Portfolio Management Risk & Return Return Income received on an investment (Dividend) plus any change in market price( Capital gain), usually expressed as a percent of the beginning market price of the investment R = D t + (P t-1 - P t ) P t-1 1
Kamal has purchased shares of A Ltd for Rs. 10 per share 1 year ago. The stock is currently trading at Rs.9.50 per share and he just received a Rs1 dividend. What return was earned over the past year? Average Rate of Return 2
Expected Return Expected Rate of Return given a probability distribution of possible returns (r i ): E(r) n E(R) = S P i R i i=1 Expected Return Economic Condition Probability Normal 40% Return 20% =.08 Bad 30% Return 5% =.015 Good 30% Return 35% =.105 =Expected ave return = 20% 3
Risk Uncertainty - the possibility that the actual return may differ from the expected return Probability - the chance of something occurring Expected Returns - the sum of possible returns times the probability of each return Measurement of Risk Studies of stock returns indicate they are approximately normally distributed. Two statistics describe a normal distribution, the mean and the standard deviation (which is the square root of the variance). The standard deviation shows how spread out is the distribution. relevant risk measure is the total risk of expected cash flows measured by standard deviation ( ). 4
Standard Deviation Standard Deviation is a statistical measure of the variability of a distribution around its mean. It is the square root of variance Variance ( 2 ) - the expected value of squared deviations from the mean 2 Variance ( ) n i 1 [R i - E(R i )] 2 P i Standard deviation is the square root of the variance i.e Kamal has invested in A Ltd shares & forecasted expected returns under different economic conditions are as follows. Depression -20% Recession 10% Normal 30% Boom 50% Determine the variance & risk of the security 5
Example 2 Suppose Kamal have predicted the following returns for stocks A and B in three possible states of nature. What are the expected returns? State Probability A B Boom 0.3 0.15 0.25 Normal 0.5 0.10 0.20 Recession 0.2 0.02 0.01 R A =.3(.15) +.5(.10) +.2(.02) =.099 = 9.99% R B =.3(.25) +.5(.20) +.2(.01) =.177 = 17.7% Consider the previous example. What are the variance and standard deviation for each stock? Stock A 2 =.3(.15-.099) 2 +.5(.1-.099) 2 +.2(.02-.099) 2 =.002029 =.045 Stock B 2 =.3(.25-.177) 2 +.5(.2-.177) 2 +.2(.01-.177) 2 =.007441 =.0863 6
Trade off between risk & return When comparing securities, the one with the largest standard deviation is the riskier If returns and standard deviations between two securities are different, the investor must make a decision between the tradeoff of the expected return and the standard deviation of each Portfolio Theory Asset may seem very risky in isolation, but when combined with other assets, risk of portfolio may be substantially less even zero When combining different securities, it is important to understand how outcomes are related to each other Returns of two or more securities are positively correlated indicating they move in same direction Returns of two or more securities are negatively correlated-move in opposite directions Combining a securities would greatly reduce the risk of the portfolio 7
Portfolios A portfolio is a collection of assets An asset s risk and return is important in how it affects the risk and return of the portfolio The risk-return trade-off for a portfolio is measured by the portfolio expected return and standard deviation, just as with individual assets Covariance & Correlation Variance & Standard deviation measures the variability of individual stock. Covariance & Correlation is determine how two variables are related with each other Covariance of Returns measure of the degree to which two variables move together relative to their individual mean values over time 8
Covariance Covariance indicates how two variables are related. A positive covariance means the variables are positively related, while a negative covariance means the variables are inversely related. The formula for calculating covariance of sample data is shown below. I.e Kamal has invested in A Ltd shares & B ltd shares forecasted expected returns under different economic conditions are as follows. A B Depression -20% 5% Recession 10% 20% Normal 30% -12% Boom 50% 9% Determine the covariance between securities of A & B 9
Correlation coefficient Correlation is another way to determine how two variables are related. In addition to telling you whether variables are positively or inversely related, correlation also tells you the degree to which the variables tend to move together. The correlation coefficient is obtained by standardizing (dividing) the covariance by the product of the individual standard deviations Correlation coefficient varies from -1 to +1 r where : r ij ij the standard deviation of R i Covij the correlatio n coefficien t of returns j i j the standard deviation of R it jt This means that returns for the two assets move together in a completely linear manner. A value of 1 would indicate perfect correlation. This means that the returns for two assets have the same percentage movement, but in opposite directions If the correlation coefficient is one, the variables have a perfect positive correlation. This means that if one variable moves a given amount, the second moves proportionally in the same direction. A positive correlation coefficient less than one indicates a less than perfect positive correlation, with the strength of the correlation growing as the number approaches one. If correlation coefficient is zero, no relationship exists between the variables. If one variable moves, you can make no predictions about the movement of the other variable; they are uncorrelated. If correlation coefficient is 1, the variables are perfectly negatively correlated (or inversely correlated) and move in opposition to each other. If one variable increases, the other variable decreases proportionally. A negative correlation coefficient greater than 1 indicates a less than perfect negative correlation, with the strength of the correlation growing as the number approaches 1. 10
