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Risk, Return, and Security Market Line

Risk, Return, and Security Market Line. Financial Management. Outline. Risk of an investment Expected return of an investment Portfolios: Portfolio expected returns Portfolio risk Risk: Systematic and Unsystematic Risk Diversification and Portfolio Risk

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Risk, Return, and Security Market Line

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  1. Risk, Return, and Security Market Line Financial Management

  2. Outline • Risk of an investment • Expected return of an investment • Portfolios: • Portfolio expected returns • Portfolio risk • Risk: Systematic and Unsystematic Risk • Diversification and Portfolio Risk • The security market line and Capital Asset Pricing Model

  3. Defining Risk • Risk refers to the chance that some unfavorable event will happen • Investment risk is the probability that actual returns may deviate from expected returns • The chance that actual returns may be lower than expected return gives rise to investment risk • Higher the probability of actual returns being less than expected, higher will be investment risk

  4. Returns • Actual Return • Realized return/historical return/return ex-post • Expected Return • Return ex-ante/anticipated return • A weighted average of all possible returns, where weights represent probability of each possible outcome • Multiply each possible outcome with its probability and add them up over all possible outcomes

  5. Measuring Expected Return • E(r) = P1 r1 + P2r2 + … + Pnrn n =  Pi ri i=1 ri is the ith possible outcome and Pi is the probability of ith outcome • Examples

  6. Measuring Risk • Risk is measured by standard deviation of possible returns n Variance (2) =  (ri – E(r))2 Pi i=1 Standard Deviation () = (2)1/2 Examples

  7. Coefficient of Variation • Standard deviation is an absolute measure of risk • We cannot rank investments only on the basis of standard deviation or on the basis of expected return • To rank investments, we need a measure of risk that is based on risk and return • Coefficient of variation is a relative measure of risk based on risk and expected return • Examples

  8. Risk and return are always positively related • Higher return is associated with high risk

  9. Portfolio Risk and Return • Meaning of Portfolio • A combined holding of more than one stock, bonds, real estate, or any other asset • Why create a portfolio? • To diversify/reduce/mitigate risk of a single security • All securities in the portfolio may not move together • If one goes down, others will go up and compensate for the loss of the first one

  10. Portfolio Expected Return • A simple weighted average of the expected return of each security in the portfolio, where weights represent the proportion of investment in each portfolio • E(rp) = (w1× E(r1)) + (w2× E(r2)) + … +(wn× E(rn)) • n • E(rp) =  wi E(ri) • i=1 • Examples

  11. Portfolio Risk • Risk of a portfolio is measured by standard deviation of the portfolio (p) • Standard deviation of a portfolio is not a simple weighted average of the standard deviations of each individual security in the portfolio • Theoretically, it is possible to combine two risky securities and create a zero risk portfolio without compromising returns. • Example

  12. Portfolio Risk • Total risk as measured by standard deviation does not matter in a portfolio context • Total risk can be divided into two categories Total Risk = Unsystematic Risk + Systematic Risk • Examples • In a well diversified portfolio, only systematic risk matters; unsystematic risk disappears and is zero.

  13. Portfolios Risk and Beta • Systematic risk of a portfolio is measured by beta of a security • Meaning of beta • Tendency of a stock to move with the market • Sensitivity of an asset’s price to the changes in the market • Beta of a risk free security • Beta of a market portfolio • Beta of a market portfolioBeta of a market portfolio

  14. Computing Portfolio Beta • A simple weighted average of the beta of each individual asset in the portfolio, where weights represent the proportion of investment in each asset in the portfolio • p = (w1× 1) + (w2× 2) + … +(wn× n) n p=  wi i i=1 • Where wi represents proportion of total investment in security i and I represents beta of security i in the portfolio • Examples

  15. Security Market Line and CAPM • Positive relationship between systematic risk and return of a portfolio • The line which gives the expected returns-systematic risk combinations of assets is called the security market line

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