Risk and Return

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Risk and Return: Portfolio Theory and Asset Pricing Models
Portfolio Theory Capital Asset Pricing Model (CAPM)
Efficient frontier Capital Market Line (CML) Security Market Line (SML) Beta calculation

Arbitrage pricing theory Fama-French 3-factor model

Portfolio Theory
• Suppose Asset A has an expected return of 10 percent and a standard deviation of 20 percent. Asset B has an expected return of 16 percent and a standard deviation of 40 percent. If the correlation between A and B is 0.6, what are the expected return and standard deviation for a portfolio comprised of 30 percent Asset A and 70 percent Asset B?

Portfolio Expected Return
ˆ ˆ ˆ rP = w A rA + (1 - w A ) rB = 0.3( 0.1) + 0.7( 0.16) = 0.142 = 14.2%.

Portfolio Standard Deviation
2 2 2 s p = WAs A + (1 - WA ) 2 s B + 2WA (1 - WA ) r AB s A s B

= 0.32 ( 0.22 ) + 0.7 2 ( 0.4 2 ) + 2( 0.3)( 0.7 )( 0.4)( 0.2)( 0.4) = 0.309

Attainable Portfolios: rAB = 0.4
? AB = +0.4: Attainable Set of Risk/Return Combinations
20%

Expected return

15% 10% 5% 0% 0%

10%

20% Risk, ? p

30%

40%

Attainable Portfolios: rAB = +1
? AB = +1.0: Attainable Set of Risk/Return Combinations 20%

Expected return

15% 10% 5% 0% 0% 10% 20% Risk, ? p 30% 40%

Attainable Portfolios: rAB = -1
? AB = -1.0: Attainable Set of Risk/Return Combinations 20%

Expected return

15% 10% 5% 0% 0% 10% 20% Risk, ? p 30% 40%

Attainable Portfolios with Risk-Free Asset (Expected risk-free return = 5%) Attainable Set of Risk/Return Combinations with Risk-Free Asset 15%

Expected return

10%

5%

0% 0% 5% 10% Risk, ? p 15% 20%

Expected Portfolio Return, rp

Efficient Set

Feasible Set

Feasible and Efficient Portfolios

Risk, sp

• The feasible set of portfolios represents all portfolios that can be constructed from a given set of stocks. • An efficient portfolio is one that offers: – the most return for a given amount of risk, or – the least risk for a give amount of return.

• The collection of efficient portfolios is called the efficient set or efficient frontier.

Expected Return, rp

IB2 I

B1

IA2 IA1

Optimal Portfolio Investor B

Optimal Portfolio Investor A

Optimal Portfolios

Risk sp

• Indifference curves reflect an investor’s attitude toward risk as reflected in his or her risk/return tradeoff function. They differ among investors because of differences in risk aversion. • An investor’s optimal portfolio is defined by the tangency point between the efficient set and the investor’s indifference curve.

What is the CAPM? n The CAPM is an equilibrium model that specifies the relationship between risk and required rate of return for assets held in welldiversified portfolios. n It is based on the premise that only one factor affects risk. n What is that factor?

What are the assumptions of the CAPM?
• Investors all think in terms of a single holding period. • All investors have identical expectations. • Investors can borrow or lend unlimited amounts at the risk-free rate.

(More...)

What are the assumptions of the CAPM?
• All assets are perfectly divisible. • There are no taxes and no transactions costs. • All investors are price takers, that is, investors’ buying and selling won’t influence stock prices. • Quantities of all assets are given and fixed.

What impact does rRF have on the efficient frontier?
• When a risk-free asset is added to the feasible set, investors can create portfolios that combine this asset with a portfolio of risky assets. • The straight line connecting rRF with M, the tangency point between the line and the old efficient set, becomes the new efficient frontier.

Efficient Set with a Risk-Free Asset
Expected Return, rp ^ rM A M Z

.

.

B

rRF

.
sM

The Capital Market Line (CML): New Efficient Set

Risk, sp

What is the Capital Market Line? • The Capital Market Line (CML) is all linear combinations of the risk-free asset and Portfolio M. •...
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