A Clearer View of Beta

In the spreadsheet below, I have first calculated the beta for Apple (AAPL) using the S&P500 as my market return, basing my beta on 5 years of monthly returns for Apple and the S&P500, then adjusting all of these returns to real returns by subtracting out the 30-Yr Zero Coupon U.S. T-Bond.  I have outlined this technique in another of my blog posts:  How to use the CAPM and beta

My calculated beta for Apple (1.29) is in cell C5 of the Analysis worksheet.  I checked this against Google’s reported beta for Apple (1.32), and Yahoo’s reported beta of 1.42.  As I have commented on in previous blog posts, Yahoo’s beta’s are not correct, while Google’s beta’s are correct, at least based on the methodology that I choose to use when determining my betas.

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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”