6][7] The index has posted annual increases 70% of the time.[5] However, the index has only made new highs on 5% of trading days, meaning that on 95% of trading days, the index has closed below its all-time high.[8]

For a list of the components of the index, see List of S&P 500 companies. The components that have increased their dividends in 25 consecutive years are known as the S&P 500 Dividend Aristocrats.[9]:25

The S&P 500 index is a capitalization-weighted index and the 10 largest companies in the index account for 26% of the market capitalization of the index. The 10 largest companies in the index, in order of weighting, are Apple Inc., Microsoft, Amazon.com, Alphabet Inc., Facebook, Johnson & Johnson, Berkshire Hathaway, Visa Inc., Procter & Gamble and JPMorgan Chase, respectively.[2]

Funds that track the index have been recommended as investments by Warren Buffett, Burton Malkiel, and John C. Bogle for investors with long time horizons.[10]

Although the index includes only companies listed in the United States, companies in the index derive on average only 71% of their revenue in the United States.[11]

The index is one of the factors in computation of the Conference Board Leading Economic Index, used to forecast the direction of the economy.[12]

The index is associated with many ticker symbols, including: ^GSPC,[13] INX,[14] and $SPX, depending on market or website.[15] The index value is updated every 15 seconds, or 1,559 times per trading day, with price updates disseminated by Reuters.[16]

The S&P 500 is maintained by S&P Dow Jones Indices, a joint venture majority-owned by S&P Global and its components are selected by a committee.[17][18]

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Indices are created by consolidating multidimensional data into a single representative measure known as an index, using a fundamental mathematical model. Most present indices are essentially the averages or weighted averages of the variables under study, ignoring multicollinearity among the variables, with the exception of the existing Ordinary Least Squares (OLS) estimator based OLS-PCA index methodology. Many existing surveys adopt survey designs that incorporate survey weights, aiming to obtain a representative sample of the population while minimizing costs. Survey weights play a crucial role in addressing the unequal probabilities of selection inherent in complex survey designs, ensuring accurate and representative estimates of population parameters. However, the existing OLS-PCA based index methodology is designed for simple random sampling and is incapable of incorporating survey weights, leading to biased estimates and erroneous rankings that can result in flawed inferences and conclusions for survey data. To address this limitation, we propose a novel Survey Weighted PCA (SW-PCA) based Index methodology, tailored for survey-weighted data. SW-PCA incorporates survey weights, facilitating the development of unbiased and efficient composite indices, improving the quality and validity of survey-based research. Simulation studies demonstrate that the SW-PCA based index outperforms the OLS-PCA based index that neglects survey weights, indicating its higher efficiency. To validate the methodology, we applied it to a Household Consumer Expenditure Survey (HCES), NSS 68th Round survey data to construct a Food Consumption Index for different states of India. The result was significant improvements in state rankings when survey weights were considered. In conclusion, this study highlights the crucial importance of incorporating survey weights in index construction from complex survey data. The SW-PCA based Index provides a valuable solution, enhancing the accuracy and reliability of survey-based research, ultimately contributing to more informed decision-making.