Chap.2_Basic models of risk in finance

Question 1

What is the one-period return of a single stock?

Answer 1

Question 2

Using one-period returns on several periods, how can you compute the return of one stock over several periods?

Answer 2

Question 3

What is the arithmetic/geometric average of returns (mathematically)?

Answer 3

Question 4

What is the difference between arithmetic and geometric average?

Answer 4

1. Geometric average takes into account the compounded interests.
2. Arithmetic average ignores this connection and considers an average of the returns taken independently.

Question 5

When do use arithmetic vs. geometric average?

Answer 5

1. We use geometric average to compute an average historical return.
2. We use arithmetic average to compute an expected (future) return, estimated based on past observed returns.

Question 6

How is risk implied by returns?

Answer 6

Risk is implied by the uncertainty of the return distribution.

Question 7

What are the characteristics of return distributions? Define them briefly.

Answer 7

Question 8

In the context of stock returns, how is risk measured mathematically?

Answer 8

By the standard deviation of returns.

Question 9

What is risk (mathematically)?

Answer 9

Mathematically, risk is how much observed returns deviate from the expected return (i.e. from the
arithmetic average return).

Question 10

What are the advantages of the standard deviation as a measure of risk? Its limitations?

Answer 10

A. Advantages of standard deviation:
1. Easy to calculate and implement
2. Takes into account both upside and downside risk
B. Drawbacks of standard deviation:
1. Investors are usually worried about the downside risk only (i.e. the risk of loss).
2. SD includes both the upside risk and the downside risk. If returns are skewed it is not the only relevant measure of risk

Question 11

What is the return of a two-asset portfolio?

Answer 11

Question 12

What is the return of a n-asset portfolio?

Answer 12

Question 13

What is the risk of a two-asset portfolio?

Answer 13

Question 14

What is the correlation between the returns of two assets (in English)?

Answer 14

The correlation between the returns of two assets is how their returns move together.

Question 15

What are the possible values of return correlation? Explain briefly what they correspond to.

Answer 15

Question 16

What is the relationship between the risk of a portfolio and the correlation of its assets?

Answer 16

The relationship is that the risk (standard deviation of a portfolio) is less than the weighted sum of the risks of each of its assets.

Question 17

How could you reduce your portfolio risk? Explain briefly.

Answer 17

1. To reduce a portfolio risk you must find assets that are less correlated. The risk of a portfolio decreases when the correlation between its assets decreases.
   In a portfolio that has two assets that are perfectly negatively correlated (correlation = - 1), when one increases the other decreases in the exact same amount. The portfolio is thus protected (i.e. bears less risk).
2. To reduce your portfolio risk you should diversify as much as you can. Generally the more assets you add in your portfolio, the lower your portfolio risk. This phenomenon is called diversification.

Question 18

What does the CAPM model try to model?

Answer 18

1. What is the theoretical return of a given asset required by investors for them to buy it.
2. What is the fair return an investor should obtain when investing in this asset.

Question 19

What are the assumptions of the CAPM model?

Answer 19

Question 20

According to the CAPM model, how the return of an asset is measured?

Answer 20

Question 21

What is the beta of an asset? How should you interpret it?

Answer 21

The beta is a measure of systematic risk. It measures by how much an individual security covary with the market.

Question 22

How do you measure total risk? How do you measure systematic risk?

Answer 22

Question 23

What are the implications of market efficiency?

Answer 23

1. If markets are indeed efficient, value is just more risky (Fama-French three-factor model).
2. If markets are not efficient, investors’ errors create the value premium (behavioral finance).

Question 24

Why does not market efficiency actually work?

Answer 24

1. The beta does not explain alone average security returns.
2. The combination of size and book to market ratios does explain average
   security returns.

Question 25

Why does the competitive markets hypothesis of the CAPM not work? (The assumption: Markets are perfectly competitive all agents borrow lend at the same rate, buy sell any asset at the same price with no taxes and no transaction costs.)

Answer 25

1. Companies, financial institutions, wealthy investors tend to borrow at a cheaper rate.
2. There are taxes: corporate taxes, income taxes.

Question 26

What is the equity premium puzzle?

Answer 26

Average US equity returns (S&P 500) have been about twice as large as those of long-term Treasuries over the last 100 years.

Question 27

Which contribution (or addition) does the Fama-French three-factor model make to the CAPM model?

Answer 27

According to the Fama-French three-factor model:
1. The beta does not explain alone average security returns
2. The combination of size and book-to-market ratios does explain average security returns.
Thus, the contributions are:
1. Size.
2. Book-to-market ratio.

Question 28

According to the Fama-French three-factor model, how is the return of an asset measured (mathematically)?

Answer 28

Question 29

Explain the three factors in the Fama-French three-factor model.

Answer 29

1. Beta or risk.
2. 𝑆𝑀𝐵𝑡 (“Small Minus Big”) is the return of a portfolio of small stocks minus the return of a portfolio of large stocks.
3. 𝐻𝑀𝐿𝑡 (“High Minus Low”) is the return of a portfolio of value stocks (with a high book-to-market ratio) minus the return of a portfolio of growth stocks (with a low book-to-market ratio).

Question 30

Which theories can explain the fact that the CAPM model is not empirically verified?

Answer 30

1 The Ferma-French three-factor model.
2. Behavioral finance: prospect theory.

Question 31

Define behavioral finance.

Answer 31

A field that studies the impact of emotion, cognitive biases, and other psychological factors on financial decision making and hence on financial markets (APA Dictionary of Psychology).

Question 32

What is the main contribution of behavioral finance to traditional portfolio theory?

Answer 32

Not all investors are rational; therefore there are systematic cognitive and heuristic biases in people.

Question 33

Cite and define five well-known (behavioral) biases in finance.

Answer 33

1. Loss aversion
2. Overconfidence
3. Overoptimism
4. Misjudgements of probabilities and laws of probabilities
5. Herding