WHY DIVERSIFY?
CHAPTER SIXTEEN
Practical Investment Management
Robert A. Strong
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Use More Than One Basket for Your Eggs
Failure to diversify may violate the terms of a fiduciary trust
Diversification is important not just in investments e.g. commercial lending, manufacturing, marketing
“Don’t put all your eggs in one basket. “
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Preliminary Steps in Forming a Portfolio
How to form a Portfolio?
Identify a collection of eligible investments known as the security universe
Look up historical prices
Convert security prices to returns
Compute statistics for the chosen securities. e.g. mean of return variance / standard deviation of return matrix of correlation coefficients
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Preliminary Steps in Forming a Portfolio
Insert Figure 16-1 here.
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Preliminary Steps in Forming a Portfolio
Insert Figure 16-2 here.
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Preliminary Steps in Forming a Portfolio
Interpret the statistics.
1. Do the values seem reasonable? Average return less than 0 (negative)?
Insurance policies have a negative long-term expected return (utility from reduced risk)
Negative expected return possible for assets that have negative correlation to the rest of the market
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Preliminary Steps in Forming a Portfolio
Interpret the statistics.
2. Is any unusual price behavior expected to recur?• Big (unusual) price jumps may bias average returns
3. Are any of the results unsustainable?• Example: A stock has an average weekly
return of 1% over the last 6 months
• Growth rates must be sustainable to be meaningful in the long run
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Preliminary Steps in Forming a Portfolio Interpret the statistics.
4. Low correlations: Fact or fantasy?• Over a short period of time, a pair of stocks
may have a negative correlation coefficient (say -0.7)
• But since common stocks share a common risk factor know as market risk, a highly negative correlation is unlikely to persist
Overall Lesson: Past information can be useful in estimating the future, but they have many potential flaws
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Covariance vs. Correlation
Insert Table 16-5 here.
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The Role of Uncorrelated Securities
The expected return of a portfolio is a weighted average of the component expected returns.
n
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where xi = the proportion invested in security i
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The Role of Uncorrelated Securities
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two-securityportfolio risk = riskA + riskB + interactive risk
The total risk of a portfolio comes from the variance of the components AND from the relationships among the components.
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The Role of Uncorrelated Securities Portfolio variance is known also as total risk
As the number of securities in the portfolio grows, so does the number of interaction terms (from the covariance matrix)
For an n size portfolio, there are n(n-1)/2 correlation terms Example: For a 12 security portfolio, there are
12(12-1)/2 = 66 interaction terms A portfolio of 50 securities has 1,225 interaction
terms
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The Role of Uncorrelated Securities
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Investors get added utility from greater return. They get disutility from greater risk.
The point of diversification is to achieve a given level of expected return while bearing the least possible risk.
•Associating realized return with the risk taken is central to determining how well an investment portfolio did
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The Role of Uncorrelated Securities
The Concept of Dominance
A portfolio dominates all others if no other equally risky portfolio has a higher expected return, or if no portfolio with the same expected return has less risk
Example: MU and INTC vs. MU and MOTWhich portfolio dominates?
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The Efficient Frontier : Optimum Diversification of Risky Assets
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Efficient frontier
The efficient frontier contains portfolios that are not dominated by any other portfolios
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The Efficient Frontier : The Minimum Variance Portfolio
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risk (standard deviation of returns)
single securitywith the highestexpected return
minimum varianceportfolio
The right extreme of the efficient frontier is a single security; the left extreme is the minimum variance portfolio.
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The Efficient Frontier : The Minimum Variance Portfolio
Note that the minimum variance portfolio is not the security with the lowest variance
In general, the further you move to the left of the efficient frontier (less risk), the greater the number of securities in the portfolio
How to determine the minimum variance portfolio ( 2 security case )
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The Efficient Frontier : The Minimum Variance Portfolio
Insert Figure 16-6 here.
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The Efficient Frontier : The Effect of a Risk-free Rate
When a risk-free investment complements the set of risky securities, the shape of the efficient frontier changes markedly.
M = Market portfolio
Rf = Risk-free rate
risk (standard deviation of returns)
Efficient frontier:Rf to M to C
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The Efficient Frontier : The Effect of a Risk-free Rate
The straight portion of the line is tangent to the risky securities efficient frontier at point M and is called the capital market line.
