Week 7 - CAPM (2)

Question 1

What occurs under a CAPM where there are restrictions under borrowing/risk free rate?

Answer 1

Every portfolio on the efficient frontier, except for the global minimum-variance portfolio, has a “companion” portfolio on the bottom (inefficient) half of the frontier

Since uncorrelated, also known as Zero Beta Portfolio

Since mkt portfolio efficient, also has 0 COV

Question 2

What does the Zero Beta portfolio do for investors?

Answer 2

Acts as the risk free asset since there are restrictions on borrowing/accessing the risk free rate

Question 3

What is the Zero Beta CAPM Equation?

Answer 3

E(ri) − E(rz ) = [E(rm) − E(rz )] x Cov (ri ,rm)/σ2m
= βi[E(rm) − E(rz )]

Where
Rz = Is the companion portfolio

(Instead of the risk free rate, rf, in the CAPM equation we have the expected rate of return on a portfolio that has zero covariance with the market portfolio) USEFUL INFO TO KNOW BUT NOT NEEDED FOR EXAM

Question 4

What did Fischer Black use this equation to display?

Answer 4

• > When investors do not have access to the risk free rate, rf rate, it means we cannot derive the Capital Market Line(CML).
• > Instead, every investor chooses a point on the efficient frontier according to their preferences (over risk and return).

->Market portfolio is a convex combination of investors’
portfolios which is efficient

Question 5

What are the implications of the zero beta CAPM?

Answer 5

Investors who wish to borrow find it impossible or costly will instead tilt portfolios toward high-beta stocks and away from low-beta ones.

As a result, prices of high beta stocks will rise, and their risk premiums will fall. The SML will be flatter than in the simple CAPM.

SEE GRAPH IN NOTES

Question 6

What are some other extensions of the CAPM?

Answer 6

1. An intertemporal model (ICAPM)
2. Multiple risk factors
3. A consumption-based model (CCAPM)
4. Incorporation of non-traded assets such as labour or human capital.
5. Non-constant beta (conditional CAPM)
6. CAPM modified for liquidity risk

Question 7

What is the CAPM and the Single Index Model combo?

Answer 7

Alternate way to derive CAPM
Single Index: Where excess stock returns, Ri are
normally distributed and driven by one systematic factor.

Question 8

How do you calculate the Single Index?

Answer 8

Ri = αi + βiRm + εi

Question 9

What are the assumptions of the CAPM/Single Index model?

Answer 9

E(Ri) = αi + βiE(Rm)
σ2i = β2i σ2m + σ2ε

2 is to the power of 2

Question 10

What is the return and VAR of the portfolio (Q), of N stocks with a weight of Wk?

Answer 10

RETURN: RQ = αQ + βQRm + εQ
VAR: σ2εQ =N∑k=1w2k σ2εk

2 is to the power of 2

Question 11

How can investors diversify the non-systematic risk?

Answer 11

Diversify the non-systematic risk and by

choosing stocks with positive alpha can increase the risk premium on Q.

Question 12

What happens if investors pursue positive Alpha Stocks?

Answer 12

->if investors pursue positive alpha stocks, prices of
positive alpha stocks will rise and prices of negative alpha stocks will fall.

->This will continue until all alpha values are driven to zero.

Here, investors content in minimising risk by removing unique risk by holding broadest mkt portfolio -> When all stocks α = 0, mkt portfolio is optimal risky portfolio
THIS IS CAPM

Question 13

What are the three steps needed to estimate the expected return on a particular stock?

Answer 13

1. To construct mkt portfolio
2. To determine expected excess return over Risk free interest rate
3. Estimate Stock beta

Question 14

How do you calculate the mkt portfolio in the CAPM and Single Index combo?

Answer 14

wi = Market Value of i /Total Market Value of All Securities in the Portfolio= MVi/ ∑j MVj

Where:
MVi = = Number of shares of i outstanding × (Price of i per share)

Question 15

What is a Value Weighted Portfolio?

Answer 15

A portfolio like the market portfolio, in which each security is held in proportion to its market capitalization

(ITS A PASSIVE PORTFOLIO)

Question 16

What are some of the mkt indexes?

Answer 16

->The S&P500 which is an index that represents a
value-weighted portfolio of 500 of the largest U.S. stocks. It represents almost 80% of the U.S. stock market in terms of market capitalization.

-> Wilshire 5000, provide a value-weighted index of all U.S. stocks listed on the major stock exchanges

->Dow Jones Industrial Average (DJIA), which consists of a portfolio of 30 large industrial stocks. The DJIA is a
price-weighted (rather than value-weighted) portfolio. A
price-weighted portfolio holds an equal number of shares of each stock, independent of their size.

FTSE 100 which is a value-weighted portfolio of the 100
largest UK stocks.

Question 17

How do you estimate the beta of a security?

Answer 17

E(Rit) = rf + βi(E(Rmt) − rf ) + αi
Where:
rf +βi(E(Rmt) − rf ) (Expected return of i from the SML)
αi (Distance above/below the SML)

Question 18

How can we interpret αi as?

Answer 18

As a risk-adjusted measure of the stock’s historical performance (Jensen’s alpha)

Question 19

In testing CAPM what are the two tests we use?

Answer 19

First-Pass Regression: For every security we estimate it’s alpha and beta using equation (2)
(2) Second-Pass Regression:
r¯ei = η0 + η1βi + η2σ2εi + vi

σ2 εi is the only case here where 2 is to the power of

Question 20

What does the CAPM predict?

Answer 20

1. η0 = 0, the average alpha in the sample will be zero;
2. η1 = rm − rf, linear SML with the slope equals the
   market-index risk premium; and
3. η2 = 0 which implies that unique risk, σ2εi, doesn’t earn a risk premium.
   4- vi is the zero mean residual of this regression.

Question 21

What did early findings on testing the CAPM show? (By John Lintner)

Answer 21

• > The estimated SML is “too flat”; that is, the η1 coefficient is too small.
• > Low-beta stocks have yielded returns, on avg, higher than they should have been on the basis of their beta.

->High beta stocks found to have on avg, lower returns than they should have on the basis of their betas.
η0 is 0.127.