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VARIANS DAN STANDAR DEVIASI PORTFOLIO Pertemuan 10 Matakuliah: F0892 - Analisis Kuantitatif Tahun: 2009

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Bina Nusantara University 3 EXPECTED RETURN SINGLE SECURITY Expected return = Where R i is return and w i is the weighting of component asset i.

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VARIANS PORTFOLIO Portfolio variance = where i≠j. Alternatively the expression can be written as: where ρ ij = 1 for i=j. Bina Nusantara University 4 Portfolio volatility=

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For a two asset portfolio:- –Portfolio return= –Portfolio variance: Bina Nusantara University 5

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6 The formula to compute the standard deviation of a portfolio of N securities is :

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7-18 The standard deviation is the square root of the variance. Note that Hence, What is the correlation coefficient between a riskfree security and a stock? Zero! Therefore, the covariance between a riskfree security and a stock is also zero! What is the formula for the standard deviation of a portfolio with two securities (say, security 1 and security 2)? Note that X 2 =1- X 1, Hence,

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Example You estimated that the standard deviations of General Electric and General Motors stocks are 18% and 31%, respectively. Also, you estimated that the correlation coefficient between the return of the two securities is 0.35. What is the standard deviation of a portfolio (including the two securities) with GE having a weight of 40%? The formula in the last slide for the standard deviation of a portfolio with two securities is

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7-21 Note that the covariance between the returns of GE and GM is 0.01953 Hence, = 0,01953

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