Chapter 4 Appendix 1 Models of Asset Pricing. Copyright ©2015 Pearson Education, Inc. All rights reserved.4-1 Benefits of Diversification Diversification.

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Chapter 4 Appendix 1 Models of Asset Pricing

Copyright ©2015 Pearson Education, Inc. All rights reserved.4-1 Benefits of Diversification Diversification makes sense! ─ Don’t put all your eggs in one basket ─ Holding many assets can reduce overall risk Simple example ─ Frivolous Luxuries, Inc. does well in a strong economy ─ Bad Times Products thrives when the economy is weak ─ Some benefit to holding both?

Copyright ©2015 Pearson Education, Inc. All rights reserved.4-2 Benefits of Diversification By holding an equal investment in each stock, the return is exactly 10%. No risk! Returns to EconomyChance FrivolousBad Times Strong50%15%5% Weak50%5%15%

Copyright ©2015 Pearson Education, Inc. All rights reserved.4-3 Benefits of Diversification Important points about diversification: Diversification is almost always beneficial to the risk-averse investor Low correlation means more risk reduction from diversification

Copyright ©2015 Pearson Education, Inc. All rights reserved.4-4 Diversification and Beta Consider the return of a portfolio of n assets:

Copyright ©2015 Pearson Education, Inc. All rights reserved.4-5 Diversification and Beta Consider the return of a portfolio of n assets: We can show that the portfolio variance is:

Copyright ©2015 Pearson Education, Inc. All rights reserved.4-6 Diversification and Beta Consider the return of a portfolio of n assets: Important point for portfolio risk: the covariance of an asset with the portfolio is more important than the individual asset’s risk.

Copyright ©2015 Pearson Education, Inc. All rights reserved.4-7 Diversification and Beta This is where we develop the concept of beta – the ratio of the covariance of an asset to the portfolio’s variance:

Copyright ©2015 Pearson Education, Inc. All rights reserved.4-8 Diversification and Beta We can also think of the return on asset i as being made up of a market movement and a random movement:

Copyright ©2015 Pearson Education, Inc. All rights reserved.4-9 Diversification and Beta Also helps with intuition: A stocks beta tells us how sensitive the returns are to market movements. We can estimate betas be regressing stock returns on market returns.

Copyright ©2015 Pearson Education, Inc. All rights reserved.4-10 Systematic and Nonsystematic Risk Using Equation 5, we can decompose an asset’s risk into two components: 1.A market risk (systematic) component 2.Unique (nonsystematic) component

Copyright ©2015 Pearson Education, Inc. All rights reserved.4-11 Systematic and Nonsystematic Risk In a well-diversified portfolio, we can shows that: 1.Beta is average portfolio beta 2.Unique (nonsystematic) component goes to zero as n (# of assets) increases

Copyright ©2015 Pearson Education, Inc. All rights reserved.4-12 Capital Asset Pricing Model Figure 1 Risk Expected Return Trade-off

Copyright ©2015 Pearson Education, Inc. All rights reserved.4-13 Capital Asset Pricing Model Figure 2 Security Market Line

Copyright ©2015 Pearson Education, Inc. All rights reserved.4-14 Capital Asset Pricing Model CAPM shows that: An asset should be priced so that is has a higher expected return its systematic risk is greater. Nonsystematic risk should not be priced.

Copyright ©2015 Pearson Education, Inc. All rights reserved.4-15 Arbitrage Pricing Theory APT is an alternative to CAPM: APT assumes there may be several sources of systematic risk. Each factor affects asset returns.

Copyright ©2015 Pearson Education, Inc. All rights reserved.4-16 Arbitrage Pricing Theory APT is an alternative to CAPM: Expected returns should be higher for more exposure to a risk factor.