Calculating Beta for Stocks

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www.invest-safely.com A “How-To” For Investors

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Investors can use the beta calculation to estimate their future returns, based on the performance of the "market".

Transcript of Calculating Beta for Stocks

Page 1: Calculating Beta for Stocks

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A “How-To” For Investors

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CALCULATING β

A Simple Guide to for Investors

Joel Wenger

Invest Safely, LLC

The information contained in this guide is for informational and educational purposes only. This publication provides general information and should not be used or taken as business, financial, tax, accounting, legal or other advice. It has been prepared without regard to the circumstances and objectives of anyone who may review it; therefore, you should not rely on this publication in place of expert advice or the exercise of your independent judgment.

The author makes no representation or warranties of any kind regarding the contents of this publication, and accepts no liability of any kind for any loss or harm arising from the use of the information contained in this publication.

The views expressed in this publication reflect those of the author and contributors and does not guarantee that the information contained in this publication is reliable, accurate, complete or current. The author and contributors assume no responsibility to update or amend the publication.

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BETA BACKGROUND

Beta (𝛽) is a measure of correlation. Calculating beta allows you to estimate how closely asset prices will mirror the rise and fall of market prices, by comparing the returns from an asset and a benchmark index.

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THE BETA EQUATION

𝛽𝑠 =𝐸 𝑟

𝑠 − 𝑟

𝑓

𝐸 𝑟𝑚

− 𝑟𝑓

𝛽𝑠 = Beta for Your Investment 𝐸 𝑟𝑠 = Expected Return from an Asset (i.e. Stock) 𝐸 𝑟𝑚 = Expected Return from a benchmark (i.e. Market) 𝑟𝑓 = Risk-Free Return

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CALCULATING BETA FOR AN ASSET

Most experts assume an expected return for the S&P500 Index at 6-8% per year.

𝐸 𝑟𝑚 = 8.00% If you’re buy an investment that mimics returns of the S&P500 Index, you would naturally expect the fund to perform the same as the index.

𝐸 𝑟𝑠 = 8.00% Unfortunately, “risk-free” returns do not exist. Today, U.S. Treasuries are considered the next best thing. Let’s assume they return 2%.

𝑟𝑓 = 2.00%

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CALCULATING BETA FOR AN ASSET

Now we can plug our numbers into the beta equation:

𝛽𝑠 =𝐸 𝑟𝑠 − 𝑟𝑓

𝐸 𝑟𝑚 − 𝑟𝑓

𝛽𝑠 =8.00% − 2.00%

8.00% − 2.00%

𝛽𝑠 = 1.00

𝐸 𝑟𝑠 = 8.00%

𝐸 𝑟𝑚 = 8.00% 𝑟𝑓 = 2.00%

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INTERPRETING BETA 𝜷𝒔 = 1

When an asset has a β of 1, the returns of the asset and the index are “correlated”. In other words, for every 1% move in the S&P500, an investment based on that index can be expected to move 1%. • If S&P500 returns rise 10%, then asset returns are

expected to rise 10%

• If S&P500 returns fall 10%, then asset returns are expected to fall 10%

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EXAMPLE BETA VALUES 𝜷𝒔

= 0 • No correlation between the benchmark and asset • If the benchmark gains 10%, then the asset gains 0%

𝜷𝒔 = 1 • “Perfect” correlation between the benchmark and asset • If the benchmark gains 10%, then the asset gains 10%

𝜷𝒔 = -1 • “Inverse” correlation between the benchmark and asset • If the benchmark gains 10%, then the asset loses 10%

𝜷𝒔 = 2 • “Double” correlation between the benchmark and asset • If the benchmark gains 10%, then the asset gains 20%

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REAL WORLD APPLICATION OF BETA Suppose that you are looking to invest in a mutual fund, and decide to purchase shares of an investment based on a stock market index, such as the S&P500. You do your homework and find a low-cost fund. Vanguard's S&P500 Index Fund (VFINX) comes to mind. Before you invest, you want to know how well the fund is managed. In other words, you want to know how closely VFINX returns will match those of the actual S&P500. Investors can answer this question using beta values.

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REAL WORLD APPLICATION OF BETA With a little research, I found that the VFINX mutual fund has an expense ratio of 0.18%. Therefore, the expected return of VFINX is equal to the expected return of the S&P500 (8%), minus the expense ratio for VFINX (0.18%), which equals 7.82%.

𝐸 𝑟𝑦𝑖 = 8.00% - 0.18% = 7.82% 𝐸 𝑟𝑚 = 8.00% 𝑟𝑓 = 2.00%

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CALCULATING BETA Now we can plug our numbers into the beta equation:

𝛽𝑦𝑖 =𝐸 𝑟𝑦𝑖 − 𝑟𝑓

𝐸 𝑟𝑚 − 𝑟𝑓

𝛽𝑦𝑖 =7.82% − 2.00%

8.00% − 2.00%

𝛽𝑦𝑖 = 0.97

𝐸 𝑟𝑦𝑖 = 7.82%

𝐸 𝑟𝑚 = 8.00% 𝑟𝑓 = 2.00%

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CALCULATING BETA

𝜷𝒔 = 0.97 With a β of 0.97, every 1% increase in the S&P500 will cause VFINX to rise 0.97%. On the flip size, every 1% decrease in the S&P500 will cause VFINX to fall 1.03%.

This is why controlling costs is so important. YOU pay fees regardless of whether you make money!

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"As to methods there may be a million and then some, but principles are few. The man who grasps principles can successfully select his own methods. The man who tries methods, ignoring principles, is sure to have trouble."

- Ralph Waldo Emerson

TM

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