FIN437 Vicentiu Covrig 1 Portfolio management Optimum asset allocation Optimum asset allocation (see chapter 7 Bodie, Kane and Marcus)

FIN437 Vicentiu Covrig 2 How Finance is organized Corporate finance Investments International Finance Financial Derivatives

FIN437 Vicentiu Covrig 3 Risk and Return The investment process consists of two broad tasks: security and market analysis portfolio management

FIN437 Vicentiu Covrig 4 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.

FIN437 Vicentiu Covrig 5 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%

FIN437 Vicentiu Covrig 6 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 (%) 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

FIN437 Vicentiu Covrig 7 Selected Realized Returns, 1926 – 2001 Average Standard Return Deviation Small-company stocks17.3%33.2% Large-company stocks L-T corporate bonds L-T government bonds U.S. Treasury bills

FIN437 Vicentiu Covrig 8 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)

FIN437 Vicentiu Covrig 9 Loss Aversion First decision: Choose between Choice 1: sure gain of $ 85,000 Choice 2: 85% chance of receiving $100,000 and 15% chance of receiving nothing Second decision: Choose between Choice 1: sure loss of $ 85,000 Choice 2: 85% chance of losing $100,000 and 15% chance of losing nothing

FIN437 Vicentiu Covrig 10 Behavioral Finance vs Standard Finance Behavioral finance considers how various psychological traits affect investors Behavioral finance recognizes that the standard finance model of rational behavior can be true within specific boundaries but argues that this model is incomplete since it does not consider the individual behavior. Currently there is no unified theory of behavioral finance, thus the emphasis has been on identifying investment anomalies that can be explained by various psychological traits.

FIN437 Vicentiu Covrig 11 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.

FIN437 Vicentiu Covrig 12 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

FIN437 Vicentiu Covrig 13 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  w 2 2  W 1 W 2 Cov(r 1 r 2 ) Cov(r 1 r 2 ) = Covariance of returns for Security 1 and Security 2

FIN437 Vicentiu Covrig 14 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

FIN437 Vicentiu Covrig 15 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

FIN437 Vicentiu Covrig % 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.

FIN437 Vicentiu Covrig 17 The Minimum-Variance Frontier of Risky Assets E(r) Efficient frontier Global minimum variance portfolio Minimum variance frontier Individual assets St. Dev.

FIN437 Vicentiu Covrig 18 Two-Security Portfolios with Various Correlations 100% bonds return  100% stocks  = 0.2  = 1.0  = -1.0

FIN437 Vicentiu Covrig 19 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

FIN437 Vicentiu Covrig 20 Estimation Issues Results of portfolio analysis depend on accurate statistical inputs Estimates of - Expected returns - Standard deviations - Correlation coefficients

FIN437 Vicentiu Covrig 21 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.

FIN437 Vicentiu Covrig 22 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

FIN437 Vicentiu Covrig 23 Capital Allocation Line E(r c ) = yE(r p ) + (1 - y)r f = r f + y[E(r p ) - r f ]  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

FIN437 Vicentiu Covrig 24 Optimal Risky Portfolios and a Risk Free Asset Example: 1 year term deposit:r f = 3%  f = 0 Bond fund:r b = 7%  b = 8.19% Equity fund:r e = 11%  e = 14.31%  (r b,r e ) = 0.3

FIN437 Vicentiu Covrig 25 M E(r p ) CAL (Global minimum variance) CAL (A) CAL (O) O A rfrf O M A G O M pp Optimal Risky Portfolios and a Risk Free Asset

FIN437 Vicentiu Covrig 26 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)

FIN437 Vicentiu Covrig 27 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 : w b = 57.8% in the bond fund w e = 42.2% in equity fund

FIN437 Vicentiu Covrig 28 Optimal Risky Portfolios and a Risk Free Asset The percentage of total portfolio invested in bonds: aw b = =0.52 or 52% equity: aw e = =0.38 or 38%

FIN437 Vicentiu Covrig 29 Optimal Risky Portfolios and a Risk Free Asset Optimum risky portfolio:Er O = 8.69%  O = 8.71% Total portfolio :Er C = 0.1x3% + 0.9x8.69% = 8.12 %  C = 0.9x8.71 = 7.84 %

FIN437 Vicentiu Covrig 30 Know the three steps of the top down asset allocation Discuss the benefits of diversification. Everything covered in these Recommended end-of chapter problems: 1,2,3 and 12 Learning objectives