6. CAPM

Question 1

What is the equation used to measure Beta?

Answer 1

where:

oim = the covariance between the stocks return and the markets return

o2m = variance of the markets return

Question 2

What is total risk equal to?

Answer 2

total risk = market risk + specific risk

Question 3

What does it mean if Amazon stock has a Beta of 1.55?

Answer 3

If we assume this carries on, say the market increases by 1%, amazon will rise by 1.55%.

Similarly, if the market falls by 2%, Amazon’s stock price will fall by 3.1% (2 * 1.55)

Question 4

What does it mean if a BETA is greater than 1?

Answer 4

BETA > 1 = Stocks that move more than one-for-one with the overall market. Most examples include luxury companies, eg. porsche. When the economy does well, consumers buy more goods.

Question 5

What does it mean if a BETA is between 0 and 1?

Answer 5

0 < BETA < 1 = Stocks that still go up in the market bus less than one-for-one. Most examples include necessity companies. When the economy does well, they will only see slight increases, whereas as it falls, it will see only a smaller drop.

Question 6

What does it mean if a BETA is smaller than 1?

Answer 6

0 > BETA = A negative beta is possible in theory. Such a stock does well when the economy does poorly. Hard to find concrete examples…

Question 7

What is the “market portfolio”?

Answer 7

The true market portfolio contains all the world’s risky assets
-> so not limited to only US stocks.

Question 8

Is it possible to find an accurate value of the “market portfolio”?

Answer 8

NO.

There is no index that measures the value of all risky assets.

Therefore, investors use a PROXY (an approximation) for the market portfolio.
-> Most often an investor will use a proxy in their home countries’ stocks, eg. in the USA many use the S&P composite index as their benchmark.

Question 9

Why do betas determine portfolio risk?

Answer 9

“The beta of a portfolio is the weighted average of the betas of the individual stocks within that portfolio”

As beta measures undiverifiable risk to begin with, there is no diversification effect when adding a stock to a portfolio.
-> the beta of a portfolio is simply the weighted-average beta of the stocks in the portfolio

Question 10

What does this curved line show?

Answer 10

The curved line illustrates how expected return and standard deviation change as you hold different combinations of both stocks…

-> In the example above, holding 60% Southwest and 40% Amazon results in an expected return of 13% with a standard deviation of 22%

Question 11

What does the gain of diversification depend on?

Answer 11

The gain from diversification depends on how highly the stocks are correlated

Question 12

If the correlation is 1, what would the impact of diversification be?

Answer 12

If the correlation is 1, there would be no gain from diversification

Question 13

If the correlation is - 1, what would the impact of diversification be?

Answer 13

If the correlation is -1 (unrealistic), the combination of both stocks would have NO risk

Question 14

What does portfolio A offer?

Answer 14

Efficient portfolio (as its on the curve)

Offers the lowest risk

Question 15

What does portfolio C offer?

Answer 15

Efficient portfolio (on the curve)

Offers the highest returns, but also the highest risk

Question 16

How can you exist outside the efficient frontier?

Answer 16

if you can lend or borrow at the risk-free rate of interest!

Question 17

If you invest in portfolio S and lend and borrow at the risk free interest rate, rf, what can you achieve?

Answer 17

You can achieve any point along the straight line from rf through to S.

Question 18

What is the Sharpe Ratio?

Answer 18

The ratio of the risk premium to the standard deviation is called the Sharpe Ratio

Question 19

What is the equation of the “sharpe ratio”?

Answer 19

-> rf is risk free interest rate

Investors will track Sharpe ratios to measure the risk-adjusted performance of investment managers

Question 20

What is the “Capital Asset Pricing Model”?

Answer 20

The capital asset pricing model (CAPM) states that the expected risk premium on each investment is proportional to its beta. This means that each investment should lie on the sloping security market line connecting Treasury bills and the market portfolio.

Question 21

What is the blue line called?

Answer 21

Security Market Line

Question 22

What is the equation of the CAPM ratio?

Answer 22

where:
r = expected return

rf = risk-free rate of interest

rm = expected return on market portfolio

Beta = sensitivity of a stocks return to the return on the market portfolio

Question 23

The security market line is essentially the _____ equation plotted

Answer 23

The CAPM equation plotted

Question 24

What are some key assumptions about CAPM?

Answer 24

• investing in US treasury bills is risk-free
• Investors can borrow money at the same rate of interest at which they can lend
  -> usually borrowing rates are higher than lending rates
• all assets are marketable

Question 25

Would you buy stock A?

Answer 25

NO. Investors would never buy stock A.

Instead of buying stock A, investors would prefer to lend part of their money and put the balance in the market portfolio. And instead of buying stock B, they would prefer to borrow and invest in the market portfolio.

Question 26

What is the difference between the capital market line and the security market line?

Answer 26

Capital market line:
- applies to efficient portfolios

• portfolios that bear specific risk lie below the line
• investor could still want to hold a stock below the market line as it is diversifiable

Security market line:
- applies to any stock or portfolio (can be inefficient)

• horizontal axis is Beta which is the market risk and undiversifiable
• the investor would be unwilling to hold stocks below the line

Question 27

Are returns unrelated to all other characteristics?

Answer 27

Empirical evidence shows that other factors (than Beta) might drive different expected returns

Question 28

What is a possible alternative to CAPM?

Answer 28

Arbitrage Pricing Theory

Question 29

What does “Arbitrage Pricing Theory” assume?

Answer 29

Assumes that each stock’s return depends partly on pervasive macroeconomic influences of “factors” and partly on “noise”

The expected risk premium on a stock should depend on the expected risk premium associated with each factor and the stock’s sensitivity to each of the factors (b1, b2, b3)

Question 30

What is the equation of the Arbitrage Pricing Theory?

Answer 30

Question 31

In the abitrage pricing theory, what if the b’s are 0?

Answer 31

if the “b”s are 0, the expected risk premium is also 0.

-> A diversified portfolio that has 0 sensitivity to each macroeconomic factor is essentially risk-free return.

-> If the portfolio DID offer a higher return, you could make a risk-free profit (“arbitrage”) by borrowing to buy the portfolio.

Question 32

What is the 1st step of carrying out the Arbitrage Pricing Theory?

Answer 32

1. Start off by making a short list of macroeconomic factors that could affect stock returns

eg.
- market factor (return on market index minus risk-free interest rate)

• size factor (return on small-firm stocks less return on large-firm stocks)
• book-to-market factor (return on high book to market ratio stocks less return on low book-to-market stocks

Question 33

What is the 2nd step of carrying out the Arbitrage Pricing Theory?

Answer 33

2. Estimate the risk premium on each of these factors:

eg:
- market risk premium 7%

• difference between annual returns on small and large capitalization stocks avg 3.2%
• difference between the returns on stocks with high and low book-to-market ratios avg 4.9%

Question 34

What is the 3rd step of carrying out the Arbitrage Pricing Theory?

Answer 34

Measure the sensitivity of each stock to the factors

and combine into final equation