Abstract
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
Highlights
IntroductionHarry Markowitz [1] developed the notion of beta as the mathematical slope in a linear regression of company rate of return onto the market rate of return
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.Harry Markowitz [1] developed the notion of beta as the mathematical slope in a linear regression of company rate of return onto the market rate of return
Beta coefficients, standard deviation of residuals and residual inter-quartile ranges for each company for each of the five regression methods, i.e., Ordinary Least Squares (OLS), lmRobMM, ltsreg, lmsreg and ms are computed
Summary
Harry Markowitz [1] developed the notion of beta as the mathematical slope in a linear regression of company rate of return onto the market rate of return. Eqn 1 below displays the equation for beta which Markowitz described as the characteristic line. Where rri - rate of return for company i rrmkt - rate of return for market - alpha, intercept - beta, slope. While Eqn 1 is straightforward, the estimation of the equation is not quite so. The conventional method to estimate the security market line alpha and beta is OLS, i.e., ordinary least squares. If the assumptions are violated, inaccurate parameter estimates for and i will be had. Results from inaccurate betas will lead to incorrect portfolio construction and unanticipated portfolio returns
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