Portfolio management

1

• Portfolio management
• Optimum asset allocation
• (see chapter 7 Bodie, Kane and Marcus)

2
How Finance is organized

• Corporate finance
• Investments
• International Finance
• Financial Derivatives

3
Risk and Return

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

4
Risk and Return

• Investors are concerned with both
• expected return
• risk
• As an investor you want to maximize the returns
  for a given level of risk.
• The relationship between the returns for assets
  in the portfolio is important.

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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.
6
Expected Rates 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

7
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

9
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
10
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.
11
The Minimum-Variance Frontierof Risky Assets
12
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
What if our risky securities are still confined
to the previous securities but now we can also
invest in a risk-free asset (e.g. T-bill)?

• You have to decide how much to invest in risky
  securities
• and how much in the risk-free rate

• You want the risky portfolio to be efficient

We use the Capital Allocation Line (CAL) to
answer this question
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Capital Allocation Line
E(rc) yE(rp) (1 - y)rf rf yE(rp) - rf
?c y ?p
is the risk premium per unit of risk also
called the reward-to-variability ratio
CAL shows all available risk-return combinations
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Optimal Risky Portfolios and a Risk Free Asset
Example 1 year term deposit rf 3 ?f
0 Bond fund rb 7 ?b 8.19 Equit
y fund re 11 ?e 14.31 ?(rb,re) 0.3
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Optimal Risky Portfolios and a Risk Free Asset
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Optimal Risky Portfolios and a Risk Free Asset
The CAL (O) corresponding to the tangency
portfolio O provides the highest reward (risk
premium) per unit of risk. Why? Because it has
the biggest slope. The efficient portfolio O is
the optimum portfolio.
The coordinates of the optimum portfolio O
are ErO 8.69 and ??O 8.71
In practice, you find the risk and return of the
optimum portfolio using a computer program that
looks for the portfolio with the highest risk
premium per unit of risk (S). (see your project)
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Optimal Risky Portfolios and a Risk Free Asset
The choice of weight a, how much to invest in the
optimum risky portfolio, depends on your
tolerance for risk and return requirement. For
example, in our case, the investor chooses to
invest a 90 of his money in the optimum risky
portfolio And portfolio O consists of wb
57.8 in the bond fund we 42.2 in equity fund
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Optimal Risky Portfolios and a Risk Free Asset
The percentage of total portfolio invested in
bonds awb 0.90.5780.52 or 52 equity
awe 0.90. 422 0.38 or 38
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Optimal Risky Portfolios and a Risk Free Asset
Optimum risky portfolio ErO 8.69 ?O
8.71 Total portfolio ErC 0.1x3 0.9x8.69
8.12 ?C 0.9x8.71 7.84
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Learning objectives

• Know the three steps of the top down asset
  allocation
• Discuss the benefits of diversification.
• Discuss the mean-variance frontier , efficient
  frontier, CAL, Reward to variability ratio use
  graphs no need to derive formulas
• Recommended end-of chapter problems 1,8a,
  13,17,21,22,23