Calculating Beta for Stocks

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

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

2. Copyright © Invest Safely, LLC. All Rights Reserved www.invest-safely.com 2
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.

3. Copyright © Invest Safely, LLC. All Rights Reserved www.invest-safely.com 3
BETA BACKGROUND
Beta (??????) 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.

4. Copyright © Invest Safely, LLC. All Rights Reserved www.invest-safely.com 4
THE BETA EQUATION
??????
�=
?????? �
�
− �
??????
??????�
??????
− �
??????

??????
� = Beta for Your Investment
?????? �
� = Expected Return from an Asset (i.e. Stock)
??????�
?????? = Expected Return from a benchmark (i.e. Market)
�
?????? = Risk-Free Return

5. Copyright © Invest Safely, LLC. All Rights Reserved www.invest-safely.com 5
CALCULATING BETA FOR AN ASSET
Most experts assume an expected return for the S&P500
Index at 6-8% per year.
??????�
?????? = 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.
?????? �
� = 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%.
�
?????? = 2.00%

6. Copyright © Invest Safely, LLC. All Rights Reserved www.invest-safely.com 6
CALCULATING BETA FOR AN ASSET
Now we can plug our numbers into the beta equation:

??????
�=
?????? �
� − �
??????
??????�
?????? − �
??????


??????
�=
8.00% −2.00%
8.00% −2.00%


??????
�=1.00
?????? �
�

= 8.00%
??????�
?????? = 8.00%
�
?????? = 2.00%

7. Copyright © Invest Safely, LLC. All Rights Reserved www.invest-safely.com 7
INTERPRETING BETA
??????
?????? = 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%

8. Copyright © Invest Safely, LLC. All Rights Reserved www.invest-safely.com 8
EXAMPLE BETA VALUES
??????
??????

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

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

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

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

9. Copyright © Invest Safely, LLC. All Rights Reserved www.invest-safely.com 9
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.

10. Copyright © Invest Safely, LLC. All Rights Reserved www.invest-safely.com 10
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%.

?????? �
???????????? = 8.00% - 0.18% = 7.82%
??????�
?????? = 8.00%
�
?????? = 2.00%

11. Copyright © Invest Safely, LLC. All Rights Reserved www.invest-safely.com 11
CALCULATING BETA
Now we can plug our numbers into the beta equation:

??????
????????????=
?????? �
???????????? − �??????
??????�
?????? − �??????


??????
????????????=
7.82% −2.00%
8.00% −2.00%


??????
????????????=0.97
?????? �
????????????

= 7.82%
??????�
?????? = 8.00%
�
?????? = 2.00%

12. Copyright © Invest Safely, LLC. All Rights Reserved www.invest-safely.com 12
CALCULATING BETA

??????
?????? = 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!

13. Copyright © Invest Safely, LLC. All Rights Reserved www.invest-safely.com 13
FIND MORE SAFE INVESTING INFORMATION…
www.invest-safely.com
blog.invest-safely.com
/InvestSafely
@InvestSafely
www.invest-safely.com/safe-investing.xml
/InvestSafely

14. "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
INVEST SAFELY, LLC
www.invest-safely.com