Estimating the Negative Impact of “Noise” on the Returns of Cap-Weighted Portfolios In Various Segments of the Equity Markets

Russell J. Fuller, Bing Han and Yining Tung

Volume 10, Number 3, Third Quarter 2012

Capital Market Theory assumes that the ex ante market portfolio (which is cap-weighted) lies on the (ex ante) efficient frontier. However, we show that ex ante cap-weighted portfolios will always be interior portfolios relative to the end-of-investment-period ex post efficient frontier. This is due to the arrival of unanticipated information, which we refer to as noise that causes unexpected price changes and creates either winner or loser stocks. By construction, ex ante cap-weighted portfolios will be overweighted in loser stocks and underweighted in winners during the return measurement period. To estimate the negative impact of noise on the returns of ex ante cap-weighted portfolios, we use the concept of a perfect foresight (PF) portfolio. The PF portfolio for any given equity segment is a buy-and-hold portfolio of all stocks in that segment with weights at the beginning of the return period set to be proportional to the market capitalization of the stocks at the end of the return period. We show that the PF portfolio will always be on the ex post efficient frontier and outperform its ex ante cap-weighted counterpart. Because the PF portfolio has risk characteristics that are similar to the ex ante capweighted portfolio for a particular equity segment, the excess return of the PF portfolio provides an estimate of the maximum annual amount of available alpha to all investors involved in that segment in a given year. For example, the total excess return of the PF portfolio for the large-cap US equity segment (which we define as the 1,000 largest US stocks based on market values at the beginning of each year) is about 7%, on average, per year. This can be thought of as the maximum amount of alpha, or ex ante mispricing (in percentage terms), available to all investors in the large-cap US equity market segment.