The In theory, all rational investors hold some combination of the market portfolio (M) and the risk-free asset. In equilibrium, M should contain ALL risky assets and should be the only risky portfolio that exists.
The only risk that matters for an individual security is the risk that it brings to the market portfolio M Beta measures this risk
The market portfolio M contains a percentage of all investable assets in proportion to their market cap. In practice, the S&P 500 index serves as a proxy for M
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The Efficient Frontier with Borrowing Since buying a Treasury bill amounts to
lending money to the U.S. Treasury, a portfolio partially invested in the risk-free rate is often called a lending portfolio.
Buying on margin involves financial leverage, thereby magnifying the risk and expected return characteristics of the portfolio. Such a portfolio is called a borrowing portfolio.
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The Efficient Frontier with Borrowing
Efficient frontier:the ray from Rf through M
If it is possible to buy stocks on margin, then the efficient frontier gets expanded again
exp
ecte
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risk (standard deviation of returns)
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M
Rf
lending
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Efficient frontier : The ray from Rf through M and beyond
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The Efficient Frontier : Different Borrowing and Lending Rates
Most of us cannot borrow and lend at the same interest rate, this leads the efficient frontier to change again (RB = borrowing rate > RL = lending rate)
exp
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M
RL
N
Efficient frontier : RL to M, the curve from M to N, then the ray from N
risk (standard deviation of returns)
RB
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The Efficient Frontier : Naive Diversification
As portfolio size increases,total portfolio risk, on average, declines. After a certain point, however, the marginal reduction in risk from the addition of another security is modest.
Naive diversification is the random selection of portfolio components without conducting any serious security analysis.
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Nondiversifiable risk(market risk)
number of securities20 40
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Capital Market Theory
The remaining risk, when no further diversification occurs, is pure market risk.
Research shows that of a single security’s total risk, about 75% is unsystematic and 25% is systematic (i.e. most risk can be diversified away)
Market risk is also called systematic risk and is measured by beta.
A security with average market risk has a beta equal to 1.0. Riskier securities have a beta greater than one, and safer securities have a beta less than 1.0
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Capital Market Theory
Capital Market Theory indicates that investors are only rewarded for bearing necessary (unavoidable) risk in the form of additional expected return
This implies that investors should always diversify, since diversification eliminates a substantial portion of portfolio risk (namely diversifiable risk)
Three main results from Evans and Archer:1. Total risk declines as the number of securities increases2. Increasing the number of portfolio securities provides
diminishing benefits as the number of securities increases3. In large portfolios, the benefits of additional diversification
may be out-weighted by the additional transaction costs More than 20-30 securities may be superfluous
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The Efficient Frontier : The Single Index Model
In order to determine portfolio variance, a pair-wise comparison of the thousands of securities in existence would be an unwieldy task. To get around this problem, the single index model compares all securities to a benchmark measure, the market portfolio.
The single index model relates security returns to their betas, thereby measuring how each security varies with the overall market. (Instead of how each security varies with respect to each other)
Using Beta, we only need to calculate a beta for each security instead of covariances
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The Efficient Frontier : The Single Index Model
Beta is the statistic relating an individual security’s returns to those of the market index.
2
,cov
m
mi
m
iimi
RR
where R = the return on the market index R = the return on security i = standard deviation of security i returns = standard deviation of market returns = correlation between security i returns and market returns
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The Efficient Frontier : The Single Index Model
E R R E R Ri f i m f
where R = riskless interest rate R = return on security i = return on the market = beta of security i
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imi
R
The relationship between beta and expected return is the essence of the capital asset pricing model (CAPM), which states that a security’s expected return is a linear function of its beta.
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Security Market Line (SML)
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The Efficient Frontier : The Single Index Model
Insert Figure 16-12 here.
Beta can be estimated from historical data using the market model- Linear Regression of Market Proxy (S&P 500) and Security excess returns
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The Efficient Frontier : The Single Index Model
The intercept from the linear regression (the market model) is know as alpha (also know as the Jensen Index), and is sometimes used as a measure of (risk-adjusted) performance Positive alpha: return earned is greater than expected
based on risk borne Negative alpha: return earned is smaller than expected
based on risk borne More useful when evaluating portfolios (like mutual funds)
In efficient markets, the expected return and the required rate of return will be equal. CAPM can be used to obtain the shareholder’s required
rate of return in the Dividend Discount Model (DDM)