Risk and Return
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.
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.