FIN 266 Lecture 3- Risk and Rates of Return 2022 PDF

Risk and Rates of Return Lecture - 3 The goal of finance manager is to : “Maximizes return for a given level of risk or minimizes risk for a given level of return...

Risk and Rates of Return Lecture - 3 The goal of finance manager is to : “Maximizes return for a given level of risk or minimizes risk for a given level of return”. © 2007 Thomson/South-Western 1  LECTURE OBJECTIVES: What does it mean to take risk when investing? How are risk and return of an investment measured? How can investors reduce risk? 2  Defining and Measuring Risk Risk is the chance that an unexpected outcome will occur. Investment risk………….???????? 3 What is the probability distribution? A probability distribution is a listing of all possible outcomes with a probability assigned to each outcome. must sum to 1.0 (100%).  Probability Distributions It either will rain, or it will not. Only two possible outcomes. Outcome (1) Probability (2) Rain 0.40 = 40% No Rain 0.60 = 60% 1.00 100% 5  Probability Distributions Martin Products and U. S. Electric Rate of Return on Stock if State of the This State Occurs Probability Economy Martin Products U.S. Electric Boom 0.2 110% 20% Normal 0.5 22% 16% Recession 0.3 -60% 10% 1.0 6  What is the Expected Rate of Return????? Rate of return expected to be realized from an investment during its life Mean value of the probability distribution of possible returns Weighted average of the outcomes, where the weights are the probabilities 7  Determining\measuring Expected Return Probability of Martin Products U. S. Electric State of the This State Return if This State Product Return if This Product: Economy Occurring Pr ( i) Occurs (ri) : x (3) (2) State Occurs (ri) (2) x (5) (1) (2) (3) = (4) (5) = (6) Boom 0.2 110% 22% 20% 4% Normal 0.5 22% 11% 16% 8% Recession 0.3 -60% -18% 10% 3% ^ ^ 1.0 rm = 15% rm = 15% 8  Expected Rate of Return rˆ Pr1r1  Pr2 r2   Prnrn n  Priri  i1 9 How do we measure the risk of an investment??????? Standard deviation Variance Coefficient of variation  Measures of Risk Risk reflects the chance that the actual return on an investment may be different than the expected return. One way to measure risk is to calculate the variance and standard deviation of the distribution of returns. 11 Comments on Standard Deviation as a Measure of Risk Standard deviation (σi) measures total, or stand-alone, risk. The larger σi is, the lower the probability that actual returns will be closer to expected returns. Larger σi is associated with a wider probability distribution of returns.  Measures of Risk We will once again use a probability distribution in our calculations. The distribution used earlier is provided again for ease of use. ( Martin product and US.  Measuring Risk: The Standard Deviation\Variance Calculating Martin Products’ Standard Deviation\ variance Expected Payoff Return ^ ^^ 2 ^ ri - r^ ^2 (r i - r) Probability (r i - r) Pr i ri r (1) (2) (1) - (2) = (3) (4) (5) (4) x (5) = (6) 110% 15% 0.2 22% 15% 0.5 -60% 15% 0.3 Variance  2 3,517.0 Standard Deviation  m   m2  3,517  59.3% 14  Measuring Risk: The Standard Deviation Calculating Martin Products’ Standard Deviation Expected Payoff Return ^ ri - r^ (r i - ^r) 2 Probability ^ Pr (r i - r) 2 r^ i ri (1) (2) (1) - (2) = (3) (4) (5) (4) x (5) = (6) 110% 15% 95 9,025 0.2 1,805.0 22% 15% 7 49 0.5 24.5 -60% 15% -75 5,625 0.3 1,687.5 Variance  2 3,517.0 Standard Deviation  m   m2  3,517  59.3% 15  Measuring Risk: The Standard Deviation\Variance n 2 Variance    ri - rˆ  Pri 2 i1 n 2 Standard deviation    r - rˆ Pr i i i1  16 Calculating US electric’ Standard Deviation\ Variance  Measuring Risk: Coefficient of Variation Calculated as the standard deviation divided by the expected return Useful where investments differ in risk and expected returns Risk  Coefficient of variation = CV =  Return rˆ 19  Example 1 The table below provides a probability distribution for the returns on stocks A and B State Probability Return On Return On Stock A Stock B 1 20% 5% 50% 2 30% 10% 30% 3 30% 15% 10% 4 20% 20% -10% The state represents the state of the economy one period in the future i.e. state 1 could represent a recession and state 2 a growth economy. The probability reflects how likely it is that the state will occur. The sum of the probabilities must equal 100%. The last two columns present the returns or outcomes for stocks A and B that will occur in each of the four states. 20  Required: You need to calculate the expected return and standard deviation for each stock. If you are a risk averse investor which stock will you choose?  Portfolio Risk and Return The simplest definition of a portfolio is a collection of assets—stocks and bonds, —owned by one person or entity. Most investors do not hold stocks in isolation. Instead, they choose to hold a portfolio of several stocks  Expected return on a portfolio rˆp ˆp r The Expected Return on a Portfolio is computed as the weighted average of the expected returns on the stocks which comprise the portfolio.  W=The weights reflect the proportion of the portfolio invested in the stocks.  