FIN352 Vicentiu Covrig 1 Risk and Return (chapter 4)

FIN352 Vicentiu Covrig 2 Risk and Return The investment process consists of two broad tasks: security and market analysis portfolio management

FIN352 Vicentiu Covrig 3 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.

FIN352 Vicentiu Covrig 4 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

FIN352 Vicentiu Covrig 5 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.

FIN352 Vicentiu Covrig 6 Components of Return Required Return - The return required to compensate for the amount of risk expected. Nominal risk-free rate - Risk-free rate - Inflation Required risk premium - Return that varies with the risk entailed

FIN352 Vicentiu Covrig 7 Computing Returns Arithmetic average return - Example 1: ( )/3 = or 4.67% - Example 2: ( )/2 = 0 or 0% Geometric mean return - Example 1: (1.1×1.08×0.96) 1/3 – 1 = or 4.48% - Example 2: (1.5×0.5) 1/2 – 1 = or -13.4%

FIN352 Vicentiu Covrig 8

FIN352 Vicentiu Covrig 9 Risk Variation, or volatility of return - Most investors probably are more interested the chance of losing money - Standard deviation - Example 1: {[( ) 2 + ( ) 2 + ( ) 2 ] / (3-1) } 1/2 = or 7.57%

FIN352 Vicentiu Covrig 10 Risk and Return Risk/Return relationship - The greater the risk, the more return should be demanded. - Coefficient of Variation CoV = 7.57% / 4.67% = 1.62

FIN352 Vicentiu Covrig 11 Annual data, 1950 to 2007 Long-TermShort-term CommonTreasury Inflation StocksBondsBillsRate Arithmetic average13.15%6.37%4.89%3.87% Median15.40%3.65%4.85%3.19% Geometric mean11.84%5.92%4.89%3.83% Standard deviation17.24%10.51%2.71%2.99% Coefficent of variation

FIN352 Vicentiu Covrig 12 More Returns Total Return - Includes dividends, interest, income, and capital gains (losses) Inflation - Reduces future buying power - Nominal return  Return with inflation included - Real return  Return with inflation removed  Return as a buying power measurement

FIN352 Vicentiu Covrig 13 Impact of Taxes Capital Gains - Only realized gains are taxed - Short-term (less than one year)  taxed at marginal income tax rate - Long-term (over one year)  Taxed at 20% Dividends - Taxed at 15% Interest Income - Taxed at marginal income tax rate

FIN352 Vicentiu Covrig 14 Forming a Portfolio Don’t put all your eggs in one basket! The purpose of owning different types of stocks and different asset classes is diversify. The main goal of diversification is to reduce overall investment risk.

FIN352 Vicentiu Covrig 15 Statistical Measures The risk of a portfolio is determined by how the individual securities co-move over time. Covariance is a measure of that co-movement: However, the standardized measure of correlation is more popular: - Between -1 and 1

FIN352 Vicentiu Covrig 16 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

FIN352 Vicentiu Covrig 17 Portfolio Risk and Return Expected Portfolio Return Standard Deviation of Portfolio Returns

FIN352 Vicentiu Covrig 18

FIN352 Vicentiu Covrig 19 Combining these investments allows for the possibility of risk reduction The goal of the investor is to form a portfolio the moves to the upper-left corner of the risk/return graph. The very highest level of return for each level of risk desired is the efficient portfolio. All the efficient portfolios make up the efficient frontier. The optimal portfolio for you is the one that maximizes your utility (given your risk aversion)

FIN352 Vicentiu Covrig 20

FIN352 Vicentiu Covrig 21

FIN352 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.

FIN352 Vicentiu Covrig 23 The Minimum-Variance Frontier of Risky Assets E(r) Efficient frontier Global minimum variance portfolio Minimum variance frontier Individual assets St. Dev.

FIN352 Vicentiu Covrig 24 Investor Perceptions of Risk Portfolio theory is based on the statistics of how investment returns co-move over time. Do people really view risk from this statistical perspective? - No, people tend to see high returns as safe. When the markets go up, people jump in. - Risk is felt after returns turn negative - Myopic view (short-term perspective)  After 3-years of losses, long-term investors become 3-year investors—they want out! - House Money Effect  After experiencing a gain, or profit, gamblers become willing to take more risk.

FIN352 Vicentiu Covrig 25 Investor Risk Perceptions Make the Use of Portfolio Theory Difficult for Real Investors People mentally keep track of things in separate mental “file folders,” called mental accounting. - The profits, losses, return of each investment are considered separately. - This makes thinking in terms of the interaction between investments difficult. The result, is that people frequently fail to diversify.

FIN352 Vicentiu Covrig 26 Learning objectives Know the concepts of risk and return. Know the components of return. Know how to calculate average and geometric mean Know how to calculate standard deviation and the coefficient of variation Firm and market specific risks Know the concepts of correlation and diversification Discuss the efficient frontier and portfolio; optimum portfolio Discuss the investors perception of risk: myopic, house money effect and mental accounting End of chapter ST4.1; questions 4.1 to 4.6; CFA problems 4.1 to 4.5