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 (훽) 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
훽푠= 퐸 푟푠 − 푟푓 퐸푟푚 − 푟푓
훽푠 = Beta for Your Investment
퐸 푟푠 = Expected Return from an Asset (i.e. Stock)
퐸푟푚 = Expected Return from a benchmark (i.e. Market)
푟푓 = 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.
퐸푟푚 = 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.
퐸 푟푠 = 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%.
푟푓 = 2.00%

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CALCULATING BETA FOR AN ASSET
Now we can plug our numbers into the beta equation:
훽푠= 퐸 푟푠 − 푟푓 퐸푟푚 − 푟푓
훽푠= 8.00% −2.00% 8.00% −2.00%
훽푠=1.00
퐸 푟푠 = 8.00%
퐸푟푚 = 8.00%
푟푓 = 2.00%

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INTERPRETING BETA
휷풔 = 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
휷풔 = 0
•No correlation between the benchmark and asset
•If the benchmark gains 10%, then the asset gains 0% 휷풔 = 1
•“Perfect” correlation between the benchmark and asset
•If the benchmark gains 10%, then the asset gains 10% 휷풔 = -1
•“Inverse” correlation between the benchmark and asset
•If the benchmark gains 10%, then the asset loses 10% 휷풔 = 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%. 퐸 푟푦푖 = 8.00% - 0.18% = 7.82% 퐸푟푚 = 8.00% 푟푓 = 2.00%

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CALCULATING BETA
Now we can plug our numbers into the beta equation:
훽푦푖= 퐸 푟푦푖 − 푟푓 퐸푟푚 − 푟푓
훽푦푖= 7.82% −2.00% 8.00% −2.00%
훽푦푖=0.97
퐸 푟푦푖 = 7.82% 퐸푟푚 = 8.00% 푟푓 = 2.00%

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CALCULATING BETA
휷풔 = 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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