5002 words - 21 pages

TOPIC THREE PORTFOLIO THEORY

AND CAPITAL ASSET PRICING MODEL (CAPM)

Reading : BKM: Chapters 7&9 Pilbeam: Chapters 7&8

OUTLINE

Section I: The concept of portfolio and diversification Calculate portfolio expected return Measuring portfolio total risk: variance and standard deviation Market portfolio Measuring systematic risk: Beta Section II: Markowitz Portfolio Theory Efficient portfolio and Efficient Frontier Capital Asset Pricing Model - CAPM CAPM lines: CML and SML

PORTFOLIO

A portfolio is a collection of assets Diversification - Strategy designed to reduce risk by spreading the portfolio across many investments. Diversification ...view middle of the document...

1% and on Embell is 9.5%. The expected return on your portfolio is:

E( rp ) wD E( rD ) wE E( rE )

Expected Return (.60 3.1) (.40 9.5) 5.7%

TWO-SECURITY PORTFOLIO: RETURN ANOTHER EXAMPLE

Suppose you invest 70% of your portfolio in Kaplan and 30% in Morris. The expected return on your Kaplan stock is 15% and on Morris is 20%. The expected return on your portfolio is:

E( rp ) wK E( rK ) wM E( rM )

Expected Return (.70 15 ) (.30 20 ) 16.5%

MEASURING RISK

Unique Risk - Risk factors affecting only that firm. Also called “diversifiable risk”, “unsystematic risk”, “firm specific risk” Market Risk - Economy-wide sources of risk that affect the overall stock market. Also called “systematic risk.” Total Risk = Market Risk + Unique Risk. Total risk = Systematic risk + Unsystematic risk The standard deviation of returns is a measure of total risk For well-diversified portfolios, unsystematic risk is very small Consequently, the total risk for a diversified portfolio is essentially equivalent to the systematic (market) risk

MEASURING RISK

Portfolio standard deviation

Unique risk Market risk

0 5 10 15 Number of Securities

COVARIANCE AND CORRELATION

Portfolio risk depends on the correlation between the returns of the assets in the portfolio

Covariance and the correlation coefficient provide a measure of the way returns of two assets vary

TWO-SECURITY PORTFOLIO: RISK

2 2 2 2 2 wD D wE E 2 wD wE CovrD , rE p

2 D 2 E

= Variance of Security D

= Variance of Security E

Cov rD , rE = Covariance of returns for

Security D and Security E

TWO-SECURITY PORTFOLIO: RISK

Cov(rD,rE) = DEDE

D,E = Correlation coefficient of returns D = Standard deviation of returns for Security D E = Standard deviation of returns for Security E

2 p

2 2 wD D

2 2 wE E

2 wD wE CovrD , rE

2 p

2 2 wD D

2 2 wE E

2 wD wE DE D E

TWO-SECURITY PORTFOLIO: RISK EXAMPLE 1- CONT.

Suppose you invest 60% of your portfolio in Dell and 40% in Embell. The expected return on your Dell stock is 3.1% and on Embell is 9.5%. Dell’s standard deviation is 15.8% and of Embell’ standard deviation is 23.7%. If the correlation coefficient between Dell and Embell is 1.0. Calculate the portfolio variance and standard deviation.

2 p

2 2 wD D

2 2 wE E

2 wD wE DE D E

Portfolio Variance [(0.60)2 x(15.8)2 ] [(0.40)2 x(23.7)2 ] 2(0.40)(0.60)(1)(15.8)(23.7) 359.48 Standard Deviation 359.48 18.96%

TWO-SECURITY PORTFOLIO: RISK EXAMPLE 1- CONT.

Suppose you invest 60% of your portfolio in Dell and 40% in Embell. The expected return on your Dell stock is 3.1% and on Embell is 9.5%. Dell’s standard deviation is 15.8% and of Embell’ standard deviation is 23.7%. What If the correlation coefficient is 0.5. Calculate the portfolio and standard deviation.

2 p

2 2 wD D

2 2 wE E

2 wD wE ...

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