Chapter 9 Risk and Return PDF

Orange or Lemon Chapter 9 Risk and Return 1  After After studying studying Risk Risk and and Return, Return, you you should sho...

Orange or Lemon Chapter 9 Risk and Return 1  After After studying studying Risk Risk and and Return, Return, you you should should be be able able to: to: 1. Understand the relationship between risk and return. 2. Define risk and return and show how to measure them by calculating expected return, standard deviation, and coefficient of variation. 3. Distinguish between avoidable (unsystematic) risk and unavoidable (systematic) risk and explain how proper diversification can eliminate one of these risks. 4. Understand Portfolio Selection and Diversification. 5. Be aware of technical analysis approach to share price analysis 2  Defining Return Income received on an investment plus any change in market price, price usually expressed as a percent of the beginning market price of the investment. D t + (P t – P t - 1 ) R= Pt - 1 3  Return Example The stock price for Stock A was $10 per share 1 year ago. The stock is currently trading at $9.50 per share and shareholders just received a $1 dividend. dividend What return was earned over the past year? $1.00 + ($9.50 – $10.00 ) R= = 5% $10.00 4  Defining Risk Risk is the variability of returns from those that are expected. Risk can be measured by looking at the variability in the probability distribution with reference being made to the mean value or average (expected return). The variability or spread, which is the risk is measured using the standard deviation. The smaller the standard deviation the lesser the risk and the larger the standard deviation the higher the risk. Before we can measure the standard deviation we need to know the expected return or mean. 5  Determining Expected Return The expected return is the return on a risky asset expected in the future. Meaning summation of the product of the respective probabilities and the returns, 6  Determining Expected Return Expected Return (ER) = ER= (R1)(P1)+ (R2)(P2)+ (R3)(P3)+ + + Pi(Ri) ER =  ( Ri )( Pi ) ER is the expected return for the asset, Ri is the return for the ith possibility, Pi is the probability of that return occurring,  The sum of the total number of possibilities. 7 Example 1. Determine the Expected Return on stock BW? 8 How How to to Determine Determine the the Expected Expected Return. Return. Example Example 1. 1. Stock BW Ri Pi (Ri)(Pi) The -0.15 0.10 –0.015 expected -0.03 0.20 –0.006 return, ER, 0.09 0.40 0.036 for Stock BW is 0.09 0.21 0.20 0.042 or 9% 0.33 0.10 0.033 Sum 1.00 0.090 9 Determining Standard Deviation (Risk Measure) = (R– ER)2( Pi ) Standard Deviation, Deviation , is a statistical measure of the variability of a distribution around its mean. It is the square root of variance. 0.4 0.35 0.3 0.25 0.2 0.15 0.1 0.05 Note, this is for a discrete distribution. 0 –0.15 –0.03 9% 21% 33% 10 Example 1. Determine the Standard Deviation on stock BW? 11 How How to to Determine Determine the the Standard Standard Deviation. Deviation. Stock BW Ri Pi (Ri)(Pi) (Ri - ER)2(Pi) –0.15 0.10 –0.015 0.00576 –0.03 0.20 –0.006 0.00288 0.09 0.40 0.036 0.00000 0.21 0.20 0.042 0.00288 0.33 0.10 0.033 0.00576 Sum 1.00 0.090 0.01728 12  Determining Standard Deviation (Risk Measure) Standard deviation =  =  ri ( - ER ) 2 Pi. Standard deviation =  = 0.01728.  = 0.1315 or 13.15% 13  Coefficient of Variation The ratio of the standard deviation of a distribution to the mean of that distribution. It is a measure of RELATIVE risk.  Coefficiet of variation (CV) =. ER 0.1315 Coefficiet of variation (CV) = 0.09 CV = 1.46 This means that for this stock BW an investor takes on 1.46 units of risk for every extra 1.0 unit of return earned. This is useful especially where standard deviations are equal or close and an investor needs to choose between two or more options for investment. 14 Example 2. The figure below shows the probability distribution for different states of an economy with probability assigned and the returns under each state of the economy. State of Economy Probability Returns of Stock A Returns of Stock B Boom 0.3 25% 19% Normal 0.4 15% 12% Recession 0.3 -10% 8% Total Probability 1 Calculate the expected rate of return for Stock A and Stock B? 15 Example 2. How to Determine the Expected Return for Stock A State of Economy Probability Returns of Stock A ER Boom 0.3 25% 7.5% Normal 0.4 15% 6% Recession 0.3 -10% -3% Total 1.0 ER 10.5% Probability 16 Example 2. How to Determine the Standard Deviation for Stock A State of Ri Pi (Ri)(Pi) (Ri - Economy ER)2(Pi) Boom 0.3 25% 7.5% 63.075 Normal 0.4 15% 6% 8.100 Recession 0.3 -10% -3% 125.075 Total 1.0 10.5% 196.25 Standard deviation =  = 196.25  = 14 17  Coefficient of Variation CV This is the risk measured per unit of return, measured as the standard deviation divided by the expected return. 