Risk Return Risk Chance that other results then

Risk - Return • Risk - Chance that other results then the expected are possible. • Investment risk pertains to the probability of actually earning a low or negative return. – The greater the chance of low or negative returns, the riskier the investment. • We will distinguish between diversifiable and non-diversifiable risk. 11/27/2020 Fin 301 -Risk and Return | Dr. Menahem Rosenberg 1

Risk Measure • Probability - the chance (measured in fraction or percentage) that a specific event will occur • Probability distribution - A listing of all possible events and their associated probabilities. 11/27/2020 Fin 301 -Risk and Return | Dr. Menahem Rosenberg 2

Probability Distributions of Returns • Assume that there are two stocks available, LORIS Inc and HIRIS Corp and each responds to the state of the economy according to the following table 11/27/2020 Fin 301 -Risk and Return | Dr. Menahem Rosenberg 3

Probability Distributions of Returns of LORIS and HIRIS 0. 5 Probability 0. 4 0. 3 0. 2 0. 1 0 40% LORIS 30% 20% Return 11/27/2020 10% HIRIS 0% Fin 301 -Risk and Return | Dr. Menahem Rosenberg -10% 4

Expected Return • Expected Return- Weighted Average return, using event probabilities as weights. • • • Both companies have the same expected return, but there is considerably more risk associated with HIRIS 11/27/2020 Fin 301 -Risk and Return | Dr. Menahem Rosenberg 5

Standard Deviation • Risk is measured with the Standard Deviation. 11/27/2020 Fin 301 -Risk and Return | Dr. Menahem Rosenberg 6

Observation • The expected returns of LORIS and HIRIS happen to be equal, but the volatility, or standard deviation, of HIRIS is higher than that of LORIS’s • However, we would expect share prices to follow a continuous distribution, rather than the discrete distribution illustrated 11/27/2020 Fin 301 -Risk and Return | Dr. Menahem Rosenberg 7

Portfolio • Let: – $P total portfolio $ value – $A , $B - Value of investment in stock A and B respectively. • Assume all the portfolio is allocated between A or B, so that P = A+ B Let : w. A, w. B, be the proportion invested in stock A and B respectively We get that 1 = w. A + w. B and w. B = 1 - w. A Let: r. P, r. A, r. B be the assets returns. Then r P = w A r A+ w B r. P = w. A r. A+ (1 - w. A ) r. B 11/27/2020 Fin 301 -Risk and Return | Dr. Menahem Rosenberg 8

Portfolio • Combine above LORIS and HIRIS stocks into a portfolio: 11/27/2020 Fin 301 -Risk and Return | Dr. Menahem Rosenberg 9

Portfolio with Assets • A portfolio with two assets, 1 and 2. • Using the past to project the future: • We can use historical return to evaluate the mean return and its standard deviation, though we should remains on watch, whether the past really projects the future. 11/27/2020 Fin 301 -Risk and Return | Dr. Menahem Rosenberg 10

Portfolio with two Assets • Use 30 month stock close prices adjusted for dividend and other distribution: 11/27/2020 Fin 301 -Risk and Return | Dr. Menahem Rosenberg 11

Portfolio with two Assets • The previous data allows us to compute GE and XON characteristic properties: • Using this data and previous formula we can compute portfolio return and standard deviation with different weights for GE and XON 11/27/2020 Fin 301 -Risk and Return | Dr. Menahem Rosenberg 12

Portfolio Line • We can plot the portfolio return against the portfolio’s variance: 11/27/2020 Fin 301 -Risk and Return | Dr. Menahem Rosenberg 13

Asset Risk • we observed that there were two kinds of risk – diversifiable or individual risk – Non-diversifiable or market risk • We also observed that in the limit as the number of securities becomes very large, the portfolio risk approaches the average covariance, which can be considered Nondiversifiable or systematic risk, . 11/27/2020 Fin 301 -Risk and Return | Dr. Menahem Rosenberg 14

• Stand-alone vs Market Risk • We saw that there was individual-stand alone risk and market risk Assume that each equity’s return is the composition of two random variables: – one associated with the market’s return – one associated with the companyspecific return Market risk is that part of a security’s standalone risk that cannot be eliminated by diversification, and is measured by beta. Firm-specific risk is that part of a security’s stand-alone risk that can be eliminated by proper diversification (2) Stand Alone Risk = Market risk +Firm-specific risk 11/27/2020 Fin 301 -Risk and Return | Dr. Menahem Rosenberg 15

CAPM • The stock compensated risk is measured as the risk it adds to a well diversified portfolio: – Case 1 : it does not add any additional risk, its return changes are the same as the markets return – Case 2: it adds risk to the portfolio, its return relative to the market volatility is higher. – Case 3: it reduces the portfolio risk, its return relative to the market volatility is lower. • CAPM will compare and determine risky assets return premium (risk premium) - their return above the risk free asset return. 11/27/2020 Fin 301 -Risk and Return | Dr. Menahem Rosenberg 16

CAPM • ri , si Security i required return and standard deviation • rm sm Market return and standard deviation • rf risk free return • Recall portfolio variance: • Or using the correlation coefficient: • The relative magnitude of the covariance term will determine the above cases 11/27/2020 Fin 301 -Risk and Return | Dr. Menahem Rosenberg 17

CAPM • The Covariance relative measure is beta: – Case 1 - the results in a b =1. 0, and the stock should have the same risk premium as the market risk premium. – Case 2 – b >1. 0 When added to the portfolio will increase the portfolio risk, therefore must add a bigger than the market risk premium. – Case 3 – b < 1. 0 When added to the portfolio will decrease the portfolio risk, therefore must add a smaller than the market risk premium. 11/27/2020 Fin 301 -Risk and Return | Dr. Menahem Rosenberg 18

Comment • Beta measures a stock’s market risk. It shows a stock’s volatility relative to the market • Beta shows how risky a stock is if the stock is held in a well-diversified portfolio. – CAPM explains the difference between the riskless interest rate and the expected rate of return on the market portfolio, but not their absolute levels – The absolute level of the equilibrium expected rate of return on the market portfolio is determined by such factors as – expected productivity – household inter-temporal preferences for consumption 11/27/2020 Fin 301 -Risk and Return | Dr. Menahem Rosenberg 19

CAPM • According the CAPM, in equilibrium, the risk premium on any asset is equal the product of – b (or ‘Beta’) – the risk premium on the market portfolio • The model states that: 11/27/2020 Fin 301 -Risk and Return | Dr. Menahem Rosenberg 20

Security Market Line – The plot of a security returns(or sometimes security risk premiums) against security beta is the Security Market Line, • Note that the slope of the security market line is the market premium • By CAPM theory, all securities must fall precisely on the SML (hence its name) 11/27/2020 Fin 301 -Risk and Return | Dr. Menahem Rosenberg 21

Security Market Line SML: ri = rf + (rm – rf ) bi ri SML rm rf . T-bills 0 11/27/2020 1 Fin 301 -Risk and Return | Dr. Menahem Rosenberg bi 22

Portfolio beta • Assume a portfolio p made of N assets with return ri that follow the CAPM relationship. The portfolio return is: • Define 11/27/2020 Fin 301 -Risk and Return | Dr. Menahem Rosenberg 23