1. CDA COLLEGE BUS235: PRINCIPLES OF FINANCIAL ANALYSIS Lecture 3 Lecture 3 Lecturer: Kleanthis Zisimos

2. Lecture Topic List Defining and Measuring risk Defining and Measuring risk Expected rate of return Expected rate of return Capital asset pricing model Capital asset pricing model Examine the Relationship between Risk and Rates of Return Examine the Relationship between Risk and Rates of Return

3. What is risk? Risk is defined as a hazard exposure to loss or injury. Thus risk refers to the chance that some unfavorable even will occur. Risk is defined as a hazard exposure to loss or injury. Thus risk refers to the chance that some unfavorable even will occur. When investors buy stocks they take the risk either to loose money or to win more money. When investors buy stocks they take the risk either to loose money or to win more money. Most investors hold portfolio of stocks and bonds instead of investing only in one stock. Can you tell me why? Most investors hold portfolio of stocks and bonds instead of investing only in one stock. Can you tell me why?

4. An outcome’s probability is defined as the chance that the event will occur. An outcome’s probability is defined as the chance that the event will occur. If all possible events are listed with the corresponding probabilities then the list is called probability distribution. If all possible events are listed with the corresponding probabilities then the list is called probability distribution. What is the probability distribution of a 10 % government bond which has 70% probability to pay the interest and 30% to default? What is the probability distribution of a 10 % government bond which has 70% probability to pay the interest and 30% to default? 4 Probability distribution

5. Outcome Probability Rate of return Pay interest 70 % 10% Default 30 % 0% Notes. The higher the probability to default the riskier the stock. As a result the required interest or rate of return will be higher. Notes. The higher the probability to default the riskier the stock. As a result the required interest or rate of return will be higher. If we multiply each possible rate of return with its probability we have the weighted average of outcomes If we multiply each possible rate of return with its probability we have the weighted average of outcomes

6. Expected rate of return The expected rate of return is the weighted average of outcomes. The expected rate of return is the weighted average of outcomes. In our example the expected rate of return is In our example the expected rate of return is 70% x 10% + 30% x 0= 7% 70% x 10% + 30% x 0= 7% It can be expressed as the following formula: n K = Σ Pi ki ki is the ith possible outcome, pi is the K = Σ Pi ki ki is the ith possible outcome, pi is the i=1 probability of the ith outcome and n is the i=1 probability of the ith outcome and n is the number of possible outcomes number of possible outcomes

7. Continues Probability distribution graph The probability distribution graph consists of all the rates of returns. The probability distribution graph consists of all the rates of returns. In real life there are unlimited outcomes and probabilities so a continues probability is more suitable to adopt. In real life there are unlimited outcomes and probabilities so a continues probability is more suitable to adopt. The tighter the probability distribution, the more likely it is that the actual outcome will be close to the expected value The tighter the probability distribution, the more likely it is that the actual outcome will be close to the expected value

8. Continues Probability distribution graph Rate of return Probability density Expected rate of return

9. The tighter the probability distribution of expected future returns, the smaller the risk of a given investment. The tighter the probability distribution of expected future returns, the smaller the risk of a given investment. The measurement of the tightness of the probability distribution is given by the standard deviation formula The measurement of the tightness of the probability distribution is given by the standard deviation formula n 2 n 2 Variance = σ2 = Σ = (Ki – k) Pi ki is expected rate of return Variance = σ2 = Σ = (Ki – k) Pi ki is expected rate of return i=1 i=1 n 2 n 2 Standard Deviation = σ = √ Σ = (Ki – k) Pi Standard Deviation = σ = √ Σ = (Ki – k) Pi i=1 i=1 Measuring risk. The standard deviation

10. Coefficient of Variation Another useful measurement of risk is the Coefficient of Variation (CV) Another useful measurement of risk is the Coefficient of Variation (CV) It shows the risk per unit of return, and provides a more meaningful basis for comparison when the expected returns on two alternatives are not the same. It shows the risk per unit of return, and provides a more meaningful basis for comparison when the expected returns on two alternatives are not the same. CV is the standard deviation divided by the expected return. CV is the standard deviation divided by the expected return. Coefficient of Variation = CV = σ Coefficient of Variation = CV = σ Κi Κi

11. Risk Aversion If you choose the less risky investment, you are risk averse. Most investors are indeed risk averse, and certainly the average investor is risk averse, at least with regard to his or her “serious money. If you choose the less risky investment, you are risk averse. Most investors are indeed risk averse, and certainly the average investor is risk averse, at least with regard to his or her “serious money. If a market is dominated by risk averse investors the riskier securities must have higher expected returns. If a market is dominated by risk averse investors the riskier securities must have higher expected returns.