14 Coefficiet of variation (CV) = 10.5 CV = 1.33 This means that for this stock A an investor takes on 1.33units of risk for every extra 1.0 unit of return earned. This is useful especially where standard deviations are equal or close and an investor needs to choose between two or more options for investment. 18  Calculate the expected rate of return for Stock for Stock B? State of Economy Probability Returns of Stock B ER Boom 0.3 19% 5.7% Normal 0.4 12% 4.8% Recession 0.3 8% 2.4% Total Probability 1.0 Expected 12.9% Return 19 Calculate the Standard Deviation for Stock for Stock B? Stock B Stateof Ri Pi (Ri)(Pi) (Ri - ER)2(Pi) Economy Boom 0.3 19% 5.7% 11.16 Normal 0.4 12% 4.8% 0.32 Recession 0.3 8% 2.4% 7.2 Total Expected Return 1 12.9% 18.69 Standard deviation =  = 18.69 s = 4.32 20  What is the Coefficient of Variation for Stock B? 4.32 CV StockB = 12.9 0.197 CV = 0.335 Which stock has a higher investment risk? Explain why? Stock A has a higher investment Risk. This means that for this stock A an investor takes on 1.33units and stock B an investor takes on 0.197 units of risk for every extra 1.0 unit of return earned. Also the Standard deviation for stock A is 14 and for Stock B is only 4.32 This observation is useful especially where standard deviations are equal or close and an investor needs to choose between two or more options for investment. 21  Portfolio Selection and Diversification Most investors tend to hold more than one investment. They hold what is known as a portfolio. A portfolio is a group of assets or investment held by an investor. The reason for holding a portfolio is to diversify the risk or reduce the level of exposure to risk associated with holding a single investment. Determining the risk in a portfolio requires knowing the portfolio expected return and the correlation or covariance of the returns among the securities that make the portfolio. 22  Portfolio expected return Expected return for a portfolio ERp=WA x ERA+WB x ERB Example 3.2 Let say you intend to hold a portfolio in which 50% of the funds are invested in A and the other half in B. The ER for A and B respectively are 10.5% and 12.9%.Let us assume that the calculated standard deviation for A and B are 14% and 4.32%.Find portfolio expected return. ERp= 0.5(10.5)+0.5(12.9) = 11.7% 23  Measuring Risk for a Portfolio A number of factors affect the risk associated with holding a portfolio; one of them is the way returns from investment move in relation to each other. Returns either move positively or negatively in relation to each other. This is known as the correlation (covariance). The COV (Ra ,Rb ) =∑P2(Ra-ERa )(Rb- covariance is measure as follows: ERb) 24 State of Economy Probability Returns of Stock A Returns of Stock B Boom 0.3 25% 19% Normal 0.4 15% 12% Recession 0.3 -10% 8% Total Probability 1 ER = 10.5% ER = 12.9% COV (Ra,Rb) =∑Pi(Ra-ERa)(Rb-ERb) =0.3(25% -10.5%)(19% - 12.9%)+0.4(15%-10.5%)(12%-12.9%)+0.3(- 10%-10.5%)(8%-12.9%) = 0.3(14.5)(6.1)+0.4(4.5)(-0.9)+0.3(-20.5)(-4.9) = 55.05% or 0.5505  This means that the relationship between the returns of A and B is positive. This will increase the risk for a portfolio. 25 To obtain the portfolio risk we need to compute the portfolio standard deviation using the formula below: 26 27 28 Negative correlation between returns from two or more investment reduces the overall risk for a portfolio, hence it is important to understand how return move when selecting investments to add to a portfolio. 29  The Efficient Frontier The Efficient Frontier represents all the dominant portfolios in risk/return space. There is one portfolio (M) which can be considered the market portfolio if we analyze all assets in the market. Hence, M would be a portfolio made up of assets that correspond to the real relative weights of each asset in the market. Assume you have several assets. With the help of the computer, you can calculate all possible portfolio combinations for a portfolio. The Efficient Frontier will consist of those portfolios with the highest return given the same level of risk or minimum risk given the same return. 30 The Efficient Frontier Graph 31 Why are they the most efficient portfolios? The reason is that it is possible to create a portfolio which gives a higher rate of return for a given level of risk, or lower level of risk for a lower level of return. 32 Risk free rate? However, there is one exception investment not inside (below and the right of) of the efficient frontier. This investment is the risk free investment. The return on govt securities is deemed risk free, where investors are confident that interest will always be paid on time and capital repaid when due, hence cash returns are known with certainty. 33 Capital market line: A graphical representation of a CML 34 Significance of the CML  The significance of the CML is that it represents the range of best investment options in terms of risk and return.  