1. CHAPTER 5: RISK AND RETURN By: Prof Dr Nik Maheran Nik Muhammad Learning Objectives: 1.Explain the concept and relationship between risk and return. 2.Identify the formula to measure risk and return

2. Fundamentals of Risk and Return  Different investment have different return and risk characteristics.  Some investments will give you immediate returns with little risk, while others may give higher returns with high risk.  Identifying investments on the basis of their return and risk characteristics is not easy. If we take more risk, we will get more return and vice versa Risk Positive Relationship The higher the return, the higher the risk

3.  Outcome or profit that we get for our investment over some period.  Ex: RM 200 investment that pays RM10 in cash dividend and worth RM208 one year late, your return would therefore be:  For investment in common stock, the return is known as Holding Period Return (HPR) and involves three cash flow elements: 1. The initial price of the stock bought (P0) 2. Periodic distribution received while the stock is held (D1) 3. The amount received when the stock is sold (P1) (RM10 + RM8) =9% RM200 Return

4.  Mathematically HPR can be expressed as follow:  Return can be classified as current return and future return. Current returns are those benefits that you expect to get on a regular basis. Dividends paid by the company to the investors or interest payment made to the bondholder annually is an example of current returns.  When an investment appreciates in value over time, this is referred to as future return. Referring to the earlier example, when your investment increased in value from RM200 to RM208 the additional RM8 is said to be your future return. Return HPR= RM5 + (RM150 - RM 100) RM100 =0.55 or 55%

5.  Conventionally, we can measure expected return as follows:  When n=the number of possible states of the economy Ri=the return/cash flow in its states of the economy P(Ri)=the probability of the return occurring Ṝ =the expected return Measuring Expected Return ( Ṝ ) Using Probability Distribution n Ṝ = ∑Ri P(Ri) i=1

6.  Hence, the expected return is simply the weighted average of the possible returns, with the weights being the probabilities of occurrence (Van Home, 1995).  Demonstrates how the expected return ( Ṝ ) is computed  As seen in the table, the expected return for the investment is 7.8 percent Measuring Expected Return ( Ṝ ) Using Probability Distribution Probability of Event Occurring Pi Possible Return, Ri Expected Return ( Ṝ ) (Ri) (Pi) 0.210.0(0.2) (10) = 2.0 0.58.0(0.5) (8) = 4.0 0.36.0(0.3) (6) = 1.8 ∑ = Ṝ = 7.8

7.  The degree of uncertainty that things will not happen as we want.  The are two types of risk: unsystematic risk and systematic risk. Risk RISKRISK Unsystematic risk systematic risk Total Risk

8. Unsystematic risk (Non diversifiable risk) 1. The portion of total risk that is unique to a firm or industry. 2. It results in the uncertainty of possible returns on the investment due to factors: incompetence of management, labour difficulties and changes in consumers’ preferences. 3. Can be reduced or eliminated through a well-diversified portfolio of investments. Systematic Risk (Diversifiable risk) 1. The portion of total risk that affects the overall market. 2. Example: Changes in the country’s economy, inflation rates and interest rates. 3. Cannot be reduced or eliminated by holding well-diversified portfolio of investments. Risk

9.  Using standard deviation (a statistical measure of the variability of a distribution around its mean, Van Home, 1995).  Measures the differences between the possible returns and the expected return. Mathematically, the standard deviation of a particular investment can be written as: σ = √ ∑ Ri P (Ri - Ṝ ) 2 Pi Measuring Risk

10.  Example:  7.8% expected return and a standard deviation of 1.4% indicate that the actual return of the investment ranges between 4% and 9.2% (7.8% ± 1.4%)  If the other investment B has the same expected return as the previous investment but a standard deviation of 3%, then, we can say that investment B is riskier since it has a higher standard deviation.  To understand the riskiness of an investment relative to another, a coefficient of variation is used. Measuring Risk Probability of Event Occurring (Pi)Possible Return, Ri (Ri - Ṝ ) 2 Pi 0.210.0(10 - 7.8) 2 (0.2) = 0.968 0.58.0(8 - 7.8) 2 (0.5) = 0.020 0.36.0(6 - 7.8) 2 (0.3) = 0.972 σ2 = 1.960 σ = 1.400 Calculating risk (σ) standard deviation

11.  Used to differentiate investments with different expected returns.  It is “ the ratio of the standard deviation to the expected return” (Winger, 1993) and measures the amount of risk for every unit of expected return.  Using the same example, if investment A has 0.18% (1.4/7.8) risk per 1.0% of return, while investment B has 0.38% (3/7.8) risk per 1.0% of return, then investment B is to be riskier not only in absolute terms but also in relative terms. Coefficient of Variation Coefficient of variation=Standard deviation Average or expected return CV= σ (Ri) E (Ri)

