Nov, 2013 Wonil Lee, Ph.D. & CFA CAU Portfolio Theory Review Lecture 6 Wonil Lee, CFA & Ph.D. Diversification and Portfolio - “Don’t put all your eggs in one basket” - Buying a large set of securities can reduce risk Development of Modern Portfolio Theory 1950 1952 1964 1966 1972 1977 1992 Conventional wisdom around (1950) Diversification and Portfolio Risk (1952) Single-factor Asset Pricing Risk/Return Model (CAPM) (1964) Efficient Market Hypothesis (1966) Option Pricing Model (1972) Database of Securities Prices (1977) 3-Factor Model (1992) “Portfolio Selection” •Correlation between risk and return •Efficient line •Small [cap] minus Large •High [book/price] minus low •Rm-Rf Technical and basic analysis established •Value evaluation of securities •Measurement of asset price •Evaluation of performance Development of derivative market “informationally efficient market” The EMH states that it is impossible to consistently outperform the market by using any information that the market already knows CRSP (The Center for Research in Securities Prices) Modern Portfolio Theory  Objective: To obtain the highest return for a given level of risk, or the lowest risk for a target level of return.  Return  Variance (volatility of individual securities)  Covariance (co-movement of asset prices)  Harry Markowitz – “Portfolio Selection” - Markowitz proposed that investors focus on selecting portfolios based on their overall risk-reward characteristics instead of merely compiling portfolios from securities that each individually have attractive risk-reward characteristics. - In brief, investors should select portfolios not individual securities.  Derives the expected rate of return for a portfolio of assets and an expected risk measure  Markowitz demonstrated that the variance of the rate of return is a meaningful measure of portfolio risk under reasonable assumptions  The portfolio variance formula shows how to effectively choose a portfolio Markowitz Portfolio Theory Assumptions of Markowitz Portfolio Theory  Investors consider each investment alternative as being presented by a probability distribution of expected returns over some holding period  Investors maximize one-period expected utility  Investors estimate the risk of the portfolio on the basis of the variance of expected returns  Investors base decisions solely on expected returns and risk, so their utility curves are a function of expected return and the expected standard deviation of returns  For a given level of risk, investors prefer higher returns to lower returns. For a given level of expected returns, investors prefer less risk to more risk Risk and Expected Rates of Return  Definition of Risk 1. Uncertainty of future outcome 2. The probability of an adverse outcome  Beta is a measure of systematic risk  Expected Rates of Return - Individual Risky Asset: Calculated by determining the possible returns ( R i ) for some investment in the future, and weighting each possible return by its own probability (P i ). E(R)= ∑P i R i - Portfolio: 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 Macroeconomic Factors Affecting Systematic Risk  Variability in growth of money supply  Interest rate volatility  Inflation  Fiscal and Monetary policy changes  War and political events  Correlation coefficient - Values of the correlation coefficient (r) go from -1 to +1 - Standardized measure of the linear relationship between two variables - Rij = Cov ij /σ i σ j Cov ij = covariance of returns for securities i and j σ i = standard deviation of returns for securities i σ j = standard deviation of returns for securities j  Covariance - Measures the extent to which two variables move together - For two assets, I and j, the covariance of rates of return is defined as: Cov ij = E{[R i ,t – E(R i )][R j ,t – E(R j )]} Variance & Standard Deviation of Returns  Σ p =√ W 2 A σ 2 A + W 2 B σ 2 B + 2 W A W B σ A σ B r If r AB = +1, then SD p = α If r AB = 0, the SD p = β If r AB = -1, SD p = γ Portfolio Standard Deviation Return Risk A B α β γ [...]... another - Portfolio give average returns, but they give lower risk - Diversification works  Even for assets that are positively correlated, the portfolio standard deviation tends to fall as assets are added to the portfolio  Combining assets together with low correlations reduces portfolio risk - The lower the risk, the lower the portfolio average return - Negative correlation greatly reduces portfolio. .. Expected return model Volatility and correlation estimates Constraints on portfolio choice e.g turnover constraints PORTFOLIO OPTIMIZATION Risk-Return Efficient Frontier Choice of Portfolio Efficient Frontier for a Multi-security Portfolio Efficient Frontier for alternative portfolios Expected return Selecting an optimal risky portfolio Expected return risk-seeking investor risk-averse investor Standard... can reduce the portfolio standard deviation to zero - This is the main reason for international investment especially emerging market investment Portfolio Risk – Standard Deviation Portfolio Diversification Total Risk Company- specific risk Unsystematic risk Diversifiable risk Market Risk Non diversifaiable or Systematic risk Number of Stocks in Portfolio Estimation Issues  Results of portfolio analysis.. .Portfolio Standard Deviation Calculation  The portfolio standard deviation is a function of the: - Weights of the individual assets - Variances of the individual assets - Covariances between the assets  The larger the portfolio, the more the impact of covariance and the lower the impact of the individual security variance Implications for Portfolio Formation  Assets... errors Beta of the Portfolio  Assuming that stock returns can be described by a single market model, the number of correlations required reduces to the number of assets  Single index market model: Ri = ai + bi Rm + εi bi = the slope coefficient that relates the returns for security I to the returns for the aggregate stock market Rm = the returns for the aggregate stock market Modern Portfolio Investment... investor Standard deviation The “Efficient Frontier” is the name given to the line that joins all portfolios that have achieved a maximum return for a given level of risk The exceptions are the end-points, which are the assets with the highest return and lowest risk, respectively Standard deviation The optimal portfolio is the point of tangency between an investor’s indifference curve and the efficient... frontier There is No Free Lunch  Most invertors would like to boost returns - through taking more risk (increase duration, raise the allocation to equities and credit)? Efficient Frontier for alternative portfolios Expected return - Reliable way to limit risk is through diversification – adding imperfectly correlated assets to raise return per unit of risk Smart but hard Investors must move beyond simple . Nov, 2013 Wonil Lee, Ph.D. & CFA CAU Portfolio Theory Review Lecture 6 Wonil Lee, CFA & Ph.D. Diversification and Portfolio - “Don’t put. variance formula shows how to effectively choose a portfolio Markowitz Portfolio Theory Assumptions of Markowitz Portfolio Theory  Investors consider each investment alternative as being presented. the market already knows CRSP (The Center for Research in Securities Prices) Modern Portfolio Theory  Objective: To obtain the highest return for a given level of risk, or the lowest risk