Ch 6.Risk, Return and the CAPM

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Ch 6.Risk, Return and the CAPM
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Goals

• To understand return and risk
• To understand portfolio
• To understand diversifiable risks and market
  (systematic) risks
• To understand CAPM

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1.Investment returns

• Dollar return amount received amount invested
• Problems
• Scale effect
• Times spent or holding period
• Rate of return (amount received amount
  invested)/amount invested

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2. Stand alone risk

• Risk the chance that some unfavorable event will
  occur. It is measured by variance or standard
  deviation distance from the average.
• (Stand-alone risk the risk an investor would
  face if he or she only held one asset)
• Ex) Historical return and risk

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Historical return and risk
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• No investment will be undertaken unless the
  expected rate of return is high enough to
  compensate the investor for the perceived risk
• To deal with unknown futures, a probability will
  be applied.

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1) Probability distributions

• Probability is the chance that the event will
  occur.
• Probability distribution A listing of all
  possible outcomes or events with a probability
  assigned to each outcome.
• Discrete Continuous probability distribution
• 68.26 of probability that actual return will be
  within a mean or 1 standard deviation.
• 95.46 of probability that actual return will be
  within a mean or 2 standard deviation
• 99.74 of probability that actual return will be
  within a mean or 3 standard deviation

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• Ex)
• State Probability (P) S B
• Strong 0.25 0.3 0.2
• Normal 0.5 0.15 0.30
• Weak 0.25 0.00 -0.10
  
• 2) Expected Rates of Returns and Risks
  Stand-alone
• Expected return

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• E(ks) 0.30.250.150.50.000.250.15
• E(kB) 0.175
• (2) Variance risk measurement
• The tighter the probability distribution, the
  more likely it is that the actual return will be
  close to the expected value. Thus the tighter the
  probability distribution, the lower the risk
  assigned. It is measured by variance

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• How to calculate?
• Standard Deviation

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• (3) The coefficient of variation standardized
  measure of the risk per unit of return. It
  provides a more meaningful basis for comparison
• CV
• CVs0.10661/0.15 0.707

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• (4) Risk Aversion and Required Returns
• Risk Aversion Investors dislike risk and require
  the higher rate return as an inducement to buy
  riskier securities. It is commonly assumed in
  finance.
• Therefore, if other things held constant, the
  higher a securitys risk, the lower its price and
  the higher its required (expected) returns.

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• 3) Portfolios Return and Risks
• Portfolios combination of assets or securities
  to minimize total risks and to improve returns
• (1) Portfolio Returns
• Simply the weighted average of the expected
  returns on individual assets in the portfolio

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• Equation

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• Ex) using the previous example with an assumption
  that weights for S and B are 40 and 60.
• Expected returns 0.4(0.15)0.6(0.175)0.165

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• Realized Rate of Return (k bar)
• The return actually earned during some past
  period. It differs from the expected returns
• (2) Risks
• Covariance measurement of the degree which two
  assets covary
• Correlation coefficient Standardization of
  covariance

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• Formulas

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• Portfolio variance (Risks)

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• In our example,
• Ws0.4 WB0.6
• rSB0.6469 ss0.1061 sB0.1639
• Portfolio risk is 0.016875

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• Lessons from Portfolio variance calculation
• (1) If the numbers of securities composing a
  portfolio increase, the number of covariance will
  be greater than number of variances. Thus, the
  variance of well diversified portfolio reflects
  the covariance.
• (2) If the correlation is less than 1, the
  covariance will reduce, leading to lower
  portfolio risks. Diversification effects
• (3) If the correlation is 1, the covariance will
  increase to the maximum value

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• (4) If the correlation is -1, then the variance
  will reduce to the minimum value. Diversification
  effects
• (5) In reality, securities correlations are
  between 0 and 1.
• 4) Diversifiable Risk and Market Risk
• Systematic risk
  Unsystematic risk
• Total Risk Market risk Firm specific risk
• Undiversifiable
  risk Diversifiable risk
• Nondiversifiable risk

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• Diversifiable risk That part of a securitys
  risk associated with random events, diversified
  away
• Market risk The part of a securitys risk that
  can not be eliminated by diversification
• If the diversifiable risks can be diversified
  away, investors are mainly concerned about the
  systematic (un-diversifiable) risks. They may
  consider the systematic risk in individual stocks
  or contribution to risks of well diversified
  portfolio to be risks compensated.

