12-1

Some Lessons from Capital Market History

Chapter 12

Copyright © 2013 by The McGraw-Hill Companies, Inc. All rights reserved.McGraw-Hill/Irwin

Chapter Outline

• Return Definitions

Dollar Return vs. Percentage Return

• Historical ReturnsAverage Returns & Variability of Returns

• Capital Market Efficiency

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Return Definitions: Dollar Returns

• Total dollar return = income from investment + capital gain (loss) due to change in price

3

Return Definitions: Percentage Returns

• Total percentage return =

(income from investment + capital gain)

beginning price

4

Return ExampleYou buy a stock for $20 per share. At the end of the year the price is $30 per share. During the year you received a $3 dollar dividend per share.

1. What is the dividend yield?

2. What is the capital gains yield?

3. What is the total percentage return?

5

Return Example

In the previous example, if you had invested $1,000, how much in dividends, capital gain, and total dollar return would you have received?

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Historical Returns, 1925-2010

Risk Premium

7

Risk Premiums

• Risk Premium: The “extra” return earned for taking on risk

• Risk premium = return - risk free rate

• Treasury bills are considered to be risk-free

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Historical Returns: Average Returns

• Average Returns = sum of returns / # of observations (T)

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T

RRRR T

...21

Historical Returns: Variance and Standard

Deviation of Returns• Variance and standard deviation measure

the volatility of asset returns• Historical variance = sum of squared

deviations from the mean / (number of observations – 1)

• Standard deviation = square root of the variance 10

1

)(...)( 2212

T

RRRRVAR T

Example

Calculate the average return and the standard deviation for the following return series:

Year Return Avg. Return Deviation Deviation2

2007 0.30

2008 0.45

2009 0.12

2010 -0.15

2011 0.24

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Summary of Historical Returns 1926-2010

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Normal Distribution• A large enough sample drawn from a normal

distribution looks like a bell-shaped curve.

In what range do the returns of large company stocks fall 68% (2/3) of the time? Avg: 11.9%, SD: 20.4%Range = avg. return +/- z (SD) => .119 +/- 1(.204)= & 13

68% => z=1

95% => z=2

99% => z=3

Efficient Capital Markets

• Stock prices are in equilibrium or are “fairly” priced.

• If this is true, then you should not be able to earn “abnormal” or “excess” returns.

• Three forms of market efficiency:- weak, semi-strong, and strong-form

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Forms of Market Efficiency• Weak Form: Prices reflect all past

(historical) market information such as price and volume=>abnormal returns cannot be earned based on historical information

• Semi-Strong Form: Prices reflect all publicly available information including trading information, annual reports, press releases, etc.=>abnormal returns cannot be earned based on public information

• Strong Form: Prices reflect all information, including public and private=>abnormal returns cannot be earned based on private information 15

The Record of Mutual Funds

Taken from Lubos Pastor and Robert F. Stambaugh, “Mutual Fund Performance and Seemingly Unrelated Assets,” Journal of Financial Economics, 63 (2002).

-2.13%

-8.45%

-5.41%

-2.17% -2.29%

-1.06%-0.51%-0.39%

All funds Small-companygrowth

Other-aggressive

growth

Growth Income Growth andincome

Maximumcapital gains

Sector

Annual return performance of different types of US mutual funds relative to a broad-based market index (1963 – 1998). Annual return performance of different types of US mutual funds relative to a broad-based market index (1963 – 1998).

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