Chapter 10: Arbitrage Pricing Theory (APT) and Multifactor Models

Question 1

what is the Law of One Price

Answer 1

If two assets are equivalent in all, econmically relevant aspects, they should have the same price

Question 2

What is the Capital Markets Theory? Also, what is the Dominance Argument?

Answer 2

Capital Market Theory:
* market and investors are rational → security prices are stable
* If arbitrage opportunities do exist → strong pressure will occur to restore stable prices
* therefore, abritrage opportunities quickly disapear

Therefore, capital market investors are rational and perfer mean variance efficiency

Dominance Argument:
* Investors want a portfolio that either gives a higher return for the same (higher) risk or lower risk for the same (lower) return.

Question 3

What is the efficient frontier?

Answer 3

An efficient frontier is a set of investment portfolios that are expected to provide the highest returns at a given level of risk/standrad devation. SML/CAPM GRAPH FOCUSES ON BETA (MARKET RISK)
* line that indicates the highest yield possible given the lowest level of risk

• picture it on a graph
  
  • there’s the main efficient frontier that represents the optimal combination of return given the level of risk
  • individual securities would be below the line
  • as you move up (y-axis) = expected return
  • as you move to the side (x-axis) = higher risk ‘
  • ideally, you want your securities in your portfolio to be close the line
  • Depending on the ratio between Stocks and Bonds, will depend where your securities ie
    
    • ex. bonds are low risk. low yield
    • stocks are high risk, high yield
    • but with both you can get medium risk and medium yield (dependent on the ratio)

Question 4

What are the two Pricing Models?

Answer 4

CAPM - Single Factor Model
APT - Multifactor Model

Purpose? They derive the required return (based on risk), which can be used to discount a firm’s future cash flows - thus leading to valuation of the firm/shares

Valuation: ∑[CFt / (1+k)t]

Question 5

Q1: The concept that investors will chooseportfoliosbased on a higher expected returnportfoliofor a given level of variance;or the lowervariance portfoliofor a given expected return is called the:

a) Law of One Price
b) Dominance Argument
c) Capital Asset Pricing Theory
d) Arbitrage Pricing Theory

Answer 5

B)

Question 6

What is the formula for Single Factor Model?

Answer 6

Rf + Beta (F - ei)

F= Unanticipated change in macro-economic factor (the SINGLE FACTOR)

ei: Firm specifc events (non-systematic components)

Question 7

What are the two different types of Risk (that make up Total Risk)

Answer 7

Unsystematic Risk: Company-specifc and unique risk
* solution: solved by diversifiying money into more companies/sectors

Systematic Risk: Risk caused macoeconomic variables, such as interest rate voltalilty, business cycles, etc.
* caused by the system aka the economy

Question 8

What does Beta measure?

Answer 8

Systematic Risk

Question 9

What does the CAPM graph tell us?

Answer 9

Security Market Line (SML): line that represnets the ideal expected return given the amount of beta, i.e. its systematic risk

• Securities above the SML line are overvalued
• securities below SML line are undervalued

Question 10

Read:
However = CAPM is criticized for:
Beta is not stable;
Difficulties in selecting a proxy for the market portfolio.;
Many unrealistic assumptions;
Research has shown that other factors besides B x (Rm-RF) drives a security’s returns.

• Said that higher beta would provide higher returns which was not the case in a canadian equity study

Answer 10

Alternative Pricing Theory was made called: Abritrage Pricing Theory

What are the flaws of CAPM and whats was made as an alternative

Question 11

Q2. The expected return based on CAPM for a stock is 10.5%. If the risk-free rate is 4%, and market return is 9%, what is the Beta of this stock?

A) 1.1
B) 1.3
C) 0.77
D) 0.29
E) 0.5

Answer 11

b)

How I did it
E(r)= rf +b (rm - rf)

10.5 = 4 + b (9-4)
10.5-4  = 6.5

6.5 = b5
6.5/5  = 1.3

Question 12

Q3. If you draw a regression line between the returns to the security over time and the returns to the market portfolio, the slope of this regression line is the:

A) security’s variance
B) market risk premium
C) risk-free rate
D) security’s beta
E) security’s standard deviation

Answer 12

d)

Question 13

APT Model uses more than one factor, rather than than the single factor Model to calculate Expected Return, what are some examples of Factors:

Answer 13

• Market Risk Premium
• GDP Growth Rate
• Expected Inflation
• Changes in Interest Rates

estimate a factor beta for each factor using multiple regression

Question 14

Define APT

Answer 14

Arbitrage Pricing Theory (APT) is a model that predicts an asset’s returns based on its relationship with several big economic factors that affect the whole market.

• used to value assets (by getting E(r) to use as discount rate) but also, identify securities that are mispriced

Question 15

APT vs CAPM

Answer 15

APT understands that certain stocks perform differently based on changes in specifc macro factors, while CAPM assumes eveyrthing changes with just Beta.

Question 16

What is at least one assumption of APT?

Answer 16

1. Capital markets are perfectly competitive
2. Investors always prefer more wealth to less wealth with certainty
3. The stochastic process generating asset returns can be expressed as a linear function of a set of K factors or indexes

Question 17

Question (can answer without data) Explain why your return on Air Canada would increase if GDP increases and decrease if Interest rates increase?

Answer 17

Answer:
* If the economy is doing well, we would expect Air Canada to do well as more people and businesses would be spending money on travel.

• However if interest rates are increasing sharply (perhaps because of inflation), many costs for Air Canada, such as oil, would be increasing and thus reducing its profit margin.

Question 18

Q6: Consider the multifactor APT with two factors. Stock A has an expected return of 16.4%, a beta of 1.4 on factor 1, and a beta of.8 on factor 2. The risk premium on the factor-1 portfolio is 3%. The risk-free rate of return is 6%. What is the risk-premium on factor 2 (i.e. the factor loading) if no arbitrage opportunities exist?

A.2.95% B.3.50% C.4.25% D.7.75% E.5.00%

Answer 18

Q6: Answer: D: 7.75%

E(RA) = R f + β1 F1 + β2F2

16.4% = 6% + 1.4 (3%) + 0.8 x F2
10.4% = 4.2% + 0.8 F2
0.80 F2 = 10.4% - 4.2%
F2 = 6.2%/0.80 = 7.75%

• remeber to multiply beta with its respective economic factor than add Risk free rate

Question 19

List 4 different factors that Fidelity uses in their factor-based (APT) models?

Answer 19

Dividend Yield.
Low Volatility.
Quality. …
Momentum. …
Value. …
Size.

Question 20

Are the Fidelity factors macro, micro, or both ?

Answer 20

Answer: They are both

• Factors such as dividends, yield and quality are micro (company basis)
• Factors such as interest rates, geopolitical are macro. (economy basis)

Question 21

What is the end goal of APT and CAPM for stocks and portfolios

Answer 21

for stocks:
Are used to derive required return (discount rate) for securities and then find intrinsic prices

• Compare the intrinsic price from the model to actual price of a security.
• Buy undervalued securities and sell short overvalued securities due to no-arbitrage theory that mispriced securities will quickly correct.

for portfolio:
Can be used to build portfolios that will do well if there are macroeconomic surprises (that you have predicted).
* For example, if you believe that inflation will increase more than what the market has anticipated, you will choose stocks who will do well in that environment

Question 22

What is Variance-Mean Efficiency

what is also its relation shoip with the efficient frontier?

Answer 22

Think of mean-variance efficiency as the “best deal” in investing:
* It’s either or:
* You want to get the most return for your risk
* or take the least risk for your desired return.

Portfolios that are mean-variance efficient form the Efficient Frontier.