Lecture 4 CAPM

1
Contemporary Issues in Corporate Finance

Lecture 4CAPM Options

2
Risk and Return

• In previous lectures
• we looked at the returns various investments
• we considered various definitions of risk
• The least risky investment was T-bills.
• The market portfolio of common stocks was much
  riskier!
• We used Standard Deviation and Beta to measure
  risk.
• Standard deviation was a measure of total risk!
• Beta was a measure of market risk.
• We understood that in a competitive market
• we can diversify away unique risk by forming
  portfolios
• we can only be compensated for market risk!
• Market risk is the relevant risk for the
  investor!
• Beta is the measure of market risk

3
Risk and Return

• We also understood that
• most investors prefer lower risk to higher risk
  and higher return to lower return
• most investors are risk averse, however the
  degree of risk aversion might change based on the
  individuals preference.
• If you wanted to increase expected return and
  reduce risk, you would end up with one of the
  portfolios on the efficient frontier.
• When we introduced borrowing and lending at the
  risk-free rate as an alternative,
• you could get the highest expected return by
  investing in a mixture of the best efficient
  portfolio and borrowing/lending.
• The efficient portfolio at the tangency point is
  better than all the others!

4
Risk and Return

• The efficient portfolio at the tangency point is
  better than all the others
• It offers the highest ratio of risk premium to
  standard deviation.
• The difference between the investments expected
  return and the risk-free rate is called the risk
  premium.

Return
.
S
Efficient Portfolio
rf
Risk
5
Risk and Return
Return

• Each investor should, then put money into two
  benchmark investments
• the risk-free rate
• the risky portfolio S!
• What does portfolio S look like?
• Market Portfolio!

.
S
Efficient Portfolio
rf
Risk
6
Security Market Line
Security Market Line

• The relevant risk measure for a well diversified
  investor is Beta.
• It measures market risk.
• Return on T-bills is fixed.
• T-bills have a beta of 0!
• The market portfolio of common stocks has an
  average market risk
• Beta of market portfolio1!
• The difference between the return on the market
  and the risk free rate is termed the market risk
  premium.
• market risk premium (rM - rf)

Return
.
S
rM
rf
Risk
(BETA)
1.0
7
Security Market Line

• The market portfolio has a risk premium of (rM -
  rf),
• T-bills have a market risk premium of zero.
• WHAT IS THE RISK PREMIUM WHEN BETA IS NOT 0 OR 1?
• Sharpe (1964) and Litner (1965) produced the
  answer.
• Capital Asset Pricing Model

Return
rm
Security Market Line (SML)
rf
BETA
1.0
8
Security Market Line
Return

• In a competitive market, the expected risk
  premium varies in direct proportion to Beta.
• An investment with a beta of 0.5 has half the
  expected risk premium on the market.
• An investment with a beta of 2 has twice the
  expected risk premium on the market.

SML
rf
BETA
1.0
SML Equation R rf B ( rm - rf )
9
Capital Asset Pricing Model
R rf B ( rm - rf )
CAPM
Expected risk premium on the stock Beta x
Expected risk premium on the market R -
rf B (rM - rf)
10
Capital Asset Pricing Model

• A stocks sensitivity to changes in the value of
  the market portfolio is known as Beta.
• We do not consider the risk of a stock in
  isolation but its contribution to the risk of a
  well diversified portfolio.
• Beta measures the marginal contribution of a
  stock to the risk of the market portfolio.
• The risk premium demanded by investors is
  proportional to Beta.

11
Capital Asset Pricing Model
Risk Premium
B
30 20 10 0
C
A

• Would you buy stock A?
• Would you buy stock B?
• Would you buy stock C?

