Risk and Return - Part 2

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Risk and Return - Part 2

• Efficient Frontier
• Capital Market Line
• Security Market Line

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Risk and Return
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Risk and Return Feasible Investments

• What does the risk-return tradeoff look like if
  we combine many securities into a portfolio?

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Risk and Return (Continued)

• Why do we care what the risk-return tradeoff
  looks like?
• Efficient Investment
• For a given level of risk, choose those
  investments that provide the highest expected
  return.
• For a given level of expected return, choose
  those investments with the lowest level of risk.
• Which investments on the graph are efficient?
• With what decisions might variations of the above
  analysis help managers and/or investors?
• The graph above includes only risky assets. What
  happens if we also include a risk-free asset?

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Risk and Return Efficient Frontier
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Risk and Return with a Risk-Free Asset
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Risk and Return Capital Market Line

• What investments are efficient if we include the
  risk-free asset?

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Risk and Return Capital Market Line

• Important conclusions so far
• When securities returns are less than perfectly
  positively correlated, diversifying enables
  investors
• to increase their investment opportunity set and
• to invest efficiently
• When investors have the same expectations about
  what opportunities for risk and return they have,
  they will invest in two sets of assets that
  include
• positive (lending) or negative (borrowing)
  amounts of the risk-free asset and
• the market portfolio that has been completely
  diversified across all risky assets.
• What are the risk/return tradeoffs in this type
  of environment?
• Risk is measured as the standard deviation of
  portfolio returns.
• Expected return is measured as the expected
  return on the portfolio.

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Risk and Return Capital Market Line

• Numerical Example Suppose the return on the
  risk-free asset is 4, the expected return on the
  market portfolio is 11, and the standard
  deviation of the return on the market is 15.
  What are the expected return and standard
  deviation of the returns on a portfolio in which
  50 of our wealth is invested in both the market
  portfolio and the risk-free asset?
• The expected return is
• The standard deviation is

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Risk and Return Capital Market Line

• Numerical Example Suppose investors want to
  earn more than the market rate of return, say
  15. What proportions of their investment must
  they invest in the risk-free asset and the market
  portfolio, respectively?
• How much risk would investors be exposed to?

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Risk and Return Capital Market Line

• For well diversified portfolios, the required
  return can be determined by what is known as the
  Capital Market Line. That is,
• Where,
• Rf is the rate of return on a risk-free asset.
• E(Rm) is the expected return on the market
  portfolio
• ?p is the standard deviation of the return on the
  portfolio in question, and
• ?m is the standard deviation of the return on the
  market portfolio.

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Risk and Return Capital Market Line

• Thought questions about the Capital Market Line
• For the numbers in the example above, what are
  the probabilities that portfolios with expected
  returns of 7.5 and 15.0 will be below the
  risk-free rate of return? Hint 1
• Z-score Rf - E(Rp)/?p
• Sharpes Ratio E(Rp) Rf/?p E(Rm) Rf/
  ?M
• How do returns on the portfolios with expected
  returns of 7.5 and 15 correlate with returns on
  the Market Portfolio? Hint 2 All investors in
  this model invest in only two assets the market
  portfolio and the risk-free asset.
• Could we use the Capital Market Line to find the
  expected and required rate of return for
  individual securities? Why or why not? Hint 3
  See Hint 2.

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Risk and Return Capital Market Line for
Individual Securities? Why or why not?
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Risk and Return The Risk of Individual
Securities in an N-stock Portfolio
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Risk and Return The Risk of Individual
Securities in an N-stock Portfolio

• Suppose N100, how many terms in the portfolio
  variance are influenced by correlations between
  returns on the different stocks?
• How many terms in the portfolio variance are not
  influenced by the correlations?
• How much risk does stock 1 contribute to the
  portfolio? How do we measure risk?

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Risk and Return The Risk of Individual
Securities in an N-stock Portfolio

• The contribution to portfolio risk made by an
  individual stock is called beta, ?.
• Do we have to calculate the correlations between
  returns on each pair of stocks in the portfolio
  to calculate ??
• No, there is a simpler approach Regression
  Analysis.
• How does this regression work?

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Risk and Return Calculating ?
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Risk and Return What does ? mean?

• As we noted earlier, ? is the contribution to
  portfolio risk made by a security (or group of
  securities) in a specific portfolio. Another
  way of saying this is that the portfolio ?p is
  the weighted average of the individual ?s in the
  portfolio. That is,
• We also said that ? is the slope from a
  regression that explains the relationship between
  returns on an individual security (or group of
  securities) and returns on the market. What does
  the slope tell us?

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Risk and Return What does ? mean?

• Because ? is the slope of the regression line, it
  tells us two things 1) the relative direction of
  the stocks movements when the market moves up or
  down, and 2) the relative amplitude of the
  stocks movements compared to the movements in
  the market. This can be shown by decomposing ?i
  as follows
• What economic significance does ? have? Could
  you estimate it without running a regression?
  What are the likely values of these components of
  ?? What determines the values of ?i,M and ?i
  /?M?

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Risk and Return Can you explain these ?s?

• Company Beta
• Microsoft 1.45
• ATT 0.86
• Novell 1.70
• Ford Motor Company 0.96
• Union Pacific Corp 0.63
• Pacificorp 0.19
• Delta Air Lines 0.75
• American Express 1.36
• Geneva Steel 0.24
• Iomega 2.07

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Risk and Return How do we use ? ? The Security
Market Line

• One way to use ? is to calculate the cost of
  equity for individual firms. This is done by
  using the Security Market Line as follows
• Where
• E(Ri) is the expected and required return on
  stock i
• Rf is the rate of return on the risk-free asset
• ?i is the beta for stock i, and
• E(Rm) is the expected and required rate of return
  on the market.
• What determines the values of these factors?

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Risk and Return How do we use ? ? The Security
Market Line
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Risk and Return How do we use ? ? The Security
Market Line

• Numerical Example Suppose three stocks have ?s
  of 1.5, .75, and -.30, respectively. We plan to
  invest 30 of our wealth in the first two stocks
  and 40 of our wealth in the third stock. If
  the risk -free rate is 4 and the expected
  (required) return on the market is 11, calculate
  the following
• The ? for the portfolio of three stocks.
• The contribution to the portfolio risk made by
  each stock.
• The required return for the portfolio.
• The required return for the individual stocks.

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Risk and Return Assignment for Next Time

• Estimate the cost of equity for Star Appliance
• Convert price and earnings per share data to
  returns for Star
• Estimate the ?
• Estimate ? without the numbers, using what you
  know about Stars product and industry.
• Estimate ? with the numbers, using regression
  analysis.
• Determine Stars cost of capital for capital
  budgeting.