Lecture 7 - Capital Asset Pricing (CAPM)

Question 1

The efficient frontier or risky investment portfolios

Answer 1

• Portfolios lying on the efficient frontier are “efficient” because they offer the maximum return possible for a given level of risk, or the minimum risk for a given level of return
• Investors use the efficient frontier to make informed decisions about asset allocation and portfolio
  optimization to achieve their investment goals

Question 2

Tangency Portfolio

Answer 2

• The best stock portfolio to combine with the risk-free asset is the tangency portfolio T
• Any portfolio on the 𝑟𝑓 − 𝑇 − 𝑌 line is superior to any portfolio on the investment opportunity set and efficient frontier

Question 3

Sharpe ratio

Answer 3

Measures risk-adjusted rate of return

Question 4

Risk preference

Answer 4

• When lending and borrowing at the risk-free rate is allowed, all investors will hold the same tangency portfolio T, regardless how much risk they are willing to take
• So, whatever the risk preference, investors will want to invest some or all their funds in Portfolio

Question 5

Tangency portfolio = Market portfolio

Answer 5

• All investors should hold the same stock portfolio
• Investors differ in how much of that portfolio they hold
• All investors hold the same portfolio, and all stocks are held (if they were not held their price would be 0) => all investors hold the market portfolio

Question 6

Market portfolio

Answer 6

• The market portfolio is the portfolio of all stocks in the economy where the weights correspond to the fraction of the overall market that each stock represents
• Since all investors hold the market portfolio then all unsystematic risk is diversified away and all that remains is the systematic risk (market risk)

Question 7

2 fund seperation theorem (Tobin’s)

Answer 7

• Although investors have different levels of tolerance to risk, they all will purchase the market portfolio
• 2 stages to the investment process:
  1. Establish tangency portfolio (highest Sharpe ratio)
  2. Borrow/lend (@risk free) to adjust for preferred risk and return combinations

Question 8

Major assumptions on which Tobin’s is founded

Answer 8

1. No transaction costs or taxes
2. Investors can borrow/lend at risk free rate
3. Investors have all relevant information
4. Maximisation of utility is the objective of all investors

Question 9

Capital Market Line

Answer 9

The straight line through portfolio T is the Capital Market Line

Question 10

Diversification for companies

Answer 10

• The fact that diversification is good for investors does not mean that it is good for companies
• It much cheaper for an investor to do it themselves
• Since investors can do it on their own, they will not be willing to pay extra for any firm that is diversified
• This is based on that the whole is worth no more than the sum of its parts (value additivity)
• It doesn’t matter how many existing businesses a company has or what these businesses are
• The value of a new project depends only on its own discounted cash flows
• Diversification does not affect the value of the firm

Question 11

Market risk

Answer 11

• The risk that a stock contributes to a well-diversified portfolio is its market risk
• Market risk is the risk that a stock shares with the market (how sensitive a stock is to market movements)

Question 12

Beta

Answer 12

This sensitivity of a stock 𝑖 with the market portfolio is called beta (𝛃)

Question 13

R squared

Answer 13

• Measures the goodness of fit
• How close the returns of the stock is to the line or how little specific risk there is

Question 14

β = 1

Answer 14

A 1% change in the market index return generally leads to a 1% change in the return on a specific share (market portfolio)

Question 15

0 < β < 1

Answer 15

• A 1% change in the market index return generally leads to a less than 1% change in the returns on a specific share
• More stable return than the market as a whole

Question 16

β > 1

Answer 16

A 1% change in market index return generally leads to a greater return than 1% on a specific company’s share

Question 17

β < 0

Answer 17

A stock whose performance is countercyclical, offsetting the overall market experience

Question 18

β = 0

Answer 18

A risk-free asset

Question 19

Betas

Answer 19

• High beta stocks pay more than low beta stocks when economy is booming and investors’ marginal utility of more money (the extra happiness from more money) is low
• When the economy is booming, investors have lower marginal utility for extra money, so they are only willing to invest in these stocks if they offer significantly higher returns to compensate for their volatility (higher risk)
• High beta stocks suffer more than low beta stocks when the market crashes and the marginal utility of more money is relatively high
• When the market crashes, high beta stocks fall much more sharply than low beta stocks because investors pull back from riskier investments preferring safer, low-beta investments that hold their value better
• Low beta stocks offer more stability and are more attractive when investors are risk-averse and value extra money more e.g. during recessions

