Mutual Investment Club of Cornell Week 8: Portfolio Theory April 7 th, 2011

Mutual Investment Club of Cornell What is Return? Risk?  Return =  Also seen as  Risk: Future uncertainty or volatility Ending Value – Beginning Value Beginning Value Ending Value Beginning Value

Mutual Investment Club of Cornell Expected Return  E[R a ] = (.2)(.30)+(.7)(.18)+(.10)(-.2)  E[R a ] = 16.6% StateProbability Return on Stock A 120%30% 270%18% 310%-20%

Mutual Investment Club of Cornell Variance  Variance: Spread of possible outcomes for an asset  V a 2 =.2( ) 2 +.7( ) 2 +.1( ) 2  V a 2 =  Standard deviation is square root of variance (V a )=.1309 StateProbability Return on Stock A 120%30% 270%18% 310%-20%

Mutual Investment Club of Cornell Expected Return of Portfolio  Weight of stocks is equal in portfolio  Weight must always be 1  E[R p ] = (.5)(16.6%)+(.5)(8.3%) = 12.45% StateProbability Return on Stock A Return on Stock B 120%30%15% 270%18%9% 310%-20%-10%

Mutual Investment Club of Cornell Portfolio Variance  Weight of A is 80%, weight of B is 20%  First find covariance of two stocks (correlation coefficient assumed to be.5)  V A,B = (.5)(.05)(.11) =  V p 2 = (.8) 2 (.0025)+(.2) 2 (.0121) +2(.8)(.2)(.00275)  V p 2 =  V p =.0544 StockE[R]VarianceStandard Deviation A B

Mutual Investment Club of Cornell Portfolio with Various Correlations  For line A, stocks have correlation of 1  Line D has correlation of -1  Point Z has zero risk

Mutual Investment Club of Cornell Diversification  As one increases the number of stocks, standard deviation usually decreases  This decreases the risk of the portfolio

Mutual Investment Club of Cornell Portfolio Construction  Efficient Frontier: minimizes risk for given return or maximizes return for given risk

Mutual Investment Club of Cornell Sharpe Ratio

Mutual Investment Club of Cornell Capital Market Line  Every investor should be on CML  Combination of risk-free rate and market portfolio

Mutual Investment Club of Cornell Risk  Unsystematic risk: variability in stock price due to factors only relating to an individual company  Systematic risk: basic variability  Some stocks more sensitive to systematic risk  Measured by beta  Systematic risk can’t be diversified away, while unsystematic risk can

Mutual Investment Club of Cornell Capital Asset Pricing Model  Investors should be compensated for taking on more risk with higher expected returns  Unsystematic risk can essentially be eliminated  Higher returns should only come from systematic risk  CAPM says returns will be related to beta

Mutual Investment Club of Cornell CAPM  Calculating return  E[R a ] = R f + β a (E[R m ] – R f )  Market premium times beta is return above risk free rate

Mutual Investment Club of Cornell Security Market Line  Expected returns against beta  Uses CAPM model to create line  Above line is considered good buy  Generates alpha

Mutual Investment Club of Cornell Arbitrage Pricing Theory  Similar to CAPM, but uses more factors  Each RP term is the risk premium associated with that factor  Factors could be commodity prices, interest rates, foreign exchange, etc.

Mutual Investment Club of Cornell Fama-French Results  Two characteristics best describe variations in returns  Firm size and Book-To-Market ratio  The smaller the firm, the greater the return  Book-To-Market is book value over market value  The higher the ratio, the larger the returns

Mutual Investment Club of Cornell Problems with MPT  Asset returns are not normally distributed variables  Correlations between assets aren’t constant  Investors aren’t always rational and may not have access to information at the same time  Investors can influence stock price with big purchases

Mutual Investment Club of Cornell What to be aware of  Utilize your strengths  Be aware of herding toward a group of assets  Don’t just accept popular ideas taken for granted  Take advantage of constraints of other investors