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Vicentiu Covrig 1 Portfolio management

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Vicentiu Covrig 2 “ Never tell people how to do things. Tell them what to do and they will surprise you with their ingenuity” General George Patton

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Vicentiu Covrig 3 How Finance is organized Corporate finance Investments International Finance Financial Derivatives

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Vicentiu Covrig 4 Risk and Return The investment process consists of two broad tasks: security and market analysis portfolio management

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Vicentiu Covrig 5 Risk and Return Investors are concerned with both: Expected return: comes from a valuation model Risk As an investor you want to maximize the returns for a given level of risk.

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Vicentiu Covrig 6 Return: Calculating the expected return for each alternative OutcomeProb. of outcomeReturn in 1(recession).1-15% 2 (normal growth).615% 3 (boom).325% k ^ =expected rate of return = (.1)(-15) + (.6)(15) +(.3)(25)=15%

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Vicentiu Covrig 7 What is investment risk? Investment risk is related to the probability of earning a low or negative actual return. The greater the chance of lower than expected or negative returns, the riskier the investment. Expected Rate of Return Rate of Return (%) 100 15 0-70 Firm X Firm Y Firm X (red) has a lower distribution of returns than firm Y (purple) though both have the same average return. We say that firm X’s returns are less variable/volatile (lower standard deviation ) and thus X is a less risky investment than Y

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Vicentiu Covrig 8 Selected Realized Returns, 1926 – 2006 Average Standard Return Deviation Small-company stocks18.4%36.9% Large-company stocks12.220.2 L-T corporate bonds 5.8 9.4 L-T government bonds 5.6 8.1 U.S. Treasury bills 3.7 3.1

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Vicentiu Covrig 9 Investor attitude towards risk: Does it matter? Risk aversion – assumes investors dislike risk and require higher rates of return to encourage them to hold riskier securities. Some individuals are risk lovers, meaning that they purchase/ invest in instruments with negative expected rate of return Ex: Risk premium – the difference between the return on a risky asset and less risky asset, which serves as compensation for investors to hold riskier securities Very often risk premium refers to the difference between the return on a risky asset and risk-free rate (ex. a treasury bond)

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Vicentiu Covrig 10 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.

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Vicentiu Covrig 11 Terminology Investment (portfolio) management: professional management of a collection (i.e. portfolio) of securities to meet specific goals for the benefit of investors Asset management is similar to Investment or Portfolio Management Wealth manager is more of a broker, financial manager or investment advisor for wealthy clients Portfolio management involve a long investment horizon Trading focuses on securities selection with a short term horizon

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Vicentiu Covrig 12 Top Down Asset allocation Capital Allocation decision: the choice of the proportion of the overall portfolio to place in risk-free assets versus risky assets Asset Allocation decision: the distribution of risky investments across broad asset classes such as bonds, small stocks, large stocks, real estate etc. Security Selection decision: the choice of which particular securities to hold within each asset class. 90% of the portfolio performance is determined by the first two steps

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Vicentiu Covrig 13 Portfolio Management A properly constructed portfolio achieves a given level of expected return with the least possible risk Portfolio management primarily involves reducing risk rather than increasing return The investment horizon is intermediate to long term Portfolio managers have a duty to create the best possible collection of investments for each customer’s unique needs and circumstances

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Vicentiu Covrig 14 Tactical Asset Allocation Also known as Market Timing Shifting the relative proportion of the asset classes in the portfolio

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Vicentiu Covrig 15 Portfolio Management The heart of the Portfolio Management is the concept of diversification The empirical evidence shows that the markets are quite efficient Passive (Indexing) vs. Active Investing

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Vicentiu Covrig 16 Expected Portfolio Rate 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

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Vicentiu Covrig 17 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

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Vicentiu Covrig 18 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

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Vicentiu Covrig 19 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

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Vicentiu Covrig 20 100% 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.

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Vicentiu Covrig 21 The Minimum-Variance Frontier of Risky Assets E(r) Efficient frontier Global minimum variance portfolio Minimum variance frontier Individual assets St. Dev.

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Vicentiu Covrig 22 Two-Security Portfolios with Various Correlations 100% bonds return 100% stocks = 0.2 = 1.0 = -1.0

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Vicentiu Covrig 23 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

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Vicentiu Covrig 24 Estimation Issues Results of portfolio analysis depend on accurate statistical inputs Estimates of - Expected returns - Standard deviations - Correlation coefficients

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Vicentiu Covrig 25 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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Vicentiu Covrig 26 M E(r p ) CAL (Global minimum variance) CAL (A) CAL (O) O A rfrf O M A G O M pp Optimal Risky Portfolios and a Risk Free Asset

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