University of the Aegean School of Business Studies

University of the Aegean School of Business Studies Shipping, Trade & Transport Dpt. MA Shipping, Trade & Transport e-course Advanced Corporate Finance THEODORE SYRIOPOULOS Professor of Finance Department of Shipping, Trade & Transport School of Business Studies UNIVERSITY OF THE AEGEAN 2 A, Korai street, 82100 Chios, Greece, Tel. : 22710 35 861, 6944 911 787 e-mail: tsiriop@aegean. gr http: //www. stt. aegean. gr/Syriopoulos. En. asp ADVFIN

Risk & Return

Learning Objectives n Understand the Concept of Risk in Finance n Explain important types & measures of Risk n Define the concept & measurement of Return n Risk & Return in a Portfolio context n Capital Asset Pricing Model (CAPM) 6

Risk & Uncertainty n n Decisions are taken in an environment of risk & uncertainty All of life is the management of risk, not its elimination ! 7

Risk aversion n Rational (average) investor: ‘risk-averse’ ! n Of two investment alternatives, targeting equal returns…. …. . investors would prefer to choose the one bearing lower level of risk ! 8

Measuring Risk & Return 9

Major categories of Risk Major Categories of RISK STRATEGIC RISK Market Risk Credit Risk BUSINESS RISK Liquidity Risk FINANCIAL RISK Operational Risk Legal Risk 10

Defining & Measuring Risk n Risk probability (chance) that an unexpected outcome will occur n a probability distribution is a listing of all possible outcomes with a probability assigned to each must sum to 1. 0 (100%) 11

Probability Distributions Martin Products & U. S. Electric State of the Probability of this state Economy occurring Boom Normal Recession 0. 2 0. 5 0. 3 1. 0 Rate of Return on Stock if this state occurs Martin Products U. S. Electric 110% 22% -60% 20% 16% 10% 12

Expected Rate of Return n Rate of return expected to be realized from an investment during its life n Mean value of the probability distribution of possible returns n Weighted average of the outcomes, where the weights are the probabilities 13

Expected Rate of Return Probability of This State of the Economy Occurring (Pr i) (1) Boom Normal Recession (2) 0. 2 0. 5 0. 3 1. 0 Martin Products Return if This State Product: Occurs (ki) (2) x (3) 110% 22% -60% ^ = km = (4) 22% 11% -18% 15% U. S. Electric Return if This Product: State Occurs (ki) (2) x (5) 20% 16% 10% ^ = km = (6) 4% 8% 3% 15% 14

Expected Rate of Return 15

Expected Rate of Return You estimate that there is 30% chance that your total return on Nokia share investment will be -3. 45%, a 30% chance that it will be 5. 17%, a 30% that it will be 12. 07% and a 10% chance that it will be 24. 14%. Calculate the expected return. 16

Measuring Risk: Variance - Standard Deviation Calculating Martin Products’ Standard Deviation Expected Payoff Return ^ ki k^ (1) (2) 110% 15% 22% 15% -60% 15% ^ ki - ^k ^^2 (ki - k) (1) - (2) = (3) (4) 95 9, 025 7 49 -75 5, 625 Probability (5) 0. 2 0. 5 0. 3 ^ ^2 (ki - k)Pr i (4) x (5) = (6) 1, 805. 0 24. 5 1, 687. 5 17

Measuring Risk: Variance - Standard Deviation § Variance V ( 2) calculation: (a) square difference between each possible occurrence & the mean (b) multiply each difference by its associated probability (c) sum them up § Square root of variance standard deviation ( ) 18

Measuring Risk: Variance - Standard Deviation - example Calculate variance & standard deviation of the Nokia share investment: 19

Measuring Risk: Variance - Standard Deviation - example n n For BFI, variance & standard deviation are: In finance, St. Dev. of a return also referred as its volatility St. D = easier to interpret because it is in same units as returns themselves 20

Measuring Risk: Standard Deviation 21

Variance - Standard Deviation as Measures of Risk Interpreting Variance - Standard Deviation • Standard Deviation tells us the probability that outcome will fall a particular distance from the mean or within a particular range: 22

Variance - Standard Deviation as Measures of Risk Historical Market Performance § On average, annual returns have been higher for riskier securities § Treasury bills have smallest standard deviation and smallest average annual return 23

