why diversify? chapter sixteen practical investment management

WHY DIVERSIFY?

CHAPTER SIXTEEN

Practical Investment Management

Robert A. Strong

South-Western / Thomson Learning © 2004 16 - 2

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. “


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



Insert Figure 16-1 here.



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



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


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


Covariance vs. Correlation

Insert Table 16-5 here.


The Role of Uncorrelated Securities

The expected return of a portfolio is a weighted average of the component expected returns.

n

iiiportfolio RExRE

1

where xi = the proportion invested in security i



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22222 12 ,

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and betweent coefficien ncorrelatio stock of deviation standard

stock in invested portfolio of proportion variance portfolio where

2

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.


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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betterperformance

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



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?


The Efficient Frontier : Optimum Diversification of Risky Assets

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ecte

d r

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risk (standard deviation of returns)

impossibleportfolios

dominatedportfolios

Efficient frontier

The efficient frontier contains portfolios that are not dominated by any other portfolios


The Efficient Frontier : The Minimum Variance Portfolio

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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.



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 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


Efficient frontier:Rf to M to C

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dominatedportfolios


M

Rf

C

E


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


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.


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

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dominatedportfolios


M

Rf

lending

borrowing

Efficient frontier : The ray from Rf through M and beyond


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)

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dominatedportfolios


M

RL

N

Efficient frontier : RL to M, the curve from M to N, then the ray from N


RB


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


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


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


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



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

miimim



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

f

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.


Security Market Line (SML)





Beta can be estimated from historical data using the market model- Linear Regression of Market Proxy (S&P 500) and Security excess returns



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)

why diversify? chapter sixteen practical investment management

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