# Chapter 8 Diversification and Portfolio Management  Diversification – Eliminating risk  When diversification works  Beta – Measure of Risk in a Portfolio.

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Chapter 8 Diversification and Portfolio Management  Diversification – Eliminating risk  When diversification works  Beta – Measure of Risk in a Portfolio  Using Beta  Company: A Portfolio of Projects  Risk and Return in a Portfolio that is Not Well Diversified

Diversification – Eliminating Risk  Easy way to lower or eliminate risk  Choose risk-free investment  Get a lower return  Task – eliminate some risk without giving up return  Don’t put all your eggs in one basket  Spread out your investment across many assets  Calculate expected return and risk

Diversification – Eliminating Risk  Example, Mars Bars and Klingon  Four states of economy  Boom, Good, Normal, and Bust  Each with probability of state  Returns in each state for two assets  Calculating Expected Return  E(r) = probability of state x conditional return  Mars Bars Inc. = 10%  Klingon LTD = 10%

Diversification – Eliminating Risk  Calculate “risk” as the standard deviation of the conditional returns  σ = [Σ (probability i x (return i – average )2 ] 1/2  Mars Bars Inc. σ = 12.02%  Klingon LTD σ = 7.63%  Combining Mars Bars and Klingon (50/50)  Same return, 10%  Lower risk, 0.82%  Spreading investment lowers risk

When Diversification Works  Co-movement of stock returns  Correlation Coefficient  Covariance of two assets divided by their standard deviations (equation 8.2)  Positive Correlation  No benefit if perfectly positively correlated  Example Peat and Repeat Companies  Negative Correlation  Eliminate all risk if perfectly negatively correlated  Example Zig and Zag Companies

Beta – Measure of Risk in a Portfolio  Systematic Risk – risk you cannot avoid  Unsystematic Risk – risk you can avoid  Beta is measure of systematic risk  Standard Deviation is measure of both systematic and unsystematic risk  Diversification can eventually eliminate all unsystematic risk  Only systematic risk counts, so use β

Beta – Measure of Risk in a Portfolio  Using Beta for finding the risk of a portfolio  In a well diversified portfolio only systematic risk remains  Systematic risk of portfolio is weighted betas  Example 8.1 (Tom’s Portfolio)  Peat’s β = 0.8, Repeat’s β = 1.2, Zig’s β = 0.6, Zag’s β = 1.4  Equally weighted portfolio (Tom’s Portfolio)  Portfolio’s β = 1.0  1.0 = 0.25 x 0.8 + 0.25 x 1.2 + 0.25 x 0.6 + 0.25 x 1.4

Using Beta  Beta Facts  Beta of zero means no risk (i.e. T-Bill)  Beta of 1 means average risk (same as market risk)  Beta < 1, risk lower than market  Beta > 1, risk greater than market  Expected Return and Beta use asset weights in portfolio for portfolio e(r) and β  Expected Return = Σ w i x return i  Beta = Σ w i x β i

Using Beta  Beta also determines expected return of individual asset  Known, risk-free rate  Estimate, expected return on market  Each asset’s expected return function of its risk as measured by beta and the risk-reward tradeoff (slope of SML)

Company: A Portfolio of Projects  All companies are a portfolio of individual projects (or products and services)  Concept of portfolio helps explain  Viewing each project or product with different level of risk (project β) and contribution (expected return)  Different project or product combinations can lower overall risk of the firm  Projects plotting above the SML (buy)  Projects plotting below the SML (sell)

Risk and Return in a Portfolio that is Not Well Diversified  George Jetson investing choice  Only four assets in portfolio (equally weighted)  Expected return = 9.35%  Standard Deviation = 4.29%  Weighted average standard deviations of four assets = 4.4%  Little benefit from diversification  Portfolio needs more assets for benefits of diversification

Problems  Problem 1 – Expected Returns  Problem 2 – Variance and Standard Deviation  Problem 3 – Portfolio Expected Return  Problem 4 – Portfolio Variance and Standard Deviation  Problem 9 – Benefits of Diversification  Problem 11 – Beta of Portfolio  Problem 12 – Expected Return of Portfolio

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