Manuel G. Russon

In the world of finance and portfolio management, “beta” refers to the sensitivity of a security’s return, to the sensitivity of the “market” portfolio and is an indication of the level of systematic risk, i.e., the amount of risk that a company’s equity shares with the entire market. Correct values for beta are crucial for institutional portfolio managers, as the client contract almost always calls for a portfolio beta approximately equal to 1.0. Typically, beta is estimated using Ordinary Least Squares, but OLS is reliant on some very stringent assumptions. Here, betas are computed and compared using OLS and four robust regression algorithms. Minimum sum regression is identified as the superior robust regression algorithm to estimate beta.

Keywords: Financial Beta, Ordinary Least Squares, Robust Regression, Portfolio Management.
JEL Classification: C21, G11

VIX, a ticker symbol for Volatility Index, measures the implied annual volatility of at-the-money SP500 Index Options. Conventional wisdom presumes VIX to measure the magnitude (positive or negative) of possible movements in future equity prices, with movements being a positive function of VIX. This research investigates the nature of the relationship between VIX and SP500 volatility, and answers the question as to whether that relationship is linear or nonlinear. Based on this research paper, the authors conclude that the realized SP500 volatility is nonlinear, and grows with the level of VIX at an increasing rate. The nonlinearity relationship between VIX and SP500 has enormous implications for investment management and hedging in the financial markets.