Econ173

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Econ173 Corporate Finance Brealey, Myers and
Allen Ch7
Lecture 2
Portfolio Theory
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The Value of an Investment of 1 in 1926
6402 2587 64.1 48.9 16.6
Index
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Year End
Source Ibbotson Associates
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The Value of an Investment of 1 in 1926
Real returns
660 267 6.6 5.0 1.7
Index
1
Year End
Source Ibbotson Associates
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Rates of Return 1926-2000
Percentage Return
Year
Source Ibbotson Associates
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Measuring Risk

• Variance (s2) and Standard Deviation (s)
• Average value of squared deviations from mean.
  A measure of volatility.

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Measuring Return and Risk

• Coin Toss Game-calculating variance and standard
  deviation

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Portfolio Returns and Risk
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Portfolio Risk
The variance of a two stock portfolio is the sum
of these four boxes
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Portfolio Risk
Example Suppose you invest 65 of your portfolio
in Coca-Cola (r110, s131.5) and 35 in Reebok
(r220, s258.5). The expected return on your
portfolio is 0.65 x 10 0.35 x 20 13.50.
Assume a correlation coefficient of 1.
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Portfolio Risk
Example Suppose you invest 65 of your portfolio
in Coca-Cola and 35 in Reebok. The expected
dollar return on your CC is 10 x 65 6.5 and
on Reebok it is 20 x 35 7.0. The expected
return on your portfolio is 6.5 7.0 13.50.
Assume a correlation coefficient of 1.
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Portfolio Risk
The shaded boxes contain variance terms the
remainder contain covariance terms.
To calculate portfolio variance add up the boxes
STOCK
STOCK
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Efficient Frontier

• Example Correlation
  Coefficient .4
• Stocks s of Portfolio Avg Return
• ABC Corp 28 60 15
• Big Corp 42 40 21
• Standard Deviation weighted avg 33.6
• Standard Deviation Portfolio 28.1
• Return weighted avg Portfolio 17.4

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Efficient Frontier

• Example Correlation
  Coefficient .3
• Stocks s of Portfolio Avg Return
• Portfolio 28.1 50 17.4
• New Corp 30 50 19
• NEW Standard Deviation weighted avg 31.80
• NEW Standard Deviation Portfolio 23.43
• NEW Return weighted avg Portfolio 18.20
• NOTE Higher return Lower risk
• How did we do that? DIVERSIFICATION

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Efficient Frontier
Return
B
A
Risk (measured as s)
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Efficient Frontier
Return
B
AB
A
Risk
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Efficient Frontier
Return
B
N
AB
A
Risk
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Efficient Frontier
Return
B
N
ABN
AB
A
Risk
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Efficient Frontier
Goal is to move up and left. WHY?
Return
B
N
ABN
AB
A
Risk
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Efficient Frontier
Return
B
N
ABN
AB
A
Risk
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Markowitz Portfolio Theory

• Combining stocks into portfolios can reduce
  standard deviation, below the level obtained from
  a simple weighted average calculation.
• Correlation coefficients make this possible.
• The various weighted combinations of stocks that
  create this standard deviations constitute the
  set of efficient portfolios.

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Efficient Frontier

• Each half egg shell represents the possible
  weighted combinations for two stocks.
• The composite of all stock sets constitutes the
  efficient frontier

Expected Return ()
Standard Deviation
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Markowitz Portfolio Theory

• Expected Returns and Standard Deviations
  vary given different weighted combinations of
  the stocks

Expected Return ()
Reebok
35 in Reebok
Coca Cola
Standard Deviation
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Exercises

• BMA Chapter 7
• Q7-1 to Q7-5, Q7-7 to Q7-9
• P7-1, P7-3 to P7-7, P7-13