1. David Kilgour Lecture 4 1 Lecture 4 CAPM & Options Contemporary Issues in Corporate Finance

2. David Kilgour Lecture 4 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. David Kilgour Lecture 4 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. David Kilgour Lecture 4 4 Risk Risk and Return Return. rfrf Efficient Portfolio 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 investment’s expected return and the risk-free rate is called the risk premium. 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 investment’s expected return and the risk-free rate is called the risk premium. S

5. David Kilgour Lecture 4 5 Risk Risk and Return Return. rfrf Efficient Portfolio 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! 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

6. David Kilgour Lecture 4 6 Security Market Line Risk Security Market Line Return (BETA). rfrf 1.0 S rMrM 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 portfolio=1! The difference between the return on the market and the risk free rate is termed the market risk premium. market risk premium = (r M - r f ) 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 portfolio=1! The difference between the return on the market and the risk free rate is termed the market risk premium. market risk premium = (r M - r f )

7. David Kilgour Lecture 4 7 Security Market Line Return BETA rfrf rmrm 1.0 Security Market Line (SML) The market portfolio has a risk premium of (r M - r f ), 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 The market portfolio has a risk premium of (r M - r f ), 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

8. David Kilgour Lecture 4 8 Security Market Line Return BETA rfrf 1.0 SML SML Equation = R= r f + B ( r m - r f ) 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. 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.

9. David Kilgour Lecture 4 9 Capital Asset Pricing Model R = r f + B ( r m - r f ) CAPM Expected risk premium on the stock = Beta x Expected risk premium on the market R - r f = B (r M - r f ) Expected risk premium on the stock = Beta x Expected risk premium on the market R - r f = B (r M - r f )

10. David Kilgour Lecture 4 10 Capital Asset Pricing Model A stock’s 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. David Kilgour Lecture 4 11 Capital Asset Pricing Model Market Portfolio 0.5 1.01.5 A C B Would you buy stock A? Would you buy stock B? Would you buy stock C? Would you buy stock A? Would you buy stock B? Would you buy stock C? 1.2 30 20 10 0 Risk Premium % Beta

12. David Kilgour Lecture 4 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. David Kilgour Lecture 4 13 Testing the CAPM Avg Risk Premium 1931-65 Portfolio Beta 1.0 SML 30 20 10 0 Investors Market Portfolio Beta vs. Average Risk Premium The SLM has actually been flat!

14. David Kilgour Lecture 4 14 Is Beta Dead? Avg Risk Premium 1966-2005 Portfolio Beta 1.0 SML 30 20 10 0 Investors Market Portfolio Beta vs. Average Risk Premium The SLM has actually been too flat! Return has not risen with Beta! Has return been related to other measures? Size? Book to Market? The SLM has actually been too flat! Return has not risen with Beta! Has return been related to other measures? Size? Book to Market?

15. David Kilgour Lecture 4 15 Testing the CAPM Average Return (%) Company size SmallestLargest Company Size vs. Average Return

16. David Kilgour Lecture 4 16 Testing the CAPM Average Return (%) Book-Market Ratio HighestLowest Book-Market vs. Average Return Noise? Data mining? Other factors? Noise? Data mining? Other factors?

17. David Kilgour Lecture 4 17 Consumption Betas vs Market Betas Stocks (and other risky assets) Wealth = market portfolio Market risk makes wealth uncertain. Standard CAPM 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 investor’s consumption! Then a stock’s expected return should move in line with its Consumption Beta! How do you estimate aggregate consumption?

18. David Kilgour Lecture 4 18 Consumption Betas vs Market Betas Stocks (and other risky assets) Wealth = market portfolio Market risk makes wealth uncertain. Stocks (and other risky assets) Consumption Wealth Wealth is uncertain Consumption is uncertain Standard CAPM Consumption CAPM

19. David Kilgour Lecture 4 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? Are there other ways of modelling risk and return? Are there better ways of modelling risk and return?

20. David Kilgour Lecture 4 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. David Kilgour Lecture 4 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 today’s 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. David Kilgour Lecture 4 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. David Kilgour Lecture 4 23 What is an Option? Example: Desert land that contains gold deposit! –What if the cost of extraction > 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