# FIN638 Vicentiu Covrig 1 Portfolio management. FIN638 Vicentiu Covrig 2 How Finance is organized Corporate finance Investments International Finance Financial.

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FIN638 Vicentiu Covrig 1 Portfolio management

FIN638 Vicentiu Covrig 2 How Finance is organized Corporate finance Investments International Finance Financial Derivatives

FIN638 Vicentiu Covrig 3 Risk and Return The investment process consists of two broad tasks: security and market analysis portfolio management

FIN638 Vicentiu Covrig 4 Risk and Return Investors are concerned with both  expected return  risk As an investor you want to maximize the returns for a given level of risk. The relationship between the returns for assets in the portfolio is important.

FIN638 Vicentiu Covrig 5 Risk Aversion Portfolio theory assumes that investors are averse to risk Given a choice between two assets with equal expected rates of return, risk averse investors will select the asset with the lower level of risk It also means that a riskier investment has to offer a higher expected return or else nobody will buy it

FIN638 Vicentiu Covrig 6 Top Down Asset Allocation 1. Capital Allocation decision: the choice of the proportion of the overall portfolio to place in risk-free assets versus risky assets. 2. Asset Allocation decision: the distribution of risky investments across broad asset classes such as bonds, small stocks, large stocks, real estate etc. 3. Security Selection decision: the choice of which particular securities to hold within each asset class.

FIN638 Vicentiu Covrig 7 Expected Rates of Return - Weighted average of expected returns (R i ) for the individual investments in the portfolio - Percentages invested in each asset (w i ) serve as the weights E(R port ) =   w i R i

FIN638 Vicentiu Covrig 8 Portfolio Risk (two assets only) When two risky assets with variances  1 2 and  2 2, respectively, are combined into a portfolio with portfolio weights w 1 and w 2, respectively, the portfolio variance is given by:  p 2 = w 1 2  1 2 + w 2 2  2 2 + 2W 1 W 2 Cov(r 1 r 2 ) Cov(r 1 r 2 ) = Covariance of returns for Security 1 and Security 2

FIN638 Vicentiu Covrig 9 Correlation between the returns of two securities Correlation,  : a measure of the strength of the linear relationship between two variables -1.0 <  < +1.0 If  = +1.0, securities 1 and 2 are perfectly positively correlated If  = -1.0, 1 and 2 are perfectly negatively correlated If  = 0, 1 and 2 are not correlated

FIN638 Vicentiu Covrig 10 Efficient Diversification Let’s consider a portfolio invested 50% in an equity mutual fund and 50% in a bond fund. Equity fundBond fund E(Return)11%7% Standard dev.14.31%8.16% Correlation-1

FIN638 Vicentiu Covrig 11 100% bonds 100% stocks Note that some portfolios are “better” than others. They have higher returns for the same level of risk or less. We call this portfolios EFFICIENT.

FIN638 Vicentiu Covrig 12 The Minimum-Variance Frontier of Risky Assets E(r) Efficient frontier Global minimum variance portfolio Minimum variance frontier Individual assets St. Dev.

FIN638 Vicentiu Covrig 13 Two-Security Portfolios with Various Correlations 100% bonds return  100% stocks  = 0.2  = 1.0  = -1.0

FIN638 Vicentiu Covrig 14 The benefits of diversification Come from the correlation between asset returns The smaller the correlation, the greater the risk reduction potential  greater the benefit of diversification If  = +1.0, no risk reduction is possible  Adding extra securities with lower corr/cov with the existing ones decreases the total risk of the portfolio

FIN638 Vicentiu Covrig 15 Estimation Issues Results of portfolio analysis depend on accurate statistical inputs Estimates of - Expected returns - Standard deviations - Correlation coefficients

FIN638 Vicentiu Covrig 16 Portfolio Risk as a Function of the Number of Stocks in the Portfolio Nondiversifiable risk; Systematic Risk; Market Risk Diversifiable Risk; Nonsystematic Risk; Firm Specific Risk; Unique Risk n  Portfolio risk Thus diversification can eliminate some, but not all of the risk of individual securities.

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