Variance - Standard Deviation as Measures of Risk Returns of Major Asset Classes 1900– 2009 24

Portfolio Risk & Return 25

Risk and Diversification The concept of diversification Ø By investing in 2 or more assets whose values do not always move in same direction at same time, investors can reduce risk of investments or portfolio 26

Portfolio Returns n Expected Return on a portfolio, = = weighted average expected returns on assets held in portfolio Portfolio: a collection of investment securities (2 assets +) 27

Portfolio Returns n Realized rate of return, k. . n the return actually earned n n actual return usually different from expected return Portfolio Weights n fraction (%) of total investment in a portfolio allocated to each individual investment (asset) in the portfolio • portfolio weights must add up to 1. 00 or 100% wi = 28

Expected Return of Portfolio – example 1 You invested € 100 000 in treasury bills that yield 4. 5%; € 150 000 in Unilever shares, which have an expected return of 7. 5%; and, € 150 000 in Royal Dutch Shell shares, which have an expected return of 9. 0%. What is the expected return of this € 400 000 portfolio? 29

Expected Return of Portfolio – example 2 n Problem n Suppose you buy 500 shares of Ford at $11 per share & 100 shares of Citigroup stock at $28 per share n If Ford’s share price goes up to $13 & Citigroup’s rises to $40, - what is the new value of the portfolio ? - what return did it earn? - after the price change, what are the new portfolio weights? 30

Expected Return of Portfolio – example 2 n Solution n Initial portfolio value: 500 * $11 + 100 * $28 = $8, 300 n New portfolio value: 500 * $13 + 100 * $40 = $10, 500 gain = $2, 200 or 26. 5% return on $8, 300 investment n Ford’s return was = $13/$11 - 1 = 18. 18% n Citigroup’s was = $40/$28 - 1 = 42. 86% 31

Expected Return of Portfolio – example 3 n Solution n Given initial portfolio weights: Ford = $5, 500 / $8, 300 = 66. 3% Citigroup = $2, 800 / $8, 300 = 33. 7% Portfolio return (Rp)= § After price change, new portfolio weights are: Ford = $6, 500 / $10, 500 = 61. 9% Citigroup = $4, 000 / $10, 500 = 38. 1% 32

Risk Diversification 33

Portfolio Risk n To find Portfolio Risk… must know the degree to which portfolio assets’ returns move together § when asset prices move in opposite directions, change in price of one asset offsets at least some of price change of other asset § portfolio risk for 2 assets is… less than sum of risks associated with each individual asset ! 34

Portfolio Risk Portfolio Variance § Portfolio risk: calculated by Portfolio Variance; for that…. Covariance is also an input to be calculated Portfolio Variance (2 assets) Var(Rp) Portfolio covariance 35

Portfolio Risk Portfolio Variance - example • Variance of annual returns of Carrefour & Deutsche Bank shares = 0. 046820 & 0. 170791 • Covariance between annual returns of Ca & DB shares = 0. 068893 • Portfolio allocation = 50% Carrefour / 50% Deutsche Bank • Calculate Portfolio Variance ? Var 36

Portfolio Risk Covariance § Covariance Cov(R 1, R 2) = of returns of 1 & 2 assets (R 1 & R 2) measures how returns on two assets co-vary (move together) Covariance calculation : similar to variance calculation; but instead of squaring difference between the value from each outcome & expected value for an individual asset, calculate the product of this difference for the 2 different assets 37

Portfolio Risk Correlation Coefficient § for easier interpretation & use of Covariance, divide it by product of Standard Deviations of the 2 assets’ returns. . . correlation coefficient ( ) - between assets’ returns 38

Portfolio Risk Correlation Coefficient § Correlation coefficient (ρ) of 2 assets… always between: – 1 & +1 39

Returns distribution for 2 perfectly Negatively stocks & portfolio WM Correlated correlation coefficient: ρ = -1. 0 Stock W Stock M Portfolio WM 25 25 25 15 15 15 0 0 0 -10 -10 40

Returns Distributions for 2 Perfectly Positively stocks & Portfolio NG Correlated correlation coefficient: ρ = 1. 0 Stock N Portfolio NG Stock G 25 25 25 15 15 15 0 0 0 -10 -10 41