ˆp w1r r ˆ1  w 2r ˆ2    w Nr ˆN N  w jr ˆj  j1 23  Portfolio Returns Expected return on a portfolio, rˆp The weighted average expected return on the stocks held in the portfolio rˆp w1rˆ1  w2rˆ2   wNrˆN  N  w jrˆj  j1 24  Portfolio Risk and Return From our previous calculations ( example), we know that: – the expected return on Stock A is 12.5% – the expected return on Stock B is 20% – the variance on Stock A is.00263 – the variance on Stock B is.04200 – the standard deviation on Stock A is 5.12% – the standard deviation on Stock B is 20.49% 25 Example -2 on portfolio……… State of the economy probability Stock A Stock B 1 20% 5% 50 2 30% 10 30 3 30% 15 10 4 20% 20 -10  solution The expected return on Stock A is 12.5%, the expected return on Stock B is 20%, What is the expected return on the portfolio???????????? If we invest 20% in stock A and 80% in stock B. r^p=  Measuring risk-portfolio Standard deviation is a little more tricky and requires that a new probability distribution for the portfolio returns be devised. formula  Portfolio Risk Correlation Coefficient,  – Measures the degree of relationship between two variables. – Perfectly correlated stocks have rates of return that move in the same direction. – Negatively correlated stocks have rates of return that move in opposite directions. 33  Returns Distributions for Two Perfectly Positively Correlated Stocks ( = +1.0) and for Portfolio MM’: Stock M Stock M’ Stock MM’ 25 25 25 15 15 15 0 0 0 -10 -10 -10 34  Returns Distribution for Two Perfectly Negatively Correlated Stocks ( = -1.0) and for Portfolio WM: Stock W Stock M Portfolio WM 25 25 25 15 15 15 0 0 0 -10 -10 -10 35  Portfolio Risk Risk Reduction – Combining stocks that are not perfectly correlated will reduce the portfolio risk through diversification. – The riskiness of a portfolio is reduced as the number of stocks in the portfolio increases. – The smaller the positive correlation, the lower the risk. 36 More on risk and rates of return  Total Risk = Systematic Risk + Unsystematic Risk Total Risk = Systematic Risk + Unsystematic Risk Systematic Risk - Market Risk Unsystematic Risk- Firm-Specific Risk  Firm-Specific Risk versus Market Risk Firm-Specific Risk (unsystematic risk): – That part of a security’s risk associated with random outcomes generated by events, or behaviors, specific to the firm. E.X failure of the firms new product, scandal involving top management or the loss of a key employee. – Firm-specific risk can be eliminated through proper diversification. 39  Firm-Specific Risk versus Market Risk Market Risk (systematic risk): – That part of a security’s risk that cannot be eliminated through diversification because it is associated with economic, or market factors that systematically affect all firms. – E.X. unexpected changes in the overall health of the economy, interest rates movements, or changes in inflation. – We can measure it using the beta coefficient. (b) 40  Beta coefficient (b) The beta coefficient tell us how much market risk a stock has relative to an average stock. By definition an average stock has the tendency to move up and down with the market. (stock exchange) It measures how sensitive is a stock to market reactions.  The Concept of Beta Beta Coefficient, : – A measure of the extent to which the returns on a given stock move with the stock market. –  = 0.5: Stock is only half as volatile, or risky, as the average stock. –  = 1.0: Stock has the same risk as the average risk. –  = 2.0: Stock is twice as risky as the average stock. – FOR A GIVEN LEVEL OF BETA WHAT RATE OF RETURN WILL YOU REQUIRE????????? 42  Capital Asset Pricing Model (CAPM) CAPM is a model that describes the relationship between risk and (required) return; in this model, a security’s (required) return is the risk-free rate plus a premium based on the systematic risk of the security.  The Required Rate of Return for a Stock C.A.P.M (capital asset pricing model) r j rRF  rM  rRF  j Security Market Line (SML): – The line that shows the relationship between risk as measured by beta and the required rate of return for individual securities. 44  The Relationship Between Risk and Rates of Return th r̂ j expected rate of return on the j stock th r j required rate of return on the j stock rRF risk  free rate of return rM =market return RPM rM - rRF  market risk premium 45  Market Risk Premium RPM is the additional return over the risk-free rate needed to compensate investors for assuming an average amount of risk. Assuming: – Treasury bonds yield = 6%, – Average stock required return = 14%, – Then the market risk premium is 8 percent: RPM = rM - rRF = 14% - 6% = 8%. 46  Security Market Line SML :rj  rRF  rM  rRF  j Required Rate of Return (%) rhigh = 22  Relatively Risky rM = rA = 14 Stock’s Market (Average Risk Stock) Risk Premium: Premium: rLOW = 10 8% 16% Safe Stock Risk Premium: 4% rRF = 6 Risk-Free Rate: 6% 0 0.5 1.0 1.5 Risk, bj 2.0 47  Portfolio Beta Coefficients The beta of any set of securities is the weighted average of the individual securities’ betas  p w 1  1  w 2  2    w n  n N  w j  j j1 48  What have we learned 1/2 What does it mean to take risk when investing? – An investment is risky if more than one outcome is possible How are risk and return of an investment measured? – By the variability of its possible outcomes - greater variability = greater risk How can investors reduce risk? – Risk can be reduced through diversification 49  What have we learned 2/2 For what type of risk is an average investor rewarded? – Investors should only be rewarded for risks they must take What actions do investors take when the return they require to purchase an investment is different from the return the investment is expected to produce? – Investors will purchase a security only when its expected return is greater than its required return 50