Organizational Instructions Assessment Basic concepts oo OO oooooooooooo Introduciotion to the course Organizational Instructions oo Assessment OO Basic concepts oooooooooooo Content *> Organizational Instructions © Assessment © Basic concepts Organizational Instructions •O Assessment OO Basic concepts oooooooooooo Portfolio Theory • Organizational Instructions /A <^ <^ V^> <^ <^ I I I Vm» I I L> Organizational Instructions om Assessment OO Basic concepts oooooooooooo Course requirements Organizational Instructions om Assessment OO Basic concepts oooooooooooo Course requirements Organizational Instructions om Assessment OO Basic concepts oooooooooooo Course requirements 1 Active participation on seminars 2 On Average 60% of total score from 2 tests Failure to f u I If i led the conditions 1 & 2 means "F" Organizational Instructions om Assessment OO Basic concepts oooooooooooo Course requirements 1 Active participation on seminars 2 On Average 60% of total score from 2 tests Failure to f u I If i led the conditions 1 & 2 means "F" 2 remediate tests Organizational Instructions om Assessment OO Basic concepts oooooooooooo Course requirements 1 Active participation on seminars 2 On Average 60% of total score from 2 tests Failure to f u I If i led the conditions 1 & 2 means "F" 2 remediate tests Every correction test for 30 points Organizational Instructions om Assessment OO Basic concepts oooooooooooo Course requirements 1 Active participation on seminars 2 On Average 60% of total score from 2 tests Failure to f u I If i led the conditions 1 & 2 means "F" 2 remediate tests Every correction test for 30 points Literature: Elton, E.: Modern Portfolio Theory and Investment Analysis Organizational Instructions Assessment Basic concepts oo •O OOOOOOOOOOOO Portfolio Theory Organizational Instructions Assessment oo om Basic concepts oooooooooooo Earned points and valuation Organizational Instructions Assessment oo om Basic concepts oooooooooooo Earned points and valuation Organizational Instructions oo Assessment OO Basic concepts •ooooooooooo Portfolio Theory Organizational Instructions oo Assessment OO Basic concepts ©•oooooooooo A few history Organizational Instructions oo Assessment OO Basic concepts ©•oooooooooo A few history Hicks, J.: Application of Mathematical Methods of the Theory of Risk (1934) Organizational Instructions oo Assessment OO Basic concepts ©•oooooooooo A few history Organizational Instructions oo Assessment OO Basic concepts ©•oooooooooo A few history Organizational Instructions oo Assessment OO Basic concepts O0OOOOOOOOOO A few history Organizational Instructions oo Assessment OO Basic concepts ©•oooooooooo A few history Hicks, J.: Application of Mathematical Methods of the Theory of Risk (1934) Markowitz, H.: Portfolio Selection (1952) Modern Portfolio Theory Sharpe, W.: Capital /Assets Prices: A Theory of Market Equilibrium under Condion of Risk (1964) Organizational Instructions oo Assessment OO Basic concepts ©•oooooooooo A few history Hicks, J.: Application of Mathematical Methods of the Theory of Risk (1934) Markowitz, H.: Portfolio Selection (1952) Modern Portfolio Theory Sharpe, W.: Capital /Assets Prices: A Theory of Market Equilibrium under Condion of Risk (1964) Ross, S.: The Arbitrage Theory of Capital Asset Pricing (1976) Organizational Instructions oo Assessment OO Basic concepts OO0OOOOOOOOO Investment Portfolio Assets assumptions: o Identifiability Measurability (Price) Investment r, a The basic premise of creating a portfolio is based on the rationality of an investor. Thus, the aim of portfolio creation is to find a composition of assets that corresponds its/her needs. Organizational Instructions Assessment Basic concepts oo OO ooo«oooooooo Return Organizational Instructions OO Assessment OO Basic concepts OOOO0OOOOOOO Return as Random Variable Organizational Instructions oo Assessment OO Basic concepts OOOO0OOOOOOO Return as Random Variable Organizational Instructions OO Assessment OO Basic concepts OOOOOOOOOOOO Return as Random Variable X r X(/i,cr) Mean {jj) : V = knY,UXi E(X,)orr °p E"=i* pi Properties of mean: E(c) = c, where c is a constant E(c*X) = c*E{X) Organizational Instructions