The Proper Use of Beta (β)

In my previous post I highlighted the flaws associated with Beta (β), in this post I would like to explore the proper use of Beta.

Studies have shown that managed portfolios only outperform the S&P500 Index about 1/3rd of the time in both bear and bull markets – this means that for 2/3rds of the time it is better to just invest your money in an index fund, and forget about it.  So how do we get in this upper 1/3rd that beats the market index?  One potential way is the proper use of Beta.

If Beta, when applied to the CAPM, gives us the required return assuming a well diversified portfolio (based on historic data), then we must earn above this required return in order to justify investing in an individual stock versus the market index.  This means that we must determine what our expected (anticipated) return is for the stock in question.

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The Problem With Using Beta (β) As A Proxy For Risk

The following is a brief list of definitions for beta from various textbooks and research papers.  Though brief, I believe that this is a representative sampling of the modern perceptions regarding beta.

Damodaran – “standardized measure of the risk that investment adds to the market portfolio.”  “Statistically, the beta of an investment measures how it co-­varies with the market portfolio and thus the risk added to that portfolio. Beta’s features: Betas are standardized around one; an investment with a beta above (below) one is an above average (below average) risk investment.“

Kpthari and Shanken – “primary measure of non-diversifiable risk.”

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Markowitz Portfolio Theory – Final Comments

In my previous two posts regarding the Markowitz Portfolio Theory, I did not consider the dividend yield in the optimization to reduce the complexity of the model.  In this post I will explore the impact of adding the dividend yield to portfolio selection, plus verify the stock’s selected by checking if they are presently undervalued.

You can download the model used for this post here: Markowitz Model

The return for the shareholder  is comprised of two parts:  the capital gains yield and the current dividend yield.  The capital gain yield is imply the percent increase in the stock price over a period of time, and is calculated by the following equation:

(Current Stock Price – Prior Stock Price) / Prior Stock Price Continue reading “Markowitz Portfolio Theory – Final Comments”


Non-Linear Optimization Using Palisade’s Evolver

In my previous post on solving the non-linear Markowitz Portfolio equation Portfolio Optimization, I used the minimization of CV as my objective function, and used Excel’s Solver (made by Frontline Solutions and bundled with Excel), and Frontline Solution’s Premium Solver to optimize a portfolio of stocks taken from the  the S&P 100 Index.   In that post I pointed out the dangers of over-constraining the model because this could lead to sub-optimal solutions.   In this post I will discuss sub-optimal solutions due to the solving engine itself. I have chosen to use the last 270 weeks of S&P 100 Index data, so this is optimization should yield potential investment targets for today.   The model used for this optimization can be downloaded here:  Optimization Model Continue reading “Non-Linear Optimization Using Palisade’s Evolver”


Further Discussion of Portfolio Optimization

Using the same model that was explored in a previous post Markowitz Portfolio Theory, but enhancing this model by using FrontlineSolver’s Risk Solver Platform, the model could be extended to more constraints.  What I wanted to explore is whether constraining the maximum percent weight of any individual stock in the portfolio would sub-optimize the solution.  In theory, the fewer constraints on the model the better, because constraints typically move the model away from its true optimum.  Think of it as a balloon filled with water, if you squeeze in one place, the balloon expands somewhere else, and if you squeeze to much, the balloon can burst, which is the equivalent of your model blowing-up and resulting in a sub-optimum solution. Continue reading “Further Discussion of Portfolio Optimization”