Sectors Most Positively Correlated to Oil 11
Sector Oil Correlation p-value Industrial Machinery 0.29 0.0117 Oil and Gas Pipelines 0.31 0.0075 Contract Drilling 0.37 0.0018 Oilfield Services Equipment 0.38 0.0016 Integrated Oil 0.41 0.0006 Oil and Gas Production 0.43 0.0003 Sectors Most Negatively Correlated to Oil 12
Sector Oil Correlation p-value Real Estate Investment Trusts -0.43 0.0003 Airlines -0.36 0.0021 Aerospace and Defense -0.34 0.0044 Multi Line Insurance -0.33 0.0053 Hotels Resorts Cruiselines -0.32 0.0067 Casinos Gaming -0.28 0.0142 Expected Returns of Portfolio The expected return of a portfolio is the weighted average of the expected returns for each asset in the portfolio You can also find the expected return by finding the portfolio return in each possible state and computing the expected value as we did with individual securities 13
i.e Kamal has invested his wealth 60% of security A & 40% in security B. Expected return from Security A is 20% & from Security B is 10% Determine the portfolio return Variance & Standard Deviation of portfolio port where : W port 2 i i Cov ij n 2 2 w i i w iw where Cov i 1 i 1 i 1 the weights of the individual the covariance ij rij i j n n the standard deviation of the portfolio the variance of rates of return for asset i j Cov weights are determined by the proportion of value in the portfolio ij assets in the portfolio, where between th e rates of return for assets i and j, 14
Steps of measure risk of Portfolio The weight of each asset The variance of each asset The correlation between two assets Or 15
Example 1 Investment 100,000 150,000 A B Expected Return 10% 15% Standard Deviation 20% 25% Correlation coefficient 0.3 Any asset of a portfolio may be described by two characteristics: The expected rate of return The expected standard deviations of returns The correlation, measured by covariance, affects the portfolio standard deviation Low correlation reduces portfolio risk while not affecting the expected return 16
Ex 3 Weighed of Investment Expected Return Standard Deviation Correlation coefficient Security A Security B 30% 70% 10% 25% 12% 15% -0.45 Determine the portfolio return & risk I.e Kamal has invested 60% of wealth in A Ltd shares & other 40% wealth B ltd shares forecasted expected returns under different economic conditions are as follows. A B Depression -20% 5% Recession 10% 20% Normal 30% -12% Boom 50% 9% Determine the return from the portfolio & standard deviation of the portfolio 17
Ex 4 Ruwan has invested 30% of his wealth in Asset A & rest in asset B. Following are the expected return of both assets under different economic conditions. Asset A Asset B Recession -10% 25% Normal 15% 20% Booming 20% 5% Determine the return of & risk of individual assets & portfolio return & risk Portfolio Risk-Return Plots for Different Weights E(R) 0.20 0.15 0.10 0.05 With uncorrelated assets it is possible to create a two asset portfolio with lower risk than either single asset j k i f g 2 h R ij = +1.00 1 R ij = 0.00-0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.10 0.11 0.12 Standard Deviation of Return 18
The Efficient Frontier The efficient frontier represents that set of portfolios with the maximum rate of return for every given level of risk, or the minimum risk for every level of return Frontier will be portfolios of investments rather than individual securities Exceptions being the asset with the highest return and the asset with the lowest risk Efficient Frontier for Alternative Portfolios E(R) Efficient Frontier B A C Standard Deviation of Return 19
Efficient Markets Efficient markets are a result of investors trading on the unexpected portion of announcements The easier it is to trade on surprises, the more efficient markets should be Efficient markets involve random price changes because we cannot predict surprises 39 Systematic Risk Risk factors that affect a large number of assets Also known as non-diversifiable risk or market risk Includes such things as changes in GDP, inflation, interest rates, etc. 40 20
Unsystematic Risk Risk factors that affect a limited number of assets Also known as unique risk and asset-specific risk Includes such things as labor strikes, part shortages, etc. 41 Diversifiable Risk The risk that can be eliminated by combining assets into a portfolio Often considered the same as unsystematic, unique or asset-specific risk If we hold only one asset, or assets in the same industry, then we are exposing ourselves to risk that we could diversify away 42 21
Total Risk Total risk = systematic risk + unsystematic risk The standard deviation of returns is a measure of total risk For well diversified portfolios, unsystematic risk is very small Consequently, the total risk for a diversified portfolio is essentially equivalent to the systematic risk 43 Measuring Systematic Risk How do we measure systematic risk? We use the beta coefficient to measure systematic risk What does beta tell us? A beta of 1 implies the asset has the same systematic risk as the overall market A beta < 1 implies the asset has less systematic risk than the overall market A beta > 1 implies the asset has more systematic risk than the overall market 22
Security Market Line-SML The security market line is commonly used by investors in evaluating a security for inclusion in an investment portfolio in terms of whether the security offers a favorable expected return against its level of risk SML line drawn on a chart that serves as a graphical representation of the capital asset pricing model (CAPM), which shows different levels of systematic, or market, risk of various marketable securities plotted against the expected return of the entire market at a given point in time 23