Risk and Return

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Risk and Return
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Objectives

• Define Expected Return
• Define Risk
• Systematic versus Unsystematic
• Examine the relationship between Asset Risk and
  Return
• Understand the effect of diversification on the
  Risk and Return of a portfolio
• Determine an investors required rate of return
  on a security as a function of its risk

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Expected Returns

• The expected benefits or returns that an
  investment generates come in the form of cash
  flows.
• Cash flows, not accounting profits, are the
  relevant variable used to measure returns.
• Conventionally, we measure the expected cash flow
  as followswhere Xi is the cash flow in the
  ith state of the economy and Pi is the
  probability of the ith state of the economy

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Expected Returns

• Similarly, the Expected Rate of Return is given
  by
• where Ri is the rate of return in the ith state
  of the economy and pi is the probability of ith
  state of the economy.

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Risk

• Risk can be defined as the possible variation in
  cash flow about an expected cash flow.
• Statistically, risk may be measured by the
  standard deviation of the random cash flow.
• The standard deviation of an asset a is denoted
  by ?a and is calculated as followswhere n is
  the number of states of the economy, Rai is the
  return in the ith state and pi is the probability
  of the ith state of the economy

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Risk
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Summary Statistics Example
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Risk

• The attractiveness of a security cannot be
  determined by standard deviation alone.
• The risk and return of a security has to be
  compared with the alternatives available for
  investment.
• If two securities have the same risk, the one
  with the higher return is preferable.
• Alternatively, if two securities have the same
  return, then the one with lower risk is
  preferable.

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Risk Diversification

• Total Risk or variability of returns can be
  divided into
• The variability of returns unique to the security
• Commonly referred to as Firm Specific Risk or
  Unique Risk or Diversifiable Risk or Unsystematic
  Risk
• The risk related to market movements
• Also referred to as Market Risk or
  Non-diversifiable Risk or Systematic Risk
• By diversifying, the investor can eliminate the
  unique security risk. The systematic risk,
  however, cannot be diversified.

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Effects of Diversification
Standard Deviation
Total Risk Unique Risk
Systematic Risk
Unique Risk
Systematic Risk
Number of Stocks in Portfolio
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Benefits of Diversification
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How do investors diversify?

• The Portfolio Problem
• Markowitz (Portfolio Selection)
• Tobin (Portfolio Separation)
• Sharpe (CAPM)

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What risk is priced?

• Risk averse investors demand higher returns, or
  equivalently, a risk premium for undertaking
  risk.
• Investors cannot expect the market to compensate
  them for risk that they can eliminate through
  diversification.
• Because stocks can be combined in portfolios to
  eliminate specific risk, only diversifiable or
  systematic risk matters, i.e. commands a risk
  premium.
• Only systematic risk contributes to the riskiness
  of a portfolio and cannot be eliminated through
  diversification.

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Measuring Systematic Risk

• Systematic Risk affects all securities.
• To measure systematic risk, we measure the
  tendency of a stock to move relative to the
  market.
• The plot of firm excess returns versus market
  excess returns is called the characteristic line,
  i.e., ERa - Rf ? (ERm - Rf)
• The measure of a stocks systematic risk or
  market risk is commonly called beta
• Beta is also the slope of the characteristic line.

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Characteristic Line
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Measuring Beta

• The beta of stock A is calculated as follows
  where Ra is the
  return on stock A and Rm is the return on the
  market portfolio and where
• The beta of a portfolio is the weighted average
  of the individual securities betas
• The beta of the market is 1.

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Required Rate of Return

• The required rate of return equals the risk free
  rate plus a return to compensate for the
  additional risk.
• The required rate of return can be expressed as
  R Rf RP,where R is the investors
  required rate of return, Rf is the risk-free
  rate, and RP is the risk premium

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The Required Rate of Return

• Capital Asset Pricing Model (CAPM)
• According to the CAPM ERa Rf ?a ERm -
  Rfwhere ERa is the expected rate of return on
  stock a and ERm is the expected rate of return
  on the market portfolio.

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The Security Market Line
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Criticisms of CAPM

• Can Beta capture all dimensions of risk? Is beta
  the appropriate measure of risk?
• Some empirical research has shown that the CAPM
  does not hold. Various anomalies such as the
  size effect and the friday the 13th effect have
  been known and investigated for some time.
• How do we determine the market portfolio?