ChapterChapter 6 6Efficient Diversification

1

Risk and ReturnRisk and Return

In previous chapters, we have calculated returns on various investments.

In chapter 5, we used the standard deviation of returns as a measure of total risk.

Now, we look at what happens to returns and risk when assets are combined into portfolios.

2

Portfolio ReturnsPortfolio Returns

The return on a portfolio is a weighted average of the returns on the assets in the portfolio.

If 2 or more assets with equal expected returns are combined, the expected return on the portfolio equals the expected return of the individual assets.

3

Portfolio RiskPortfolio Risk

In general, the risk (standard deviation) of a portfolio is lower than the risk of the individual assets.

This reduction in risk is referred to as diversification.

Diversification can reduce risk, but cannot eliminate it.

4

Portfolio RiskPortfolio Risk

On average, the standard deviation of returns of a single stock is about 35-40%.

The standard deviation of returns of the S&P 500 is 20%.

By investing in an S&P 500 index, the risk is about half as great as investing in a single stock.

You still face the risk of a decline in the market: market risk.

5

Components of RiskComponents of Risk

Market or systematic risk: risk related to macroeconomic conditions, or of a decline in the overall market

Nonsystematic or firm specific risk: risk that is unique to a particular industry or firm

Total risk = Systematic + Nonsystematic

6

Market riskMarket risk

Three terms that are used interchangeably are:◦Market risk◦Systematic risk◦Nondiversifiable risk

These refer to the part of risk that cannot be eliminated by diversification

7

Nonsystematic RiskNonsystematic Risk

Four terms used interchangeably:◦Nonsystematic risk◦Firm-specific risk◦Diversifiable risk◦Unique risk

These refer to the part of risk that can be eliminated by diversification

8

Portfolio RiskPortfolio Risk

To maximize the risk reduction benefit of diversification, combine securities whose returns have a low (or negative) correlation.

9

Efficient PortfolioEfficient Portfolio

An efficient portfolio is one that offers:◦The lowest risk for a given expected return◦Or, the highest expected return for a given risk

level

10

Extending Concepts to All Extending Concepts to All SecuritiesSecuritiesThe optimal combinations result in lowest

level of risk for a given returnThe optimal trade-off is described as the

efficient frontier, or investment opportunity set

Portfolios on the efficient frontier dominate all other portfolios of risky assets

11

E(r)E(r) The minimum-variance frontier of The minimum-variance frontier of risky assetsrisky assets

EfficientEfficientfrontierfrontier

GlobalGlobalminimumminimumvariancevarianceportfolioportfolio MinimumMinimum

variancevariancefrontierfrontier

IndividualIndividualassetsassets

St. Dev.12

Extending to Include Riskfree Extending to Include Riskfree AssetAsset

The optimal combination becomes linearThe optimal portfolio of risky assets (M)

combined with the riskless asset will dominate

Combinations of the risk-free asset and a risky asset or portfolio of risky assets is referred to as a CAL, or capital allocation line.

13

E(r)E(r)

CAL (GlobalCAL (Globalminimum variance)minimum variance)

CAL (B)CAL (B)CAL (M)CAL (M)

BB

MM

rfrf

MM rf&Mrf&M BB

GG

MM

BB

ALTERNATIVE CALSALTERNATIVE CALS

14

Dominant CAL with a Riskfree Dominant CAL with a Riskfree Investment Investment

CAL(M) dominates other lines -- it has the best risk/return tradeoff or the steepest slope. It is referred to as the Capital Market Line, or CML.

Regardless of risk preferences combinations of M & rf dominate

15