What is the historical performance of investments in the stock market? The answer to this question usually prompts one to look at the average returns of a stock market index (portfolio) such as the S&P 500 or the CRSP Value-Weighted. The answer is about 7 percent in real value, averaged over the last 70 or so years. A wholly different question, at least in principle, asks how an investment in the firms trading in the stock market 70 years ago has performed. A portfolio constructed to answer the second question will be called a vintage stock market.
Each observation in the CRSP monthly value-weighted return series is the return on a portfolio of NYSE stocks with weights based on the relative market value of those stocks at the beginning of each month. At the beginning of the next month, a new set of weights is chosen to replicate the new composition of the stock market.
The market value of a stock is the price of a share times the number of shares outstanding. Its weight in the portfolio is its market value divided by the total value of the stock market. Portfolio weights based on market values change for two reasons: 1) Stock prices change, and 2) the number of shares change. Weight changes in the portfolio due to price movements occur automatically without the need to adjust shares held. Changes in the number of shares outstanding for a stock require the rebalancing of the portfolio (an adjustment to the number of shares held) to maintain the weights. Rebalancing is required whenever there is entry or exit and stock issue or repurchase.
The weights of a fixed-holding portfolio do not adjust when shares outstanding change, although they change due to the movements of the prices of stocks held. In other words, it is not rebalanced. A stock market portfolio of vintage t is defined to be a fixed-holding portfolio with initial weights chosen to be those of the value-weighted portfolio at time t. The returns on a vintage t portfolio may be said to represent the payment stream to the acquisition of the property rights to the stock market portfolio at t. In contrast, the connection between the property rights and a payment stream to the usual rebalanced value-weighted portfolio is fuzzy since the property rights are continually changing.
Each observation in the CRSP value-weighted index can be associated with a unique vintage stock market. The collection of these vintage stock markets may be thought of as a sequence of series, or triangular array. In this context, the weights of the CRSP value-weighted index are simply the first set of weights for each vintage stock market portfolio.
This paper explores the theoretical and empirical implications of the sequence-of-series view of the stock market. It is hypothesized that the characteristics of the payment stream to a certain aggregate fixed asset, a vintage stock market, will be different from the characteristics of a stock market index with property rights that are changing each period. In particular, it examines how much the time-series of returns from vintage stock market portfolios differ from that of the usual rebalanced version.
In order to provide an empirical test of this question, I construct vintage stock market portfolios from the monthly security-level data in the CRSP NYSE files from 1926 to 1997. Statistical and economic tests using CRSP NYSE monthly data show that the vintage stock market portfolios differ in important ways from the rebalanced portfolio. For example, the average returns on the vintage portfolios are higher and their standard deviations are generally lower, than the conventional rebalanced measure of stock market performance, a result at odds with the predictions of standard economic theory. Taking into account the additional transaction costs required to rebalance the CRSP value-weighted index portfolio, the disparity is even greater. Sources of this apparent puzzle are discussed, as well as possible explanations.
I also plan to continue my study of intra-day stock market return volatility using the TAQ transaction data. This line of research has great potential. In order to analyze the dataset, I have built an elaborate set of routines in C++ that are capable of constructing aggregate porfolios of various types and analyzing the data over several years.
Furthermore, I want to proceed with my study of the sources of technological progress. 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