Chapter 10: Arbitrage Pricing Theory (APT) and Multifactor Models Flashcards
what is the Law of One Price
If two assets are equivalent in all, econmically relevant aspects, they should have the same price
What is the Capital Markets Theory? Also, what is the Dominance Argument?
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.
What is the efficient frontier?
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)
What are the two Pricing Models?
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]
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
B)
What is the formula for Single Factor Model?
Rf + Beta (F - ei)
F= Unanticipated change in macro-economic factor (the SINGLE FACTOR)
ei: Firm specifc events (non-systematic components)
What are the two different types of Risk (that make up Total Risk)
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
What does Beta measure?
Systematic Risk
What does the CAPM graph tell us?
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
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
Alternative Pricing Theory was made called: Abritrage Pricing Theory
What are the flaws of CAPM and whats was made as an alternative
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
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
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
d)
APT Model uses more than one factor, rather than than the single factor Model to calculate Expected Return, what are some examples of Factors:
- Market Risk Premium
- GDP Growth Rate
- Expected Inflation
- Changes in Interest Rates
estimate a factor beta for each factor using multiple regression
Define APT
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
APT vs CAPM
APT understands that certain stocks perform differently based on changes in specifc macro factors, while CAPM assumes eveyrthing changes with just Beta.
What is at least one assumption of APT?
- Capital markets are perfectly competitive
- Investors always prefer more wealth to less wealth with certainty
- The stochastic process generating asset returns can be expressed as a linear function of a set of K factors or indexes
Question (can answer without data) Explain why your return on Air Canada would increase if GDP increases and decrease if Interest rates increase?
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.
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%
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
List 4 different factors that Fidelity uses in their factor-based (APT) models?
Dividend Yield.
Low Volatility.
Quality. …
Momentum. …
Value. …
Size.
Are the Fidelity factors macro, micro, or both ?
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)
What is the end goal of APT and CAPM for stocks and portfolios
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
What is Variance-Mean Efficiency
what is also its relation shoip with the efficient frontier?
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.
