risk and returns

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Concepts of Risk and Returns Presented by: Ananya Akshata Akanksha Devendra Priyanka :

1 Concepts of Risk and Returns Presented by: Ananya Akshata Akanksha Devendra Priyanka

Introduction to Risk and Return:

Introduction to Risk and Return Risk and return are the two most important attributes of an investment. Research has shown that the two are linked in the capital markets and that generally, higher returns can only be achieved by taking on greater risk. Risk isn’t just the potential loss of return, it is the potential loss of the entire investment itself (loss of both principal and interest). Consequently, taking on additional risk in search of higher returns is a decision that should not be taking lightly. 2 Risk Premium Real Return Expected Inflation Rate

The Concept of Risk Aversion Revisited:

3 The Concept of Risk Aversion Revisited Diversification is logical If you drop the basket, all eggs break Diversification is mathematically sound Most people are risk averse People take risks only if they believe they will be rewarded for taking them

The Concept of Risk Aversion Revisited (cont’d):

4 The Concept of Risk Aversion Revisited (cont’d) Diversification is more important now Journal of Finance article shows that volatility of individual firms has increased Investors need more stocks to adequately diversify

Variance of A Linear Combination:

5 Variance of A Linear Combination One measure of risk is the variance of return The variance of an n-security portfolio is:

Variance of A Linear Combination (cont’d):

6 Variance of A Linear Combination (cont’d) The variance of a two-security portfolio is:

Variance of A Linear Combination (cont’d):

7 Variance of A Linear Combination (cont’d) Return variance is a security’s total risk Most investors want portfolio variance to be as low as possible without having to give up any return Total Risk Risk from A Risk from B Interactive Risk

Variance of A Linear Combination (cont’d):

8 Variance of A Linear Combination (cont’d) If two securities have low correlation, the interactive risk will be small If two securities are uncorrelated, the interactive risk drops out If two securities are negatively correlated, interactive risk would be negative and would reduce total risk

Portfolio Programming in A Nutshell:

9 Portfolio Programming in A Nutshell Various portfolio combinations may result in a given return The investor wants to choose the portfolio combination that provides the least amount of variance

Portfolio Programming in A Nutshell (cont’d):

10 Portfolio Programming in A Nutshell (cont’d) Example Assume the following statistics for Stocks A, B, and C: Stock A Stock B Stock C Expected return .20 .14 .10 Standard deviation .232 .136 .195

Portfolio Programming in A Nutshell (cont’d):

11 Portfolio Programming in A Nutshell (cont’d) Example (cont’d) The correlation coefficients between the three stocks are: Stock A Stock B Stock C Stock A 1.000 Stock B 0.286 1.000 Stock C 0.132 -0.605 1.000

Portfolio Programming in A Nutshell (cont’d):

12 Portfolio Programming in A Nutshell (cont’d) Example (cont’d) An investor seeks a portfolio return of 12%. Which combinations of the three stocks accomplish this objective? Which of those combinations achieves the least amount of risk?

Portfolio Programming in A Nutshell (cont’d):

13 Portfolio Programming in A Nutshell (cont’d) Example (cont’d) Solution: Two combinations achieve a 12% return: 50% in B, 50% in C: (.5)(14%) + (.5)(10%) = 12% 20% in A, 80% in C: (.2)(20%) + (.8)(10%) = 12%

Portfolio Programming in A Nutshell (cont’d):

14 Portfolio Programming in A Nutshell (cont’d) Example (cont’d) Solution (cont’d): Calculate the variance of the B/C combination:

Portfolio Programming in A Nutshell (cont’d):

15 Portfolio Programming in A Nutshell (cont’d) Example (cont’d) Solution (cont’d): Calculate the variance of the A/C combination:

Portfolio Programming in A Nutshell (cont’d):

16 Portfolio Programming in A Nutshell (cont’d) Example (cont’d) Solution (cont’d): Investing 50% in Stock B and 50% in Stock C achieves an expected return of 12% with the lower portfolio variance. Thus, the investor will likely prefer this combination to the alternative of investing 20% in Stock A and 80% in Stock C.

Introduction:

17 Introduction Harry Markowitz’s “Portfolio Selection” Journal of Finance article (1952) set the stage for modern portfolio theory The first major publication indicating the important of security return correlation in the construction of stock portfolios Markowitz showed that for a given level of expected return and for a given security universe, knowledge of the covariance and correlation matrices are required

Capital Market Line and the Market Portfolio:

18 Capital Market Line and the Market Portfolio The tangent line passing from the risk-free rate through point B is the capital market line (CML) When the security universe includes all possible investments, point B is the market portfolio It contains every risky assets in the proportion of its market value to the aggregate market value of all assets It is the only risky assets risk-averse investors will hold

Capital Market Line and the Market Portfolio (cont’d):

19 Capital Market Line and the Market Portfolio (cont’d) Implication for investors: Regardless of the level of risk-aversion, all investors should hold only two securities: The market portfolio The risk-free rate Conservative investors will choose a point near the lower left of the CML Growth-oriented investors will stay near the market portfolio

Capital Market Line and the Market Portfolio (cont’d):

20 Capital Market Line and the Market Portfolio (cont’d) Any risky portfolio that is partially invested in the risk-free asset is a lending portfolio Investors can achieve portfolio returns greater than the market portfolio by constructing a borrowing portfolio

Capital Market Line and the Market Portfolio (cont’d):

