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Portfolio management

Portfolio management. How Finance is organized. Corporate finance Investments International Finance Financial Derivatives. Risk and Return. The investment process consists of two broad tasks: security and market analysis portfolio management. Risk and Return.

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Portfolio management

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  1. Portfolio management

  2. How Finance is organized • Corporate finance • Investments • International Finance • Financial Derivatives

  3. Risk and Return • The investment process consists of two broad tasks: • security and market analysis • portfolio management

  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.

  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

  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.

  7. Expected Rates of Return • Weighted average of expected returns (Ri) for the individual investments in the portfolio • Percentages invested in each asset (wi) serve as the weights E(Rport) = Swi Ri

  8. Portfolio Risk (two assets only) When two risky assets with variances s12 and s22, respectively, are combined into a portfolio with portfolio weights w1 and w2, respectively, the portfolio variance is given by: p2= w1212 + w2222 + 2W1W2 Cov(r1r2) Cov(r1r2) = Covariance of returns for Security 1 and Security 2

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

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

  11. 100% stocks 100% bonds 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.

  12. E(r) Efficient frontier Individual assets Global minimum variance portfolio Minimum variance frontier St. Dev. The Minimum-Variance Frontierof Risky Assets

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

  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 r = +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

  15. Estimation Issues • Results of portfolio analysis depend on accurate statistical inputs • Estimates of • Expected returns • Standard deviations • Correlation coefficients

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

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