Last Topics Study

• Markowitz Portfolio Theory• Risk and Return Relationship• Efficient Portfolio

Today’s Study Topics

• Borrowing & Lending• Efficient Frontier• Security Market Line• CAPM• Validity of CAPM• Testing the CAPM

Borrowing and Lending

• Lending and borrowing extend the range of investment possibilities.

• If you invest in portfolio S and lend or borrow at the risk-free interest rate, rf, you can achieve any point along the straight line from rf through S. – This gives you a higher expected return for any

level of risk than if you just invest in common stocks.

Efficient Frontier

Standard Deviation

Expected Return (%)

•Lending or Borrowing at the risk free rate (rf) allows us to exist outside the efficient frontier.

rf

Lending

Borro

wingT

S

Efficient Portfolio

• If you can borrow money at the risk-free rate, you can extend your possibilities beyond S.

• You can also see that regardless of the level of risk you choose, you can get the highest expected return by a mixture of portfolio S and borrowing or lending.

– S is the best efficient portfolio. There is no reason ever to hold, say, portfolio T.

Efficient FrontierExample Correlation Coefficient = .4Stocks % of Portfolio Avg ReturnABC Corp 28 60% 15%Big Corp 42 40% 21%

Standard Deviation = weighted avg = 33.6 Standard Deviation = Portfolio = 28.1 Return = weighted avg = Portfolio = 17.4%

Efficient FrontierExample Correlation Coefficient = .4Stocks % of Portfolio Avg ReturnABC Corp 28 60% 15%Big Corp 42 40% 21%

Standard Deviation = weighted avg = 33.6 Standard Deviation = Portfolio = 28.1 Return = weighted avg = Portfolio = 17.4%

Let’s Add stock New Corp to the portfolio

Efficient FrontierExample Correlation Coefficient = .3Stocks % of Portfolio Avg ReturnPortfolio 28.1 50% 17.4%New CorpNew Corp 3030 50%50% 19% 19%

NEW Standard Deviation = weighted avg = 31.80 NEW Standard Deviation = Portfolio = 23.43 NEW Return = weighted avg = Portfolio = 18.20%

Efficient FrontierExample Correlation Coefficient = .3Stocks % of Portfolio Avg ReturnPortfolio 28.1 50% 17.4%New Corp30 50% 19%

NEW Standard Deviation = weighted avg = 31.80 NEW Standard Deviation = Portfolio = 23.43 NEW Return = weighted avg = Portfolio = 18.20%

NOTE: Higher return & Lower risk How did we do that? DIVERSIFICATION

Efficient Frontier

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Return

Risk (measured as )

Efficient Frontier

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Efficient Frontier

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Return

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Efficient Frontier

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Efficient Frontier

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Goal is to move up and left.

WHY?

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Efficient FrontierReturn

Risk

Low Risk

High Return

High Risk

High Return

Low Risk

Low Return

High Risk

Low Return

Efficient FrontierReturn

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Low Risk

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High Risk

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THE RELATIONSHIP BETWEEN RISK AND RETURN

• The least risky investment was U.S. Treasury bills.

• Since the return on Treasury bills is fixed, it is unaffected by what happens to the market. – In other words, Treasury bills have a beta of 0.

• We also considered a much riskier investment, the market portfolio of common stocks. – This has average market risk: Its beta is 1.0.

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• Wise investors don’t take risks just for fun.

• Therefore, they require a higher return from the market portfolio than from Treasury bills.

– The difference between the return on the market and the interest rate is termed the market risk premium.

Security Market LineReturn

Risk

.

rf

Risk Free

Return =

Efficient Portfolio

Market Return = rm

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• What is the expected risk premium when beta is not 0 or 1?

• In a competitive market, the expected risk premium varies in direct proportion to beta.

• This means that all investments must plot along the sloping line, known as the security market line.

• The expected risk premium on an investment with a beta of .5 is, therefore, half the expected risk premium on the market;

Security Market LineReturn

.

rf

Risk Free

Return =

Efficient Portfolio

Market Return = rm

BETA1.0

Security Market LineReturn

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rf

Risk Free

Return =

BETA

Security Market Line (SML)

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• We can write this relationship as;

– Expected risk premium on stock = beta x expected risk premium on market

r - rf = beta(rm - rf )

Security Market LineReturn

BETA

rf

1.0

SML

SML Equation = rf + B ( rm - rf )

Capital Asset Pricing Model

R = rf + B ( rm - rf )

CAPM

CAPM• These estimates of the returns expected by

investors in July 2001 were based on the capital asset pricing model.

• We assumed 3.5% for the interest rate rf and 8 percent for the expected risk premium rm - rf.

CAPM

• For example, suppose that you are analyzing a proposal by Pfizer to expand its capacity. – At what rate should you discount the forecast

cash flows? • According to Table 2, investors are looking for

a return of 9.2% from businesses with the risk of Pfizer.

• So the cost of capital for a further investment in the same business is 9.2%.

Review of the Capital Asset Pricing Model

• 1. Investors like high expected return and low standard deviation. Common stock portfolios that offer the highest expected return for a given standard deviation are known as efficient portfolios.

• 2. If the investor can lend or borrow at the risk-free rate of interest, one efficient portfolio is better than all the others: the portfolio that offers the highest ratio of risk premium to standard deviation (that is, portfolio S).

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• 3. The composition of this best efficient portfolio depends on the investor’s assessments of expected returns, standard deviations, and correlations.

Validity of CAPM

• First, few people quarrel with the idea that investors require some extra return for taking on risk. – That is why common stocks have given on average

a higher return than U.S. Treasury bills.

• Second, investors do appear to be concerned principally with those risks that they cannot eliminate by diversification.

Testing The CAPM

• The capital asset pricing model states that the expected risk premium from any investment should lie on the market line.

• The dots show the actual average risk premiums from portfolios with different betas. The high-beta portfolios generated higher average returns, just as predicted by the CAPM.

• But the high-beta portfolios plotted below the market line.

Testing the CAPM

Avg Risk Premium 1931-65

Portfolio Beta1.0

SML

30

20

10

0

Investors

Market Portfolio

Beta vs. Average Risk Premium

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• The relationship between beta and actual average return has been much weaker since the mid-1960s.

• The CAPM predicts that the risk premium should increase in proportion to beta, so that the returns of each portfolio should lie on the upward sloping security market line.

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• The portfolios of investors 1 and 10 had very different betas but both earned the same average return over these 25 years. – Of course, the line was correspondingly steeper

before 1966.

Testing the CAPM

Avg Risk Premium 1966-91

Portfolio Beta1.0

SML

30

20

10

0

Investors

Market Portfolio

Beta vs. Average Risk Premium

Summary

• Borrowing & Lending• Efficient Frontier• Security Market Line• CAPM• Validity of CAPM• Testing the CAPM