The risk of using the S&P500 as a market proxy in the calculation of alpha and beta
Investors, relying on distorted parameters, can be induced to make distorted strategic choices
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For several decades (the theory dates back to the 1950s), the most commonly adopted model for analysing stock market trends is the Capital Asset Pricing Model (Capm). The two key parameters are alpha and beta calculated on the basis of the correlation of a security's return to the movements of the 'market portfolio', i.e. a portfolio composed of all assets in which one can invest, including illiquid assets such as houses and land, works of art, diamonds or shares in unlisted companies, with weights proportional to their market value. Beta measures systematic risk, i.e. how much the return of a security varies in relation to the market portfolio. A value greater than 1 indicates a greater reaction of the security to the general trend and vice versa if less than 1. Alpha is a performance metric, the difference between the actual return of a security and the theoretical return predicted by the historical correlation with the market portfolio. Therefore, it is interpreted as the 'managerial ability', the 'added value', the quid of a company.
A positive alpha shows that the manager or strategy has managed to 'beat the market' or the benchmark and determines whether the return achieved justifies the risk taken compared to a passive investment implemented by purchasing an ETF. A negative alpha indicates that the risk taken has not been repaid, or that the management has 'destroyed value' compared to a simple passive investment. A fund with high alpha and low beta is well managed because it earns extra return without taking excessive risk.
These two parameters, therefore, form the cornerstone of risk and performance assessment, and are crucial for constructing or analysing investment strategies.
Capm theory states that alpha and beta are calculated using the 'market portfolio' but in reality accurate, reliable and high-frequency data to construct the true market portfolio does not exist, so it is replaced in the calculations by a stock market index such as the S&P500.
This approach has been justified by dozens of academic researches aimed at demonstrating that a sufficiently broad stock market index is an accurate proxy for the 'market portfolio' proposed by the underlying theory because it is sufficiently diversified and sufficiently correlated with the performance of all other asset classes.
