Risk, Return,

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Risk, Return, the Security Market line

• Chapter Thirteen
• Ross, Westerfield, Jordan, Roberts

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Risk Return unequal probabilities

• Expected return
• Standard deviation
• Covariance

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An example
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Statistics - Risky, Ltd.
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Statistics - Sleepy Time Ltd.
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Relevant measure of risk Covariance
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Covariance matrix

• RR 0.228, SDR 0.2418
• RST 0.102, SDST 0.0987
• RM 0.128, SDM 0.156

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Correlation

• Correlation normalizes covariance
• value of 1 means perfect positive correlation
• value of 0 means independence between data series
• value of -1 means perfect negative correlation

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Diversification

• Correlation is a measure of how two assets react
  together to economic market conditions
• High positive correlation
• Two assets are affected similarly by economic
  events
• High negative correlation
• Two assets are affected in completely opposite
  ways by economic events
• Independence -zero correlation
• Two assets are act independent of each other
  relative to economic events

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Correlation matrix
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Portfolio Statistics
Expected return to the portfolio of multiple
assets
Standard deviation to a portfolio of multiple
assets
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Portfolio expected return, two assets different
proportions
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Portfolio standard deviation
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Portfolio Risk
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Two-asset Portfolio
Preferred Portfolio
Ep
Efficient Set
Opportunity Set
Risk preferences
SDP
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Implications of Correlation Statistics

• The lower the pair-wise correlation of two
  assets, the greater the diversification benefit
  of adding those assets to your portfolio
• Adding assets which have low pair-wise
  correlation with each other to your portfolio
  reduces overall portfolio risk

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Affects of Correlation
Ep
High Correlation
Low Correlation
SDP
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Three-asset Portfolio
Ep
SDP
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Calculating Portfolio values - three asset
portfolio
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Multiple-asset Portfolio
Ep
SDP
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Systematic Risk
SDp
SDM
N
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Systematic Risk

• As you diversify your portfolio by adding assets,
  your portfolio standard deviation decreases
• Optimal approx 20 assets 21.68
• 2010020 40,000 buying individual stocks
• Buy funds which are already diversified
• When you are fully diversified, your risk is the
  risk of the market portfolio
• By changing portfolio proportions you can modify
  risk to suit your preferences

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Optimal Portfolio
U2
U1
Capital Market Line
Less risk averse
EM
More risk averse
SDM
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Relevant statistic for a fully diversified
portfolio - Beta

• Beta measures only the systematic risk of an
  assets
• Beta is also a covariance but normalized the
  market variance

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The Risk-free Asset

• The risk-free asset does not exist except as a
  theoretical concept
• One less-risky asset is the T-bill
• Low default risk - government backing
• Low interest rate risk - very short-term
  security
• One month 4.22 (unusual)
• Least risky Bank of Canada bank rate
• 4.75

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Capital Asset Pricing Model

• Prices the risk of asset relative to its
  systematic risk
• gives the required rate of return relative to its
  systematic risk

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Security Market Line
rM
1
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Security Market Line - Change in rate of
inflation
rM
rM
Inflation adjustment
1
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Security Market Line -Change in Risk Premium
rM
rM
Slope change reflecting increased Systematic Risk
1
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Own Statistics for five assets

• Expected returns and standard deviations for some
  securities

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Pairwise Covariance

• Covariance Matrix

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Questions

• How do you determine the best two assets to
  include into your portfolio
• What is the covariance of the risk free asset
  with any other asset
• Calculate some statistics for portfolios of two,
  three, and four assets
• plot an efficient set for assets for assets two
  and five

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Questions cont

• Does the required rate of return equal the
  expected return on all assets
• What happens if they are not equal?