Chapter 5 Portfolio Allocation

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Chapter 5Portfolio Allocation
2
Some Data ()
3
Factors in Portfolio Choice

• Wealth
• Expected Return
• Risk
• Liquidity
• Information costs

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Wealth

• As wealth increases, the amount held of all
  assets tends to increase
• Demand for some assets increases more than in
  proportion and others, less
• Wealth elasticity of demand
• change in amount held/ change in wealth

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Facts about Wealth Elasticity E

• As wealth increases,
• The assets share in the portfolio falls if E
• (Such assets are called necessities)
• The share stays constant if E 1
• The share rises if E 1
• (Such assets are called luxuries)
• E averages 1 across the portfolio so the
  typical asset has E 1

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Example

• Consider a person who allocates her wealth of 100
  as follows 50 in bonds, 50 in stock.
• Suppose her wealth rises 10 to 110, and she
  holds 53 in bonds (6 more) and 57 in stock (14
  more).
• Wealth elasticity of bonds 6/10 0.6
• Wealth elasticity of stocks 14/10 1.4
• The wealth elasticity must average 1
• (50/100)?0.6 (50/100)?1.4 1.

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Expected Return

• The most important factor
• The higher an assets expected return is relative
  to other assets, the more is held
• Example The expected return of an asset rises
  while the expected returns on all other assets
  remain unchanged. Result More of the former and
  less of the latter are held.

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Riskiness

• Next in importance after expected return
• An asset is risky if its return cant be
  predicted perfectly.
• The riskier an asset is relative to other assets,
  the less of it is held
• Example The risk of one asset rises while the
  risks on all other assets remain unchanged.
  Result Less of the former and more of the latter
  are held.

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Example 1 NYSE Stock

• Until recently, the expected real rate of return
  on the typical NYSE stock was about 8/yr since
  1926
• The standard deviation was 49/yr
• Implications
• One year in six, real return 8 49 57
• One year in six, real return
• 10K becomes 15.7K with probability 1/6 and 5.9K with probability 1/6.
• High expected return but very risky!

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Example 2 Treasury Bills

• Expected real return on Tbills has been about
  1/yr since 1926
• Standard deviation has been about 1/yr
• Implications
• One year in six, real return 1 1 2
• One year in six, real return
• 10K becomes 10.2K with probability 1/6 and 10K with probability 1/6.
• Low expected return but not very risky

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Risk Preferences

• Risk-adverse persons prefer less risk to more and
  give up expected return for risk reduction (Most
  asset holders)
• Risk-neutral persons only care about expected
  return (Firms in theory)
• Risk-loving persons give up expected return for
  extra risk (Buyers of lottery tickets, gamblers
  in Los Vegas)

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Liquidity

• The more liquid an asset is relative to other
  assets, the more is held
• Liquidity is valued because it may be important
  to be able to quickly sell an asset
• Illiquid assets require higher expected returns
  than liquid assets
• Cash is perfectly liquid

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Information Costs

• The more transparent and anonymous an asset is
  and the less monitoring it requires relative to
  other assets, the more is held.
• Example Treasury bills vs. limited partnerships

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Diversification

• Holding many assets with returns that do not move
  in lockstep reduces portfolio risk
• Example Two assets A and B
• Four possible cases 1, 2, 3, 4
• A earns 20 in cases 1 and 2 and 0 in cases 3
  and 4
• B earns 20 in cases 1 and 3 and 0 in cases 2
  and 4
• Each case has probability ¼ of happening

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Table
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Calculations

• Expected returns
• A ¼x20 ¼x20 ¼x0 ¼x0 10
• B ¼x20 ¼x0 ¼x20 ¼x0 10
• ½A½B ¼x20 ¼x10 ¼x10 ¼x0 10
• Standard Deviations
• A ¼(20-10)2 ¼(20-10)2 ¼(0-10)2
  ¼x(0-10)21/2
• 1001/2 10
• B ¼(20-10)2 ¼(0-10)2 ¼(20-10)2
  ¼(0-10)21/2
• 1001/2 10
• ½A½B ¼(20-10)2 ¼(10-10)2 ¼(10-10)2
  ¼(0-10)21/2
• 501/2 7.07

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On average, portfolios of N randomly selected
NYSE stocks had annual returns with the following
standard deviations as a function of N
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Limits to Diversification

• Diversification can greatly reduce risk but
  cannot eliminate it
• It eliminates unsystematic or idiosyncratic risk
• It cannot eliminate systematic or market risk
• The systematic risk of an asset is measured by
  its beta

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Beta

• Beta gets its name from a statistical procedure
  called regression, which estimates relationships
  among variables.
• The beta of an asset measures how closely its
  return moves with the return on a portfolio of
  all assets.

Rit
Regression equation Rit ai ßiRmt eit
Slope ßi
Std dev measures idiosyncratic risk.
ai
2/3 points w/i dashed lines
Rmt
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More on Beta

• Examples
• If an assets beta .5, its return moves half as
  much on average as the markets.
• If an assets beta 2, its return moves twice
  as much on average as the markets.
• An assets expected return is higher, the higher
  its beta

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Examples of Some Betas
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Postwar Portfolio Changes

• Checking accounts fell from 13 in 1950 to 1 in
  2000
• Wealth elasticity
• Deregulation afforded more choice i.e. higher
  expected returns became available elsewhere
• SDs and TDs fell from 23 in 1970 to 15 in 2000
• Deregulation again i.e. higher expected returns
  became available elsewhere
• Bonds etc. fell from 24 in 1950 to 8 in 2000
• Supply changes changes in relative expected
  returns

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More on Postwar Portfolio Changes

• Rise in equity mutual funds from 2 in 1970 to
  11 in 2000
• Computer revolution and its effect on expected
  returns
• Decline in life insurance reserves from 13 in
  1950 to 3 in 2000
• Effects of deregulation and term life on expected
  return available elsewhere
• Rise in pension reserves from 6 in 1950 to 35
  in 2000
• Wealth elasticity 1
• Changes in the tax system and their effects on
  expected returns