OO Assessment OO Basic concepts OOOO0OOOOOOO Return as Random Variable X r X(/i,cr) Mean {jj) : V = knY,UXi E(X,)orr °p E"=i* pi Properties of mean: E(c) = c, where c is a constant E(c*X) = c*E{X) E(X + Y) = E(X) + E(Y) Organizational Instructions oo Assessment OO Basic concepts OOOO0OOOOOOO Return as Random Variable X r X(/i,cr) Mean {jj) : V = knY,UXi E(X,)orr °p E"=i* pi Properties of mean: E(c) = c, where c is a constant E(c*X) = c*E{X) E(X + Y) = E(X) + E(Y) E(X* Y) = E(X)*E(Y) Organizational Instructions Assessment Basic concepts oo OO OOOOO0OOOOOO Return Organizational Instructions Assessment oo oo Basic concepts oooooo«ooooo Despersion of Random Variable Organizational Instructions Assessment OO OO Basic concepts oooooo«ooooo Despersion of Random Variable Organizational Instructions Assessment oo oo Basic concepts oooooo«ooooo Despersion of Random Variable Organizational Instructions Assessment OO oo Basic concepts oooooo«ooooo Despersion of Random Variable Organizational Instructions Assessment oo oo Basic concepts oooooo«ooooo Despersion of Random Variable Organizational Instructions Assessment Basic concepts OO OO ooooooo»oooo Properties of variance a2(c + X) = a2{c) + a2{X) = 0 + a2{X) Organizational Instructions Assessment Basic concepts OO OO ooooooo»oooo Properties of variance a2(c + X) = a2{c) + a2{X) = 0 + a2{X) a2(c*X) = c2*a2(X) Organizational Instructions oo Assessment OO Basic concepts ooooooo»oooo Properties of variance a2(c + X) = a2{c) + a2{X) = 0 + a2{X) a2(c*X) = c2*a2(X) a2(X + Y) = a2(X) + a2(Y) ...X & Y independent Organizational Instructions oo Assessment OO Basic concepts ooooooo«oooo Properties of variance a2(c + X) = a2(c) + a2(X) = 0 + a2{X) a2(c*X) = c2*a2(X) a2(X + Y) = a2(X) + a2( Y) ... X & Y independent otherwise, a2(X +Y) = a2{X) + a2(Y) + 2* cov{X, Y) Organizational Instructions Assessment Basic concepts oo OO oooooooo»ooo Risk of assets Organizational Instructions Assessment Basic concepts oo OO oooooooo»ooo Risk of assets Organizational Instructions Assessment Basic concepts oo OO OOOOOOOO0OOO Risk of assets Organizational Instructions Assessment Basic concepts oo OO ooooooooo«oo Relation between RV's Organizational Instructions Assessment Basic concepts OO OO ooooooooo«oo Relation between RV's Organizational Instructions Assessment Basic concepts oo OO ooooooooo«oo Relation between RV's Organizational Instructions oo Assessment OO Basic concepts oooooooooo«o Properties of covariance Organizational Instructions OO Assessment OO Basic concepts oooooooooo«o Properties of covariance Organizational Instructions Assessment Basic concepts oo OO oooooooooo«o Properties of covariance Organizational Instructions Assessment Basic concepts oo OO oooooooooo«o Properties of covariance Organizational Instructions OO Assessment OO Basic concepts oooooooooo«o Properties of covariance cov(X, Y) = 0; E(X + Y) = OifE(X) = 0&E(X) o cov(X, Y) = cov(Y,X) cov(X + a,Y + b) = cov(X, Y) cov(a * X, b* Y) = a * b* cov(X, Y) o cov(X,X) = var(X) Range of cov (—00; 00) —> standardization = 0 Organizational Instructions Assessment OO OO Basic concepts ooooooooooo» Pearson 's correlaton coefficien Organizational Instructions Assessment OO oo Basic concepts ooooooooooo* Pearson 's correlaton coefficien The absolute dimension of covariance is relativized ai i Pi i = —7^ r'd (7j*(7j Describe a linear dependence Organizational Instructions oo Assessment OO Basic concepts ooooooooooo* Pearson's correlaton coefficien The absolute dimension of covariance is relativized ai i Pi i = —7^ r'd (7j*(7j Describe a linear dependence On the interval < —1; 1 > Organizational Instructions oo Assessment OO Basic concepts ooooooooooo* Pearson's correlaton coefficien The absolute dimension of covariance is relativized ai i Pi i = —7^ r'd (7j*(7j Describe a linear dependence On the interval < —1; 1 > Pij = 1 ... straight line Organizational Instructions OO Assessment OO Basic concepts ooooooooooo* Pearson's correlaton coefficien The absolute dimension of covariance is relativized ai i Pi i = —7^ r'd (7j*(7j Describe a linear dependence On the interval < —1; 1 > Pij = 1 ... straight line Coefficient of determination OLS . .. p2