FIN 437 Vicentiu Covrig Portfolio management Optimum asset

FIN 437 Vicentiu Covrig Portfolio management Optimum asset allocation (see chapter 8 RN) 1

FIN 437 Vicentiu Covrig How Finance is organized n Corporate finance n Investments International Finance n Financial Derivatives n 2

FIN 437 Vicentiu Covrig Risk and Return The investment process consists of two broad tasks: • security and market analysis • portfolio management 3

FIN 437 Vicentiu Covrig 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. 4

FIN 437 Vicentiu Covrig Risk Aversion Portfolio theory assumes that investors are averse to risk n 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 n It also means that a riskier investment has to offer a higher expected return or else nobody will buy it 5

FIN 437 Vicentiu Covrig 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. 6

FIN 437 Vicentiu Covrig 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) = S wi Ri 7

FIN 437 Vicentiu Covrig Portfolio Risk (two assets only) When two risky assets with variances 12 and 22, respectively, are combined into a portfolio with portfolio weights w 1 and w 2, respectively, the portfolio variance is given by: p 2 = w 12 12 + w 22 22 + 2 W 1 W 2 Cov(r 1 r 2) = Covariance of returns for Security 1 and Security 2 8

FIN 437 Vicentiu Covrig Correlation between the returns of two securities Correlation, : a measure of the strength of the linear relationship between two variables n n -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 9

FIN 437 Vicentiu Covrig 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 10

FIN 437 Vicentiu Covrig 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. 11

FIN 437 Vicentiu Covrig E(r) The Minimum-Variance Frontier of Risky Assets Efficient frontier Individual assets Global minimum variance portfolio Minimum variance frontier St. Dev. 12

FIN 437 Vicentiu Covrig return Two-Security Portfolios with Various Correlations 100% stocks = -1. 0 = 0. 2 100% bonds 13

FIN 437 Vicentiu Covrig The benefits of diversification n Come from the correlation between asset returns n The smaller the correlation, the greater the risk reduction potential greater the benefit of diversification n 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 14

FIN 437 Vicentiu Covrig Estimation Issues n n Results of portfolio analysis depend on accurate statistical inputs Estimates of - Expected returns - Standard deviations - Correlation coefficients 15

FIN 437 Portfolio Risk as a Function of the Number of Stocks in the Portfolio Vicentiu Covrig 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 16

FIN 437 Vicentiu Covrig Optimal Risky Portfolios and a Risk Free Asset What if our risky securities are still confined to the previous securities but now we can also invest in a risk-free asset (e. g. T-bill)? ·You have to decide how much to invest in risky securities and how much in the risk-free rate ·You want the risky portfolio to be efficient We use the Capital Allocation Line (CAL) to answer this question 17

FIN 437 Vicentiu Covrig Capital Allocation Line E(rc) = y. E(rp) + (1 - y)rf = rf + y[E(rp) - rf ] c = y p is the risk premium per unit of risk also called the reward-to-variability ratio CAL shows all available risk-return combinations 18

FIN 437 Vicentiu Covrig Optimal Risky Portfolios and a Risk Free Asset Example: 1 year term deposit: rf = 3% f = 0 Bond fund: rb = 7% b = 8. 19% Equity fund: re = 11% e = 14. 31% (rb, re) = 0. 3 19

FIN 437 Vicentiu Covrig Optimal Risky Portfolios and a Risk Free Asset CAL (O) CAL (A) E(rp) M M O O A CAL (Global minimum variance) A G rf O M 20 p

FIN 437 Vicentiu Covrig Optimal Risky Portfolios and a Risk Free Asset The CAL (O) corresponding to the tangency portfolio O provides the highest reward (risk premium) per unit of risk. Why? Because it has the biggest slope. The efficient portfolio O is the optimum portfolio. The coordinates of the optimum portfolio O are: Er. O = 8. 69% and O = 8. 71% In practice, you find the risk and return of the optimum portfolio using a computer program that looks for the portfolio with the highest risk premium per unit of risk (S). (see your project) 21

FIN 437 Vicentiu Covrig Optimal Risky Portfolios and a Risk Free Asset The choice of weight a, how much to invest in the optimum risky portfolio, depends on your tolerance for risk and return requirement. For example, in our case, the investor chooses to invest a = 90% of his money in the optimum risky portfolio And portfolio O consists of : wb = 57. 8% in the bond fund we = 42. 2% in equity fund 22

FIN 437 Vicentiu Covrig Optimal Risky Portfolios and a Risk Free Asset The percentage of total portfolio invested in bonds: a • wb = 0. 9 • 0. 578=0. 52 or 52% equity: a • we = 0. 9 • 0. 422 =0. 38 or 38% 23

FIN 437 Vicentiu Covrig Optimal Risky Portfolios and a Risk Free Asset Optimum risky portfolio: Er. O = 8. 69% O = 8. 71% Total portfolio : Er. C = 0. 1 x 3% + 0. 9 x 8. 69% = 8. 12 % C = 0. 9 x 8. 71 = 7. 84 % 24

FIN 437 Vicentiu Covrig Learning objectives • Know the three steps of the top down asset allocation • Discuss the benefits of diversification. • Everything covered in these Recommended end-of chapter Questions: 1 to 5, 7, 9, 10, 13, 14 25