7. Empirical Evidence on Security Returns

Question 1

CAPM predicts

Answer 1

that expected returns increase with beta: stocks with higher betas should earn higher returns on average

Question 2

How would you test CAPM

Answer 2

• Time series: one firm over multiple periods
• Cross-section: multiple firms at one point in time -> focus on cross-section test of CAPM: do riskier/higher beta firms have higher returns

Question 3

CAPM in theory

Answer 3

o Expected stock and market returns
o Beta is known
o Greek letters
o Slope of SML = market risk premium
o CAPM: no other risk factor should explain differences in returns

Question 4

CAPM in reality

Answer 4

o Realized stock and market returns
o Beta is measured (not known)
o Normal letters (or hats)
o Slope of SML is flatter than market risk premium
o Other factors play a role (size, btm, momentum)

Question 5

Cross-section

Do riskier/higher beta firms have higher returns?

Two options to perform test:

Answer 5

1. Average returns over time and regress on constant beta

2. For every month regress monthly returns on time-varying beta -> Fama-MacBeth.

Question 6

Both ways test hypothesis:

Answer 6

Higher betas lead to higher returns

Positive relation between beta (systematic risk) and expected/average returns

Question 7

First stage and second stage

Answer 7

First stage: estimating betas

Second stage: regressing returns on betas

Question 8

If CAPM is true, ..

If CAPM holds, ..

Answer 8

• No other factors should explain time-series and cross-sectional difference in returns -> all other variables should be 0
• Returns only depend on beta of market.

Question 9

In reality SML is flatter, consequences:

Answer 9

• Fisher Black: “Even if line is flat for investors and corporations, beta is essential for making investment decisions. Beta more useful if line is flat than if it is steep as theory predicts”
• AQR sets up ‘betting against beta’ strategy

Question 10

If line is too flat:

Answer 10

• Empirical finding is well known (Fama-French 1992): investors take this into account by setting up investment strategy

Question 11

Roll’s Criticism

Answer 11

• Only testable hypothesis is whether market portfolio is mean-variance efficient
• CAPM isn’t testable unless exact composition of market portfolio is known and used in tests

Question 12

Other risk factors that investors demand compensation for

Answer 12

• Labor risk
• Consumption risk
• Unexpected inflation
• Changes in investment opportunity set

Question 13

Fama-French

Size and book to market explain cross-sectional differences in return

Answer 13

• Smaller firms experience higher returns than predicted by CAPM
• High book to market firms experience higher returns than predicted by CAPM

Question 14

Two interpretation camps:

Answer 14

1. Risk-based explanations

2. Behavioural explanations

Question 15

Risk-based explanations

Answer 15

Size and value are priced risk factors (CAPM model is incomplete ->
more risk factors).

Question 16

Risk-based explanations

Liew and Vassalou

Answer 16

SMB and HML seem to predict GDP growth and relate size and value premium to business cycle -> proxy for business cycle risk

Question 17

Risk-based explanations

Petkova and Zang

Answer 17

If economy is expanding, value β < growth β (value less risky), if economy is in recession, value beta > growth beta (value more risky)

Question 18

Behavioural explanations

Answer 18

Premiums could be due investor irrationality or behavioural biases (underlying assumption CAPM is wrong -> investors aren’t rational)

Question 19

Survivorship bias

Answer 19

Estimating risk premiums of most successful stocks and ignoring evidence from stock markets that didn’t survive for full sample period will impart upward bias in estimates of expected returns