21 Capital Market Line and the Market Portfolio (cont’d) Standard Deviation Expected Return R f A B C

Security Market Line:

22 Security Market Line The graphical relationship between expected return and beta is the security market line (SML) The slope of the SML is the market price of risk The slope of the SML changes periodically as the risk-free rate and the market’s expected return change

Security Market Line (cont’d):

23 Security Market Line (cont’d) Beta Expected Return R f Market Portfolio 1.0 E(R)

Expansion of the SML to Four Quadrants:

24 Expansion of the SML to Four Quadrants There are securities with negative betas and negative expected returns A reason for purchasing these securities is their risk-reduction potential E.g., buy car insurance without expecting an accident E.g., buy fire insurance without expecting a fire

Security Market Line (cont’d):

25 Security Market Line (cont’d) Beta Expected Return Securities with Negative Expected Returns

PowerPoint Presentation:

26 Affect of Perfectly Negatively Correlated Returns Elimination of Portfolio Risk Time 0 1 2 If returns of A and B are perfectly negatively correlated, a two-asset portfolio made up of equal parts of Stock A and B would be riskless. There would be no variability of the portfolios returns over time. Returns % 10% Returns on Portfolio 5% 15% 20% Returns on Stock B Returns on Stock A

PowerPoint Presentation:

27 Example of Perfectly Positively Correlated Returns No Diversification of Portfolio Risk Time 0 1 2 If returns of A and B are perfectly positively correlated, a two-asset portfolio made up of equal parts of Stock A and B would be risky. There would be no diversification (reduction of portfolio risk). Returns % 10% 5% 15% 20% Returns on Stock A Returns on Stock B Returns on Portfolio

Definitions:

28 Definitions Systematic risk is the risk that remains after no further diversification benefits can be achieved Unsystematic risk is the part of total risk that is unrelated to overall market movements and can be diversified Research indicates up to 75 percent of total risk is diversifiable

Definitions (cont’d):

29 Definitions (cont’d) Investors are rewarded only for systematic risk Rational investors should always diversify Explains why beta (a measure of systematic risk) is important Securities are priced on the basis of their beta coefficients

Diversification and Beta:

30 Diversification and Beta Beta measures systematic risk Diversification does not mean to reduce beta Investors differ in the extent to which they will take risk, so they choose securities with different betas E.g., an aggressive investor could choose a portfolio with a beta of 2.0 E.g., a conservative investor could choose a portfolio with a beta of 0.5

Introduction:

31 Introduction The capital asset pricing model (CAPM) is a model that provides a framework to determine the required rate of return on an asset and indicates the relationship between return and risk of the asset. It was introduced by William Sharpe in 1964.

CAPM:

32 CAPM The more risk you carry, the greater the expected return:

CAPM EXAMPLE:

CAPM EXAMPLE Find the required return on a stock given that the risk-free rate is 8%, the expected return on the market portfolio is 12%, and the beta of the stock is 2. K i = K rf + b i (K m - K rf ) K i = 8% + 2(12% - 8%) K i = 16% 33

CAPM (cont’d):

34 CAPM (cont’d) CAPM assumptions: Variance of return and mean return are all investors care about Investors are price takers They cannot influence the market individually All investors have equal and costless access to information There are no taxes or commission costs

CAPM (cont’d):

35 CAPM (cont’d) CAPM assumptions (cont’d): Investors look only one period ahead Everyone is equally adept at analyzing securities and interpreting the news

SML and CAPM:

36 SML and CAPM If you show the security market line with excess returns on the vertical axis, the equation of the SML is the CAPM The intercept is zero The slope of the line is beta

Note on the CAPM Assumptions:

37 Note on the CAPM Assumptions Several assumptions are unrealistic: People pay taxes and commissions Many people look ahead more than one period Not all investors forecast the same distribution Theory is useful to the extent that it helps us learn more about the way the world acts Empirical testing shows that the CAPM works reasonably well

LIMITATIONS OF CAPM:

LIMITATIONS OF CAPM Unrealistic assumptions Testing CAPM Stability of Beta 38

39 Equity Risk Premium Equity risk premium refers to the difference in the average return between stocks and some measure of the risk-free rate The equity risk premium in the CAPM is the excess expected return on the market Some researchers are proposing that the size of the equity risk premium is shrinking

Arbitrage Pricing Theory:

40 Arbitrage Pricing Theory APT background The APT model Comparison of the CAPM and the APT

APT Background:

41 APT Background Arbitrage pricing theory (APT) states that a number of distinct factors determine the market return Roll and Ross state that a security’s long-run return is a function of changes in: Inflation Industrial production Risk premiums The slope of the term structure of interest rates

APT Background (cont’d):

42 APT Background (cont’d) Not all analysts are concerned with the same set of economic information A single market measure such as beta does not capture all the information relevant to the price of a stock

The APT Model:

43 The APT Model General representation of the APT model:

Comparison of the CAPM and the APT:

44 Comparison of the CAPM and the APT The CAPM’s market portfolio is difficult to construct: Theoretically all assets should be included (real estate, gold, etc.) Practically, a proxy like the S&P 500 index is used APT requires specification of the relevant macroeconomic factors

Comparison of the CAPM and the APT (cont’d):

45 Comparison of the CAPM and the APT (cont’d) The CAPM and APT complement each other rather than compete Both models predict that positive returns will result from factor sensitivities that move with the market and vice versa

PowerPoint Presentation:

46 