Organisation Portfolios Modern Portfolio Theory . First expounded in 1952 by Harry Markowitz · A portfolio is a group of at least two constituents (i.e. securities, businesses or capital investment projects) under common ownership · The theory assumes that investors make rational decisions based purely on: · Expected returns; and · Risk, measured by the standard deviation of expected returns Rational Investors · Rational investors apply mean-variance analysis: . Will choose an investment that has a higher expected return and a lower risk than another · When two investments have the same expected return, will choose the investment that has the lowest risk · When two investments have the same risk, will choose the investment that has the highest expected return · When an investment has a lower risk and a lower return than another (and vice versa), the choice will depend on the investor's degree of risk-aversion The Portfolio Effect · A portfolio has: . An expected return that is equal to the weighted average of its constituents' expected returns; but . A standard deviation that is lower than the weighted average of its constituents' standard deviations · The extent of the portfolio effect (the risk reduction) depends on: . The relative sizes of the constituents; and · The (expected and constant) correlation coefficients (p) between the returns of the constituents · Correlation coefficients (p) between the portfolio constituents: · Perfect positive correlation (p = +1) · Constituents are the same so no risk reduction · Perfect negative correlation (p = - 1) · Constituents are opposites so highest risk reduction · One portfolio will completely eliminate risk · Intermediate correlation (-1 < p < +1) · Constituents are similar (p > 0) or dissimilar (p ? 0)
. The level of risk reduction increases as the correlation coefficient falls from +1 to -1 Two Asset Formula Expected Return of Portfolio: Er p=x Er A+(1-x) Er D • Where: • Erp Expected return of portfolio · ErA Expected return of constituent A(lpha) • ErD Expected return of constituent D(elta) · X Percentage of portfolio in constituent A . 1 - x Percentage of portfolio in constituent D exp Ret of Portf =(% of portf Econs A x exp ret Cons A )+ (% of port Econs D) x (exp ret of cons D) Risk: 0 p=VX 0'A+(1-x)2 0'p+2x (1-x)JAODPAD • Where: • 0p Standard deviation of portfolio • JA Standard deviation of constituent A · OD Standard deviation of constituent D • x Percentage of portfolio in constituent A • 1 - x Percentage of portfolio in constituent D • PAD Correlation coefficient between A and D S. D. of Portf = v % of port Econs A2 x S. D. of cons A2 )+(% of portEcons D)2 +(2 x% of port Econs A ) x Example- Expected Return:
· Expected return of portfolio (70% A, 30% D): Formula: Er, = x Er + (1 -x) ErD 1 1 1 1 0.7 80,000 0.3 40,000 Erp => (0.7 x