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Slide 9.1

Investments

Chapter 9: Portfolio Diversification

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Slide 9.2

Diversification:The ‘Free Lunch’ of Finance

An investor can achieve higher returns for a given level of risk through diversification.

Principle: In terms of Chapter 8: diversification raises the Markowitz mean-variance efficient frontier.

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Slide 9.3

Three Ways to Diversify

1. Diversification across sectors and industries.

2. Diversification across asset classes.

3. Diversification across regions and countries.

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Slide 9.4 Three Ways to Diversify – Illustration

Exhibit 9.1 Correlation matrix for regions, sectors and asset classes (1994–2003)Source: mba.tck.dartmouth.edu/pages/faculty/ken.french/

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Slide 9.5

Systemic Risk vs. Nonsystemic Risk

• Systemic RiskThe risk that comes from the individual exposure of assets to their individual risk factors. Can be diversified away.

• Nonsystemic RiskThe risk that comes from the common exposure of assets to economy-wide risk factors. Can’t be diversified away.

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Slide 9.6

International Diversification: I

Principle:

Since international markets are not perfectly correlated investors can achieve reductions in risk BEYOND portfolios with only domestic assets.

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Slide 9.7

International Diversification: II

Nowadays, the benefits of international diversification seem to have diminished.

Reasons:

1. (For US investors) superior returns in US marketsduring the 1990s.

2. Increased correlation between developed countries.3. Increased correlation during international market

crises.

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Slide 9.8

‘A Little Diversification Goes a Long Way’

The incremental contribution to the reduction of a portfolio’s variance of adding extra assets to a portfolio REDUCES as the number of assets in a portfolio increases.

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Slide 9.9 ‘A Little DiversificationGoes a Long Way’ – Illustration

(The above results differ for different correlation coefficients. These coefficients can be interpreted as the systemic risk that cannot be diversified away)

Exhibit 9.4(b) Effect of the number of assets and the correlation coefficient on a portfolio’s variance (individual assets are identical)

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Slide 9.10

Barriers to Diversification

Main Barriers:

1. Information Costs

2. Transaction Costs

Possible solution for small investors:

Mutual Funds

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Slide 9.11

Estimation Error: I

Construction of efficient portfolios requires the means, variances and covariances of all individual assets.

Often-used Method:

Assume historical observations are representative for the future return distribution of assets, assigning equal weight to all observations.

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Slide 9.12

Estimation Error: IIProblem:

Time variation of the return distribution.

Result: Estimation Errors.

Related Problem:

The construction of efficient portfolios is extremely sensitive to estimation errors.

Solution: Confidence Intervals.

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Slide 9.13 Human Capital and Property Holdings

• Single most valuable asset most people have is their Human Capital.

Ideally, investors should incorporate their human capital in their portfolio analysis.

• The same holds for property holdings.

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Slide 9.14

Actual Diversification by Households

Empirical evidence indicates household portfolios are often under-diversified.

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Slide 9.15 Portfolio Risk as a Function of the Number of Stocks in the Portfolio

Nondiversifiable risk; Systematic Risk; Market

Risk

Diversifiable Risk; Nonsystematic Risk; Firm Specific Risk;

Unique Risk

n

In a large portfolio the variance terms are effectively diversified away, but the covariance terms are not.

Thus diversification can eliminate some, but not all of the risk of individual securities.

Portfolio risk

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Slide 9.16 The Efficient Set for Many Securities

Consider a world with many risky assets; we can still identify the opportunity set of risk-return combinations of various portfolios.

retu

rn

P

Individual Assets

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Slide 9.17The Efficient Set for Many Securities

Given the opportunity set we can identify the minimum variance portfolio.

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minimum variance portfolio

Individual Assets

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Slide 9.18The Efficient Set for Many Securities

The section of the opportunity set above the minimum variance portfolio is the efficient frontier.

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minimum variance portfolio

efficient frontier

Individual Assets

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Slide 9.19Optimal Risky Portfolio with a Risk-Free Asset

In addition to stocks and bonds, consider a world that also has risk-free securities like T-bills

100% bonds

100% stocks

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Slide 9.20 Riskless Borrowing and Lending

Now investors can allocate their money across the T-bills and a balanced mutual fund

100% bonds

100% stocks

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Balanced fund

CML

Levy and Post, Investments © Pearson Education Limited 2005

Slide 9.21 Riskless Borrowing and Lending

With a risk-free asset available and the efficient frontier identified, we choose the capital allocation line with the steepest slope

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efficient frontier

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Slide 9.22 Market Equilibrium

With the capital allocation line identified, all investors choose a point along the line; some combination of the risk-free asset and the market portfolio M. In a world with homogeneous expectations, M is the same for all investors.

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efficient frontier

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M

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Slide 9.23 The Separation Property

The Separation Property states that the market portfolio, M, is the same for all investors—they can separate their risk aversion from their choice of the market portfolio.

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Slide 9.24 The Separation Property

Investor risk aversion is revealed in their choice of where to stay along the capital allocation line—not in their choice of the line.

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Levy and Post, Investments © Pearson Education Limited 2005

Slide 9.25Optimal Risky Portfolio with a Risk-Free Asset

The optimal risky portfolio depends on the risk-free rate as well as the risky assets.

100% bonds

100% stocks

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First Optimal Risky

Portfolio

Second Optimal Risky Portfolio

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