Unit 6 Notes: CAPM

Corporate Finance lecture notes for the EMBA at UNSW.

Understanding Risk

Systematic risk (β)
Uncertainty or volatility in returns caused by factors that affect all risky assets such as GDP, interest rates, inflation that cannot be eliminated by diversification.

Beta

Measures systematic risk of a risky asset
σ_i,m = covariance asset vs market
= variance of market
ρ_i,m = correlation asset vs market; between -1 and 1

If β>1 for an individual risky asset
above average sensitivity to economic factors
market moves 1% ➤asset often moves > 1%
If β<1 for an individual risky asset
below average sensitivity to economic factors
market moves 1% ➤ asset often moves <1%
If β=0 then it is a risk free asset
Betas change over time
Beta is dependent on historical data to calculating it. If you calculate the covariance between stock returns and market Index in different years, the beta changes as well – Covariance of firm’s cash flows with market index can vary over due to firm and industry factors. This can be an issue – if we are trying to get expected future returns from CAPM then we need to use Beta of the future returns.

However – Even though it changes over the years, it doesn’t vary a lot within a window. This is because company doesn’t change enormous over the years or doesn’t change exposure to an industry or change in debts on the firm’s balance sheet.

So we can assume it can ok to use Beta of past returns to predict future expected returns.

Calculating beta of a portfolio

Calculate past portfolio returns then calculate beta

Portfolio beta example

Calculate the beta of a portfolio that consists of the following shares:

Would you expect the portfolio to out perform or under perform the ASX200 in downturn?

CBA0.91$20,0000.20.182WAN0.81$25,0000.250.2025WOW0.73$25,0000.250.1825Total $100,000 1.041

Portfolio beta = 1.041 is slightly above market beta of 1.0.

Risk and reward
Should we expect to be rewarded for no risk?
Yes since money has a time value e.g. Risk-free return on government bonds
Should we expect to be rewarded for additional risk?
Yes, since why choose higher risk for the same return?

CAPM Model

Assumptions

1. Investors prefer high returns over lower returns;
2. Individuals are risk averse;
3. Investors diversify to reduce Total risk;
4. Investors are concerned about risk of overall portfolio than one stock;
5. Covariance risk dominates in large portfolio;
6. Investors demand premium for covariance risk;

Expected return on a risky asset = Basic return offered by asset with zero systematic risk + Unit of systematic risk x Bonus expected return of diversified portfolio above risk-free asset (a.k.a Market risk premium)

What should be used for rf, β and E[rm]?
rf = match a government bond rate to length of E[ri];
E[rm] – rf = usually use 3% to 5% (but should make sure E[rm] used makes sense);
βi = usually use past 5 years or so (adjusted for change in leverage if necessary);

CAPM has problems

1. Uncertainty with variables
2. Error estimating future beat and market returns;
3. Fama and French
4. Company size and book to market ratio also explain stock returns so CAPM is incomplete model;
5. Market portfolio
6. Makes consistent errors
   Often underestimates at low beta and overestimates at high beta;
   Investor behavioural finance
   Not all investment decisions are rational;