Portfolio management

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• Portfolio management

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Never tell people how to do things. Tell them
what to do and they will surprise you with their
ingenuity General George Patton
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How Finance is organized

• Corporate finance
• Investments
• International Finance
• Financial Derivatives

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Risk and Return

• The investment process consists of two broad
  tasks
• security and market analysis
• portfolio management

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Risk and Return

• Investors are concerned with both
• Expected return comes from a valuation model
• Risk
• As an investor you want to maximize the returns
  for a given level of risk.

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Return Calculating the expected return for each
alternative
Outcome Prob. of outcome Return in
1(recession) .1 -15 2 (normal
growth) .6 15 3 (boom) .3 25 k expected
rate of return (.1)(-15) (.6)(15)
(.3)(25)15
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What is investment risk?

• Investment risk is related to the probability of
  earning a low or negative actual return.
• The greater the chance of lower than expected or
  negative returns, the riskier the investment.

Firm X
Firm Y
Rate of Return ()
15
100
0
-70
Expected Rate of Return
Firm X (red) has a lower distribution of returns
than firm Y (purple) though both have the same
average return. We say that firm Xs returns are
less variable/volatile (lower standard deviation
?) and thus X is a less risky investment than Y
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Selected Realized Returns, 1926 2006

• Average Standard
• Return Deviation
• Small-company stocks 18.4 36.9
• Large-company stocks 12.2 20.2
• L-T corporate bonds 5.8 9.4
• L-T government bonds 5.6 8.1
• U.S. Treasury bills 3.7 3.1

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Investor attitude towards riskDoes it matter?

• Risk aversion assumes investors dislike risk
  and require higher rates of return to encourage
  them to hold riskier securities.
• Some individuals are risk lovers, meaning that
  they purchase/ invest in instruments with
  negative expected rate of return
• Ex
• Risk premium the difference between the return
  on a risky asset and less risky asset, which
  serves as compensation for investors to hold
  riskier securities
• Very often risk premium refers to the difference
  between the return on a risky asset and risk-free
  rate (ex. a treasury bond)

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Top Down Asset Allocation
1. Capital Allocation decision the choice of the
proportion of the overall portfolio to place
in risk-free assets versus risky assets.
2. Asset Allocation decision the distribution of
risky investments across broad asset
classes such as bonds, small stocks, large
stocks, real estate etc.
3. Security Selection decision the choice of
which particular securities to hold within
each asset class.
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Terminology

• Investment (portfolio) management professional
  management of a collection (i.e. portfolio) of
  securities to meet specific goals for the benefit
  of investors
• Asset management is similar to Investment or
  Portfolio Management
• Wealth manager is more of a broker , financial
  manager or investment advisor for wealthy clients
• Portfolio management involve a long investment
  horizon
• Trading focuses on securities selection with a
  short term horizon

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Top Down Asset allocation

• Capital Allocation decision the choice of the
  proportion of the overall portfolio to place in
  risk-free assets versus risky assets
• Asset Allocation decision the distribution of
  risky investments across broad asset classes
  such as bonds, small stocks, large stocks, real
  estate etc.
• Security Selection decision the choice of which
  particular securities to hold within each asset
  class.
• 90 of the portfolio performance is determined by
  the first two steps

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Portfolio Management

• A properly constructed portfolio achieves a given
  level of expected return with the least possible
  risk
• Portfolio management primarily involves reducing
  risk rather than increasing return
• The investment horizon is intermediate to long
  term
• Portfolio managers have a duty to create the best
  possible collection of investments for each
  customers unique needs and circumstances

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Tactical Asset Allocation

• Also known as Market Timing
• Shifting the relative proportion of the asset
  classes in the portfolio

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Portfolio Management

• The heart of the Portfolio Management is the
  concept of diversification
• The empirical evidence shows that the markets are
  quite efficient
• Passive (Indexing) vs. Active Investing

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Expected Portfolio Rate of Return

• Weighted average of expected returns (Ri) for the
  individual investments in the portfolio
• Percentages invested in each asset (wi) serve as
  the weights
• E(Rport) S wi Ri

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Portfolio Risk (two assets only)
When two risky assets with variances s12 and
s22, respectively, are combined into a portfolio
with portfolio weights w1 and w2, respectively,
the portfolio variance is given by ?p2
w12?12 w22?22 2W1W2 Cov(r1r2) Cov(r1r2)
Covariance of returns for
Security 1 and Security 2
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Correlation between the returns of two securities
Correlation, ? a measure of the strength of the
linear relationship between two variables

• -1.0 lt r lt 1.0
• If r 1.0, securities 1 and 2 are perfectly
  positively correlated
• If r -1.0, 1 and 2 are perfectly negatively
  correlated
• If r 0, 1 and 2 are not correlated

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Efficient Diversification
Lets consider a portfolio invested 50 in an
equity mutual fund and 50 in a bond fund.
Equity fund Bond fund E(Return) 11 7 St
andard dev. 14.31 8.16 Correlation -1
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100 stocks
100 bonds
Note that some portfolios are better than
others. They have higher returns for the same
level of risk or less. We call this portfolios
EFFICIENT.
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The Minimum-Variance Frontierof Risky Assets
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Two-Security Portfolios with Various Correlations
return
100 stocks
? -1.0
? 1.0
? 0.2
100 bonds
?
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The benefits of diversification

• Come from the correlation between asset returns
• The smaller the correlation, the greater the risk
  reduction potential ? greater the benefit of
  diversification
• If r 1.0, no risk reduction is possible
• Adding extra securities with lower corr/cov with
  the existing ones decreases the total risk of the
  portfolio

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Estimation Issues

• Results of portfolio analysis depend on accurate
  statistical inputs
• Estimates of
• Expected returns
• Standard deviations
• Correlation coefficients

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Portfolio Risk as a Function of the Number of
Stocks in the Portfolio
Thus diversification can eliminate some, but not
all of the risk of individual securities.
?
Diversifiable Risk Nonsystematic Risk Firm
Specific Risk Unique Risk
Portfolio risk
Nondiversifiable risk Systematic Risk Market
Risk
n
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Optimal Risky Portfolios and a Risk Free Asset