II: Portfolio Theory II 5: Modern Portfolio Theory.

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Presentation transcript:

II: Portfolio Theory II 5: Modern Portfolio Theory

Chapter 5: Modern Portfolio Theory © Oltheten & Waspi 2012 Theory vs Practice  Theory: Efficient portfolios  Practice: Calculate correlation coefficients for all possible pairs of over 10,000 stocks? (?!)  Perhaps measure the portfolio directly.

Chapter 5: Modern Portfolio Theory © Oltheten & Waspi 2012 Limits of Diversification  Unsystematic Risk  Industry or firm specific – can be diversified away  Systematic Risk  Economy wide - cannot be diversified away

Chapter 5: Modern Portfolio Theory © Oltheten & Waspi 2012 Modern Portfolio Theory  Calculate the correlation with the basic underlying value that all stocks have in common: the market.

Chapter 5: Modern Portfolio Theory Modern Portfolio Theory Tardis Intertemporal Proctor & Gamble Caterpillar Microsoft Exxon Mobile US Steel Citigroup Ford Boeing Hypothetical Resources © Oltheten & Waspi 2012

Chapter 5: Modern Portfolio Theory Modern Portfolio Theory Hypothetical Resources Tardis Intertemporal Proctor & Gamble Caterpillar Microsoft Exxon Mobil US Steel Citigroup Ford Boeing Market © Oltheten & Waspi 2012

Chapter 5: Modern Portfolio Theory © Oltheten & Waspi 2012 Market Model  R Stock =  + β R Market Return for taking market risk Return for taking undiversifiable, firm- specific risk

Chapter 5: Modern Portfolio Theory © Oltheten & Waspi 2012 Market Model  R Stock =  + β R Market  β =  (Rs,Rm) *.  Rs.  Rm  Captures the correlation between Rs and Rm.  Reflects market risk exposure

Chapter 5: Modern Portfolio Theory Market Model © Oltheten & Waspi 2012

Chapter 5: Modern Portfolio Theory Market Model © Oltheten & Waspi 2012

Chapter 5: Modern Portfolio Theory © Oltheten & Waspi 2012 Capital Asset Pricing Model  E[R] = rf + β( E[RM] – rf)  E[R] is the normal return for an investment with a risk exposure = β

Chapter 5: Modern Portfolio Theory Capital Asset Pricing Model © Oltheten & Waspi 2012

Chapter 5: Modern Portfolio Theory © Oltheten & Waspi 2012 CAPM - Example  You have $1,000,000 to invest and can invest in:  T-Bills (E[R]=1.0%, β=0)  Equity Index Fund (E[R]=6.3%, β=1)  The beta of a portfolio equals the weighted average of the betas of the components Completely Diversified

Chapter 5: Modern Portfolio Theory © Oltheten & Waspi 2012 CAPM  β = 0  $1,000,000 in T-Bills $1,000,000=> __ __. __% CAPM: 1.0% + __.__ (6.3% - 1.0%) => __ __. __% BetaE[R]

Chapter 5: Modern Portfolio Theory © Oltheten & Waspi 2012 CAPM  β = 1  $1,000,000 in the Equity Fund $1,000,000=> __ __. __% CAPM: 1.0% + __.__ (6.3% - 1.0%) => __ __. __% BetaE[R]

Chapter 5: Modern Portfolio Theory © Oltheten & Waspi 2012 CAPM  β = 0.5  $500,000 in the Equity Fund  $500,000 in T-Bills $1,000,000=> __ __. __% CAPM: 1.0% + __.__ (6.3% - 1.0%) => __ __. __% BetaE[R]

Chapter 5: Modern Portfolio Theory © Oltheten & Waspi 2012 CAPM  β = 2.0  in the Equity Fund  $1,000,000=> __ __. __% CAPM: 1.0% + __.__ (6.3% - 1.0%) => __ __. __% BetaE[R]

Chapter 5: Modern Portfolio Theory © Oltheten & Waspi 2012 CAPM – Example  1.0% (6.3% - 1.0%) Spread: Borrow at 1.0% to invest at 6.3% The first million you borrow from yourself

Chapter 5: Modern Portfolio Theory © Oltheten & Waspi 2012 Security Market Line  For any Beta  we can generate a portfolio composed of T- Bills (or borrowing) and Equity Index Funds with that Beta  The portfolio has a normal return of E[R] where E[R] = rf + β (E[RM] – rf)

Chapter 5: Modern Portfolio Theory © Oltheten & Waspi 2012 Security Market Line SML: Normal Return Slope: Spread on risky asset

Chapter 5: Modern Portfolio Theory © Oltheten & Waspi 2012 CAPM: Investment by Investment  For any investment with market risk exposure β,  we can see if the investment generated any abnormal return

Chapter 5: Modern Portfolio Theory © Oltheten & Waspi 2012 CAPM – Investment by Investment  Hypothetical Resources  Market Model:  E[R] = 9.56%  β = 1.20 Expectations of actual return formed from past data

Chapter 5: Modern Portfolio Theory © Oltheten & Waspi 2012 CAPM – Investment by Investment  Hypothetical Resources  Market Model:  E[R] = 9.56%  β = 1.20  CAPM:  E[R] = 7.36%  β =1.20  Abnormal return = Expectations of actual return formed from past data Expectations of normal return formed from the CAPM

Chapter 5: Modern Portfolio Theory © Oltheten & Waspi 2012 CAPM – Example

Chapter 5: Modern Portfolio Theory © Oltheten & Waspi 2012 Risk Adjusted Measures  CV:  Sharpe Ratio:  Treynor Ratio:

Chapter 5: Modern Portfolio Theory Practice Questions © Oltheten & Waspi 2012

Chapter 5: Modern Portfolio Theory © Oltheten & Waspi 2012  Derive the CAPM Equation  Graph the normal and abnormal return on Discovery Café in this market  Calculate the risk-adjusted returns Q&P 5-2: InvestmentAnnual Return Standard Deviation Beta T-Bills 3.3% 0.0% Market Index Fund12.3%15.0% Discovery Café14.8%27.3%0.8

Portfolio Theory II