Portfolio Risk Annual Volatility & Correlation – selected firms 42

Diversification reduces RISK n combining assets that are not perfectly correlated will reduce portfolio risk through diversification n portfolio risk can be broken-down into 2 components: 1. unsystematic or diversifiable or unique risk that can be diversified away (company-specific) 2. systematic or non-diversifiable risk that cannot be diversified away (market-specific) 43

Limits of Diversification • most risk-reduction benefits from diversification can be achieved in a portfolio of 15 -20 assets • with complete diversification, all diversifiable risk is eliminated from portfolio BUT investor still faces systematic risk 44

Systematic vs. Unsystematic Risk 45

Measuring Systematic Risk § standard deviation not appropriate as portfolio risk measure St. D measures total risk § a firm’s systematic risk measured relative to market portfolio = portfolio containing all assets in market of interest 46

Measuring Systematic Risk § a stock’s systematic risk is estimated by… measuring its returns’ sensitivity to changes relative to a stock market index (e. g. S&P 500 index) § this sensitivity factor is… stock’s beta coefficient 47

Measuring Systematic Risk with the BETA coefficient βs > 1 aggressive stock behaviour vs. market portfolio βs < 1 defensive stock behaviour vs. market portfolio βs = 1 neutral stock behaviour vs. market portfolio βmp = 1 48

Beta coefficients of S&P 500, US stock sample (2007 -2012)

Beta coefficients of S&P 500, US stock sample (2007 -2012) Sources for β’s available free on Web: Yahoo! Finance; Value Line; Google Finance

Portfolio β-coefficient § β-portfolio (of any set of securities) = weighted average of individual securities’ betas 51

Compensation for Bearing Systematic Risk Portfolio Beta Example You invested 25% of your wealth in a fully diversified market fund, 25% in risk-free treasury bills & 50% in a house with twice as much systematic risk as the market. What is the β of your overall portfolio? 52

Basics on CAPM Model Pricing Asset Capital 53

Capital Asset Pricing Model (CAPM) § CAPM allows to identify the efficient portfolios of risky assets (best risk - return combination) § CAPM assumes that… rate of return for any asset’s (stock’s / portfolio’s) = risk-free rate of return + risk premium 54

Market Risk Premium § RPM = market risk premium: additional return over risk-free rate to compensate investors for market risk § assume: • Treasury bonds yield (RRF) • average stock/portfolio required return (market portfolio, E(RM)) • § market risk premium (RPM) = = 6% = 14% 8% RPM = (E(RM ) - RRF) = 14% - 6% = 8% Treasury Bills - safest investment available; TB yield used as proxy for risk-free rate 55

Capital Asset Pricing Model describes the relationship between asset risk & expected return: E(Ri) = Rrf + βi * (E(Rm) – Rrf) (RPM = market risk premium) βi • • • E(Ri) = expected (required) return rate on asset i (stock / portfolio / company) Rrf = risk-free rate (E(RM) – Rrf)) = market risk premium (RPM) E(RM) = market portfolio return βi = beta coefficient of asset i By default: βMarket Portfolio = 1 56

Capital Asset Pricing Model: example 1 A share has a beta ( ) of 1. 5. Expected return on market portfolio = 10% & risk-free rate = 4%. What is the expected return of this share? E(Ri) = Rrf + βi x (E(Rm) – Rrf) = 0. 04 + [1. 5×(0. 10 – 0. 04)] = 13% 57

Expected Portfolio Return: example 2 What rate of return would you expect to earn from a portfolio, if risk-free rate = 4%, β portfolio =1. 25 & Market Risk Premium = 6% ? E(R n Asset Portfolio) = Rrf + βn Asset Portfolio(E[Rm] – Rrf) = 0. 04 + (1. 25 × 0. 06) = 0. 115, or 11. 5 % 58

Security (Capital) Market Line (SML) n Security Market Line (SML): n line that graphs relationship between risk as measured by beta & required rate of return 59

Security Market Line (SML) s anie p m o 12. 5 nies a p com / s t e ass 1 e v si βs < efen ag /c sets s a 1 ive s s βs > e gr d CAPM depicts asset's expected return vs. risk (beta) as a linear relationship represented by the Security Market Line 60

Historical Tradeoff between Risk-Return in Large Portfolios Source: CRSP, Morgan Stanley Capital International

End of Session 62