Market Portfolio
Beta
1.0
1.5
1.2
0.5
12
Testing the CAPM

• Investors require extra return for taking on
  risk!
• Investors are concerned with the risks they can
  not diversify away!
• CAPM captures these ideas in a very simple way.
• A very convenient tool for understanding the risk
  return relationship.
• Easy to estimate, easy to understand
• Popular among practitioners and academics!
• Any economic model is a simplified statement of
  reality!
• Assumptions of CAPM?
• Are investments in T-bills risk free?
• Can we lend and borrow at the same rate?
• Will investors invest in a limited number of
  benchmark portfolios?
• T-bills and Market portfolio?
• Can we define market risk depending on other
  benchmark portfolios?
• Are there better ways of modelling risk and
  return?

13
Testing the CAPM
Beta vs. Average Risk Premium
Avg Risk Premium 1931-65
SML
30 20 10 0
Investors

• The SLM has actually been flat!

Market Portfolio
Portfolio Beta
1.0
14
Is Beta Dead?
Beta vs. Average Risk Premium
Avg Risk Premium 1966-2005

• The SLM has actually been too flat!
• Return has not risen with Beta!
• Has return been related to other measures?
• Size?
• Book to Market?

30 20 10 0
SML
Investors
Market Portfolio
Portfolio Beta
1.0
15
Testing the CAPM
Company Size vs. Average Return
Average Return ()
Company size
Smallest
Largest
16
Testing the CAPM
Book-Market vs. Average Return
Average Return ()

• Noise?
• Data mining?
• Other factors?

Book-Market Ratio
Highest
Lowest
17
Consumption Betas vs Market Betas
Stocks (and other risky assets)

• People invest to provide future consumption!
• Most important risks are those that might
  cut-back future consumption.
• We can measure risk by measuring the sensitivity
  of a security to investors consumption!
• Then a stocks expected return should move in
  line with its Consumption Beta!
• How do you estimate aggregate consumption?

Market risk makes wealth uncertain.
Standard CAPM
Wealth market portfolio
18
Consumption Betas vs Market Betas
Stocks (and other risky assets)
Stocks (and other risky assets)
Wealth is uncertain
Market risk makes wealth uncertain.
Consumption CAPM
Standard CAPM
Wealth
Consumption is uncertain
Wealth market portfolio
Consumption
19
Modelling Risk and Return

• Investors require extra expected return for
  taking on risks!
• Investors are concerned with the risks they can
  not eliminate by diversification!

• Are there other ways of modelling risk and
  return?
• Are there better ways of modelling risk and
  return?

20
Topics Covered

• Hedging
• Forwards and Futures
• Calls, Puts
• Financial Alchemy with Options
• What Determines Option Value
• Option Valuation
• Binomial model
• Black-Scholes formula

21
Hedging

• Business has risk
• They insure or hedge to reduce risks! Not to make
  money!
• HOW? Kellogg produces cereal.
• A major component and cost factor is sugar.
• To fix your sugar costs, you would ideally like
  to purchase all your sugar today, since you like
  todays price, and made your forecasts based on
  it. But, you can not!
• You can, however, sign a contract to purchase
  sugar at various points in the future for a price
  negotiated today.
• This contract is called a Futures Contract.
• This technique of managing your sugar costs is
  called Hedging.

22
Forward and Futures Contracts

• 1- Spot Contract
• A contract for immediate sale delivery of an
  asset.
• 2- Forward Contract
• A contract between two people for the delivery of
  an asset at a negotiated price on a set date in
  the future.
• 3- Futures Contract
• A contract similar to a forward contract, except
  there is an intermediary that creates a
  standardized contract.
• Thus, the two parties do not have to negotiate
  the terms of the contract. The intermediary
  guarantees all trades provides a secondary
  market for the speculation of Futures.
• Not an actual sale!
• Always a winner a loser!

23
What is an Option?

• Example Desert land that contains gold deposit!
• What if the cost of extraction gt current price of
  gold?
• Is it worthless?
• No if there is uncertainty about gold prices!
• The option to expand?
• The option to abandon?
• The option to default?
• Traded options?
• Common stocks
• Stock indices
• Bonds
• Commodities
• FX