12.  Was developed by Sharpe (1964), Lintner (1965) and Mossin (1966).  A model was generated to predict about the risk and return characteristics of individual assets by specifying how they could covary with the market portfolio of all risky assets.  Therefore the specific measure of systematic risk use in CAPM is called asset’s beta, ßi, and is defined as the correlation of the asset’s return with the return on the market portfolio, Rm, as specified in the equation below: Capital Asset Pricing Model (CAPM) βiβi=COV (Ri, Rm) Where, Var Rm βiβi=The beta coefficient of security j COV im= covariance of the returns on security j with the return on the market Beta (βi)=COV im S2mS2m S2mS2m=variance

13.  This is a direct, linear estimate of the degree of co-movement between an asset’s return and the return on the market portfolio.  Beta is the number that measures non-diversifiable, or market risk., indicates how the price of a security responds to market forces. The more responsive the price of a security is to changes in the market, the higher that security’s beta.  Found by relating the historical returns for a security to the market return. (Market return is the average return for all stock).  The beta for the market is 1.00. Stocks with betas greater than 1.00 are more responsive to changes in the market return and therefore are more risky than the market. Stocks with betas less than 1.00 are less risky than the market. Therefore the higher the stock beta, the greater should be its level of expected return. Capital Asset Pricing Model (CAPM)

14.  To make the final step to the CAPM we must incorporate the option of investing in the risk-free asset, as well as investing in the market portfolio of risky assets.  Risk–free rate is the interest rate that can be earned with certainty. The rate that one can earn from the government securities (treasury bills) or bank can be considered as risk-free rate.  Since investors can choose combinations of this portfolio and the risk- free asset, we can specify the CAPM predicted return for any risky asset as equation below:  Where (Rm – RF) term is called the market risk premium (or equity risk premium), since it is the additional return required by investors in order to hold the market portfolio instead of the risk-free assets. Capital Asset Pricing Model (CAPM) Required Return on Investment j = Risk free rate + [Beta for investment j x (Market return - risk free rate)] E(R j )=R F + [ß i x (R m – R F )]

15.  Reward is measured as the difference between the expected HPR on the index stock fund and the risk-free rate, that is the rate you can earn by leaving money in risk-free assets such as T-bills, money market fund or the bank. We call this difference the risk premium on common stock.  Therefore it is define as:  Risk premium for investment is risk faced by the investors depending on type of vehicle (stock, bond, etc) financial condition of the company and etc. Risk premium can be define as 1. The expected return over the risk-free return. For example, if the risk- free rate is 6% per year, and the expected index fund return is 14%, then the risk premium on stocks is 8% per year. 2. The additional compensation above the risk-free return. Capital Asset Pricing Model (CAPM)

16. Example:  Assume you are considering security Z with a beta of 1.25. The risk-free rate is 6% and the market return is 10%.  If the beta were lower, say 1.00, the required return would be lower Capital Asset Pricing Model (CAPM) E(R j ) =R F + [ß i x (R m – R F )] =6 % + [1.25 x (10% - 6 % )] 6% + 5 % =11% E(R j )=R F +[ß i x (R m – R F )] =6 % + [1.00 x (10% - 6 % )] 6% + 4 % =10%

17.  The CAPM is presented graphically, where expected return is again on the y-axis, by now beta (rather than standard deviation) is on the x-axis. The ray extending up to the right from R F is referred to Security Market Line.  For each level of non diversifiable risk (beta), SML reflects the required return the investor should earn in the market place The security Market Line (SML) 6 1.01.25 11 10 SML Required return (%) Risk (beta) SML depict the tradeoff between risk and return. At beta of 0, the required return is the risk free of 6%. At a beta of 1.0 the required return is market return of 10%. Given these data, the required return on an investment with a beta of 1.25 is 11% 0

18. 1. Sambal Daging Inc is evaluating an investment. With the following information, calculate the investment’s expected risk and return. Should or not Sambal Daging Inc invest if the Treasury bill carries a return of 9.40% Questions/Exercises ProbabilityReturn 0.155% 0.307% 0.4010% 0.1515%

19. Answer…. No, Sambal Daging Inc should not invest in the investment because the level of risk is excessive for return which is lower than the return offered by the Treasury bills. Questions/Exercises ABA x B Weighted Deviation [ (Ri - Ṝ ) 2 Pi ] Probability (Pi) Return Expected (Ri) Return ( Ṝ ) 0.155%0.75%2.52 0.307%2.10%1.32 0.4010%4.00%0.32 0.1515%2.25%5.22 Ṝ = 9.10% σ2 = 9.39% σ = 3.06%

20. 2. Consider a Malaysian firm making an investment that produces cash flows in Japan Yen. If the firm invested ¥12,000 today and expects to get ¥15,000 one year from today, what is the firm’s HPR? Answer…. Questions/Exercises HPR=D1 + (P1 — P0) P0 =0 + (15,000 — 12,000) 12,000 =25%