Portfolio Theory: Understanding Risk and Diversification in Finance - Prof. Montllor, Apuntes de Administración de Empresas

¡Descarga Portfolio Theory: Understanding Risk and Diversification in Finance - Prof. Montllor y más Apuntes en PDF de Administración de Empresas solo en Docsity! Faculty of Economics and Business Department of Business FINANCE I (102329) – Group 3 – 2012-13 Study Guide. Dr. Maria-Antonia Tarrazon & Dr. Joan Montllor 1 TOPIC 3: PORTFOLIO THEORY (I) Contents: Summary (I) 1. Return on the stock price as a random variable If there is market efficiency stock prices cannot be predicted. This means that the return on any stock behaves like a random variable. An annual rate of return can be calculated as: 0 01 ~ ~ P PSRDPP R j   ( 1 ) being 1 ~ P = stock price (random variable) at the end of the year 0P = stock price at the beginning of the year or price paid for one stock at the beginning of the period D = dividend paid during the year PSR = preferential subscription rights (or preferential stock right) awarded to the stock’s owner if additional capital has been raised during this year. For stock price changes, see, for example, Brealey/Myers, section 8.1. 2. Risky portfolios: Combining stocks into portfolios  If stock prices follow a random walk, so do risky portfolios. Therefore, the rate of return (as a random variable) on any portfolio p can be calculated as: j n j jp RxR ~~ 1   ( 2 ) where pR ~ = portfolio rate of return (random variable). There are n stocks in portfolio p. jR ~ = rate of return on stock j jx = weight of stock j in portfolio p, being 1 1   n j jx . ( 3 ) Faculty of Economics and Business Department of Business FINANCE I (102329) – Group 3 – 2012-13 Study Guide. Dr. Maria-Antonia Tarrazon & Dr. Joan Montllor 2  Expected return on an a risky portfolio p: )()( 1 j n j jp RExRE   ( 4 ) which expressed in words means that the expected portfolio return is equal to the weighted average of the expected returns on the stocks included in the portfolio. )( pRE = expected return on portfolio p )( jRE = expected return on stock j jx = weight of stock j in portfolio p, as before.  Portfolio variance and standard deviation: ''' ' 1 1' 2 1 22 jjjjj jj n j n j jj n j jp xxx       ( 5 ) 2/1 ''' ' 1 1' 2 1 2                jjjjj jj n j n j jj n j jp xxx  ( 6 ) being 2 j = variance of the return on stock j j = standard deviation (or square root of the variance) of the return on stock j ', jj = correlation coefficient between the return on stock j and the return on stock j’ and, therefore, ',''', ··) ~ , ~ cov( jjjjjjjj RR   The covariance measures how much the rates of return on two stocks move in tandem. A positive covariance is due to a positive correlation coefficient and means that stock returns move in the same direction (both positively or both negatively). A negative covariance is caused by a negative correlation coefficient and means that asset returns vary inversely (one moving up and the other down). 2 p = portfolio variance p = portfolio standard deviation