A risk averse investor will invest in a risk free investment, while an investor willing to accept risk will invest at point M (market portfolio)  M represents the market portfolio. This argument is dependent on three valid assumptions; i. Investors are rational, are all aiming to achieve an optimum combination of risk and return ii. All investors have perfect information about investments that are available and their risks and return iii. All investors are free to buy any investments without impediments such as transaction costs or taxes. 35  Therefore all investors will identify point M as the best portfolio to invest in. Portfolio theory is concerned with selecting and optimizing a set of investments by checking their returns against their risks. But there are limitations to the use of portfolio theory, mainly stemming from the assumptions that are postulated by the model. 36  Total Risk = Systematic Risk +Unsystematic Risk Systematic Risk is the variability of return on stocks or portfolios associated with changes in return on the market as a whole. Systematic risk arises due to the changes in local and global macroeconomic parameters which include economic policy decisions made by governments, decisions of central banks that affect the lending interest rates and even waves of economic recession. These are some of the systematic risk examples. They arise due to the inherent dynamic nature of an economy and the flow of resources around the world. Examples are wars, rising inflation ,Financial crisis 2008  Unsystematic Risk is the variability of return on stocks or portfolios not explained by general market movements. It is avoidable through diversification. Some of the unsystematic risk examples are labour strikes, drop in sales of a company or any other problem which arises due to human level error in judgment at the managerial level, that affects your stock or securities investment. 38 Capital Capital Asset Asset Pricing Pricing Model Model (CAPM) (CAPM) CAPM is a model that describes the relationship between risk and expected (required) return; in this model, a security’s expected (required) return is the risk-free rate plus a premium based on the systematic risk of the security.  Characteristic Characteristic Line Line EXCESS RETURN Narrower spread ON STOCK is higher correlation M Beta = N W EXCESS RETURN ON MARKET PORTFOLIO N Characteristic Line  What What is is Beta? Beta? An index of systematic risk. risk It measures the sensitivity of a stock’s returns to changes in returns on the market portfolio. The beta for a portfolio is simply a weighted average of the individual stock betas in the portfolio. Risk can also be measured in terms of the volatility of particular assets returns to movements in the returns from the market as a whole. The coefficient that measures this risk is known as a Beta β. It measures systematic risk or market risk.  Characteristic Characteristic Lines Lines and and Different Different Betas Betas EXCESS RETURN Beta > 1 ON STOCK (High risk) Beta = 1 Each characteristic (Average risk) line has a Beta < 1 different slope. (Low risk) EXCESS RETURN ON MARKET PORTFOLIO  The The CAPM CAPM formula formula R = Rf + (ERM – Rf) R is the required rate of return for a stock Rf is the risk-free rate of return,  is the beta of stock (measures systematic risk of stock ) ERM is the expected return for the  Security Security Market Market Line Line R = Rf + (ERM – Rf) Required Return ERM Risk Premium Rf Risk-free Return M = 1.0 Systematic Risk (Beta)  Determination of the Required Rate of Return ( Using the CAPM formula) Example 1. Lisa Miller at Basket Wonders is attempting to determine the rate of return required by their stock investors. Lisa is using a 6% Rf and a long-term market expected rate of return of 10%. 10% A stock analyst following the firm has calculated that the firm beta is 1.2. 1.2 What is the required rate of return on the stock BWs BWs Required Required Rate Rate of of Return Return R = Rf + (ERM – Rf) RBW = 6% + (10% – 6%) 6% 1.2 RBW = 10.8% The required rate of return exceeds the market rate of return as BW’s beta exceeds the market beta (1.0).  Determination of the Required Rate of Return ( Using the CAPM formula)  Using the CAPM it is possible to determine the required return on a given stock if the beta is known and the risk premium is also known. Example 1.  A stock has a beta of 1.2 and the risk premium for this stock is 6%.Given that T bills offer 8% risk free return. What required rate of return will investors demand on this stock? 47  Risk premium R = Rf + (ERM – Rf) = 8% + (6%)() = 15.2% 48 When the risk is adjusted the return responds likewise. Suppose the beta was increased to 2.0. R = 8% + (6%() = 20% The same would happen if the beta was reduced to 0.5. R = 8% + (6%)()= 11% 49