Question 20

Timings of returns

Answer 20

• When choosing stocks, you do not only care about expected returns but also about when the expected returns materialize
• So, the timing of returns matters
• It’s not just about how much you earn, but when you earn it
• A stock with high expected returns is less attractive if those returns come only in booms and disappear in crashes
• Investors consider both expected returns and the timing of those returns before making investment decisions
• A stock’s expected return isn’t enough - you also need to think about how it performs in different economic conditions

Question 21

True market portfolio

Answer 21

• The true market portfolio contains all the world’s risky assets (tradable and non-tradable, bonds, commodities, foreign securities etc)
• Because the market portfolio is the aggregation of all investors’ risky portfolios, each of which is identical, it too will have those same weights

Question 22

Proxy

Answer 22

• In practice, there is no index that measures the value of all risky assets, so investors use an approximation (a proxy)
• This proxy is usually an aggregate stock market index such as the S&P500 for US investors, the FTSE100 Index returns for the UK stock market

Question 23

Risk measure

Answer 23

• The risk of a well-diversified portfolio is proportional to the portfolio beta which equals the average beta of the securities included in the portfolio
• Beta measures market risk (undiversifiable), so there is no diversification effect when
  adding a stock to a portfolio
• The risk measure (beta) for individual portfolios is linearly additive when assets
  are combined into portfolios
• The beta of a portfolio is the sum of the weight of each asset times the beta of each asset

Question 24

Individual Stocks

Answer 24

• Capital market line which shows the expected return for an efficient portfolio that allows borrowing/lending
• It doesn’t apply to individual stocks because they are not efficient as standalone assets
• Part of their risk can be diversified away, so investors will not be rewarded for bearing unsystematic risk
• Therefore, the CML does not apply to them

Question 25

Risk and Return with CAPM

Answer 25

- An investor should only be rewarded for bearing a stock’s market risk, because only this risk can’t be gotten rid of through diversification - As all investors are assumed to hold the market portfolio, an asset 𝑖 will have a risk that is defined as the amount of risk that it adds to the market portfolio

Question 26

Market risk premium

Answer 26

In a competitive market, the expected risk premium on any security – not just efficient portfolios - is its beta multiplied by the market risk premium (𝒓𝑴−𝒓𝒇)

Question 27

Security Market Line

Answer 27

- Is a graphical depiction of the CAPM - In equilibrium all stocks should lie on the SML

Question 28

Expected return-beta relationship

Answer 28

The expected return-beta relationship of the CAPM tells us that the total expected return of security i is the sum of the risk-free rate plus a risk premium

Question 29

Size of risk premium

Answer 29

- The product of a benchmark risk premium (broad market portfolio) + the relative risk of an individual asset as measured by its beta (its contribution to the risk of overall risky portfolio) - If CAPM holds, the CAPM equation can give you an estimate for a stock’s expected return

Question 30

Capital Market Line and Security Market Line

Answer 30

- Both lines have expected returns on the vertical axis but: CML has total risk on the horizontal axis measured by σi - And SML has market risk βi - CML applies to efficient portfolios only - Inefficient portfolios that bear specific risk lie below CML (higher risk for set return) but investors are still willing to hold them - When held as part of a well-diversified portfolio diversifiable risk goes away - Security Market Line applies to all stocks and portfolios, efficient or not - Market risk βi measures the systematic risk and investors need to be rewarded for all of it, as it cannot be diversified away - So, all securities must be on the SML - The equation of the SML, which is the CAPM, holds for all assets - Efficiency only matters at portfolio level - An efficient portfolio is comprised of individually inefficient assets

Question 31

CAPM and its assumptions

Answer 31

1. Investors choose portfolios based on expected return and variance (risk) 2. All investors have the same estimates of mean returns, variances + covariances (costless availability of info) 3. Investors trade in perfect capital markets (no taxes, no transaction costs, no restrictions on short sales, can borrow and lend at the same risk-free rate) 4. Investors are price takers 5. The supply of all assets is fixed: all assets are traded and perfectly dividable