Risk, Return, and Security Market Line

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

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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

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Measuring Expected Return

• E(r) P1 r1 P2r2 Pnrn
• n
• ? Pi ri
• i1
• ri is the ith possible outcome and
• Pi is the probability of ith outcome
• Examples

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Measuring Risk

• Risk is measured by standard deviation of
  possible returns
• n
• Variance (?2) ? (ri E(r))2 Pi
• i1
• Standard Deviation (?) (?2)1/2
• Examples

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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

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

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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

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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)
• i1
• Examples

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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

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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.

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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 assets 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

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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
• i1
• Where wi represents proportion of total
  investment in security i and ?I represents beta
  of security i in the portfolio
• Examples

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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