12. Capital asset pricing model We have seen so far the riskness of stocks when held in isolation. If we want to analyze the riskness of stocks held in portfolios we use the Capital asset pricing model. We have seen so far the riskness of stocks when held in isolation. If we want to analyze the riskness of stocks held in portfolios we use the Capital asset pricing model. A stock held as part of a portfolio is less risky than the same stock held in isolation A stock held as part of a portfolio is less risky than the same stock held in isolation The expected return on a portfolio, (kp), is simply the weighted average of the expected returns on the individual stocks in the portfolio, with the weights being the fraction of the total portfolio invested in each stock. The expected return on a portfolio, (kp), is simply the weighted average of the expected returns on the individual stocks in the portfolio, with the weights being the fraction of the total portfolio invested in each stock.

13. n Portfolio expected return = Σ w i k i i=1 i=1 K i are the expected returns on the individual W i are the weights N are the number of stocks in the portfolio Portfolio expected return

14. Portfolio risk Although the expected return of the portfolio is simply the weighted average of the expected returns of the individual stocks this does not happen with the riskness of the portfolio. Although the expected return of the portfolio is simply the weighted average of the expected returns of the individual stocks this does not happen with the riskness of the portfolio. As a rule the riskiness of a portfolio is reduced as the number of stocks in the portfolio increases. As a rule the riskiness of a portfolio is reduced as the number of stocks in the portfolio increases. This rule applies only if we use stocks with small correlation coefficient, r This rule applies only if we use stocks with small correlation coefficient, r

15. Portfolio Risk and the Correlation coefficient Correlation coefficient, (r) is the tendency of two variables to move together. Correlation coefficient, (r) is the tendency of two variables to move together. If we combine stocks with negative Correlation coefficient (-1) then we reduce the risk of the portfolio. If we combine stocks with negative Correlation coefficient (-1) then we reduce the risk of the portfolio. In reality stocks are positively correlated with an average r=+0,6 so we need to minimize this correlation to 0 as possible. In reality stocks are positively correlated with an average r=+0,6 so we need to minimize this correlation to 0 as possible.

16. Portfolio risk, Company versus market risk The Portfolio risk is affected by the company- specific or diversifiable risk and the market or nondiversifiable risk The Portfolio risk is affected by the company- specific or diversifiable risk and the market or nondiversifiable risk Company-specific risk is the part of the portfolio risk that can be eliminated by diversification i.e using stocks with negative correlation coefficient Company-specific risk is the part of the portfolio risk that can be eliminated by diversification i.e using stocks with negative correlation coefficient Market risk is that part of risk that can not be eliminated by diversification. Market risk is that part of risk that can not be eliminated by diversification. We can see that only market risk is important to an investor because he can eliminate company specific risk with diversification We can see that only market risk is important to an investor because he can eliminate company specific risk with diversification

17. Portfolio risk- Market risk Market risk can be measured by the degree to which a given stock tends to move up and down with the market. Market risk can be measured by the degree to which a given stock tends to move up and down with the market. This tendency of the stock is called beta coefficient, b This tendency of the stock is called beta coefficient, b The portfolio risk finally is the weighted average beta of the stocks, bp The portfolio risk finally is the weighted average beta of the stocks, bp

18. Portfolio risk and portfolio beta coefficient Portfolio beta coefficient is the appropriate measure of the portfolio’s risk Portfolio beta coefficient is the appropriate measure of the portfolio’s risk n bp =portfolio beta (risk) n bp =portfolio beta (risk) bp = Σ wibi wi is the fraction of the portfolio invested ith stock bp = Σ wibi wi is the fraction of the portfolio invested ith stock i=1 bi is the beta of the ith stock i=1 bi is the beta of the ith stock

19. The relationship between risk and rates of return For a given level of beta what rate of return will investors require on a stock in order to compensate them for assuming the risk? For a given level of beta what rate of return will investors require on a stock in order to compensate them for assuming the risk? The answer is given by the Security Market Line equation (SML) which shows the relationship between a security’s risk and its required rate of return. The answer is given by the Security Market Line equation (SML) which shows the relationship between a security’s risk and its required rate of return. SML=Ki = KRF + (KM – KRF)bi SML=Ki = KRF + (KM – KRF)bi

20. Ki = required rate of return on the stock. Ki = required rate of return on the stock. K e = expected rate of return on the stock. K e = expected rate of return on the stock. K RF = risk free rate of return. K RF = risk free rate of return. bi = beta coefficient of the stock. bi = beta coefficient of the stock. K M = Required rate of return on a portfolio of all stocks, which is the market portfolio. K M = Required rate of return on a portfolio of all stocks, which is the market portfolio. From the definitions we can also observe that From the definitions we can also observe that RPm=KM-KRF= market risk premium RPi = (KM-KRF)bi = Risk Premium on the ith Stock The relationship between risk and rates of return