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• The systematic risk is a market risk inherent in
  market
• 4) The concept of beta
• How to measure the systematic risk?
• It can be measured by the degree to which a given
  stock tends to move up or down with the market
  (stock market). It is called beta

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• Three meanings of beta
• to changes in the return of the market portfolio.
• the comovement of an asset i's return (price)
  to the market portfolio's return (price)
• beta is a measure of the undiversifiable (market,
  systematic) risk of the asset i.

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• Graphically, it is a slop of a line in the
  scatter plot composed of market returns and
  individual stock returns
• Beta of a portfolio
• 5) CAPM (Capital Asset Pricing Model)
• Based on the beta estimate, we are able to come
  up with CAPM that will estimate a required rate
  of return in individual stock.

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• CAPM
• risk free rate market risk premiumbeta
• kRF risk free rate
• kM market return
• Here market risk premium (RPM) is the extra rate
  of return that investors require to invest in the
  stock market rather than purchase risk-free
  securities. It is determined by the degree of
  risk aversion that investors have on average.
• Risk premium (RPi) for stock i market risk
  premiumbeta

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• Ex) Currently, T-bill and SP 500 are offering 3
  and 5. F503 stocks beta is 0.7. Required rate
  of return 0.030.7(0.05-0.03)

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• SML (security market line)
• Equilibrium relationship between the expected
  returns and the systematic risk of assets
  (individual stocks or portfolios).
• Graphical description of CAPM.
• Underpriced when an asset lies above the SML.
  Then demand will increase and price will
  increase, leading the current return to a
  required return on SML (CAPM).

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• Overpriced when an asset lies below the SML.
  Then demand will decrease and price will
  decrease, leading the current return to a
  required return on SML (CAPM).
• Therefore, in equilibrium, all assets lies on the
  SML.
• 6) Impacts of Inflation.
• It will not change market risk premium but
  increase risk free rate, shifting SML upward

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• Thus, it will increase a required rate of return
  from CAPM
• 7) Impact of risk aversion.
• The slope of SML reflects the extent to which
  investors are averse to risk. The steeper the
  slope of the line, the greater the average
  investors risk aversion.
• The increasing risk aversion will increase market
  premium but not change risk free rates

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• SML rotates counterclockwise.
• Equilibrium required rate of return according to
  the CAPM increases for assets with positive ?.
• Equilibrium required rate of return according to
  the CAPM decreases for assets with negative ?.
• 8) Impact of changing betas.
• Without changing risk free rate and slop of SML,
  it will increase a required rate of return

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• 9) Form of the Efficient Markets Hypothesis
• - weak form all past information is fully
  reflected in current market price. E.g)
  technical analysis
• - semi-strong form current stock price reflects
  all publicly available information. E.g)
• - strong form

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• 10) Empirical tests joint test of the EMH and an
  asset pricing model. Whether a certain strategy
  can beat the market.
• Most studies showed that the stock market is
  highly efficient in the weak form, with two
  exceptions long term reversals and short term
  momentum. Strategies based on reversal and
  momentum tend to generate an excess return over a
  return from CAPM. But it is small when
  transaction cost is considered.
• The stock market is reasonable efficient in the
  semi-strong form. It is difficult to use public
  information to generate consistent greater
  returns than those predicted by CAPM. But two
  exceptions small size and high book to market
  ratio. Stocks with these traits tend to generate
  a greater return than that predicted by CAPM.

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•  

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• 11) Behavior Finance
• We experienced bubbles in the market. But there
  was no clear explanation why. Factor models
  could not explain these bubbles. Behavior finance
  based on human psychology, however, offers
  possible explanations overconfidence, anchoring
  bias, and herding.
• (1) Overconfidence in part stems from two other
  biases self attribution and hindsight bias.
• - self attribution peoples tendency to ascribe
  any success to their own talents while blaming
  failure on bad luck.
• - hindsight tendency of people to believe they
  can predict the future than they actually can.
• (2) Anchoring bias tendency of people to rely
  too much on recent events when predicting the
  future.

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• (3) Herding behavior tendency of investors
  emulate other successful investors and chase
  asset classes (eg. Smart money) which are doing
  well.
• Additional one Loss aversion.
• It means that human tends to show a different
  attitude, depending on receiving or paying money.
  When receiving money, people want to have
  certainty. But when they need to pay, they want
  to take a chance.
• E.g) 500 sure or 1000 on the face of a coin and
  nothing on the tail of the coin. If you receive
  money, you may want 500. But if you have to pay,
  you may want to go for the coin.