Portfolio Weights

1
Portfolio Weights

• Portfolio Weights
• The fraction of the total investment in the
  portfolio held in each individual investment in
  the portfolio
• The portfolio weights must add up to 1.00 or 100.

2
Portfolio Return

• Then the return on the portfolio, Rp , is the
  weighted average of the returns on the
  investments in the portfolio, where the weights
  correspond to portfolio weights.

3
Portfolio Risk

• By combining stocks into a portfolio, we reduce
  risk through diversification.
• The amount of risk that is eliminated in a
  portfolio depends on the degree to which the
  stocks face common risks and their prices move
  together.
• To find the risk of a portfolio, one must know
  the degree to which the stocks returns move
  together.

4
Portfolio Risk Depends on

• Covariance
• The expected product of the deviations of two
  returns from their means
• Correlation
• A measure of the common risk shared by stocks
  that does not depend on their volatility

5
Variance of a portfolio
6
The Effect of Correlation

• Correlation has no effect on the expected return
  of a portfolio. However, the volatility of the
  portfolio will differ depending on the
  correlation.
• The lower the correlation, the lower the
  volatility we can obtain. As the correlation
  decreases, the volatility of the portfolio falls.
  
• The curve showing the portfolios will bend to
  the left to a greater degree as shown on the
  next slide.

7
Effect on Volatility and Expected Return of
Changing the Correlation
8
Portfolio Beta

• The beta of a portfolio is the weighted average
  beta of the securities in the portfolio.

9
Beta and the Required Return
10
The Security Market Line

• In equilibrium, all assets and portfolios must
  have the same reward-to-risk ratio and they all
  must equal the reward-to-risk ratio for the
  market

11
The Security Market Line

• The security market line (SML) is the
  representation of market equilibrium
• The slope of the SML is the reward-to-risk ratio
  (E(RM) Rf) / ?M
• But since the beta for the market is ALWAYS equal
  to one, the slope can be rewritten
• Slope E(RM) Rf market risk premium

12
The Capital Asset Pricing Model (CAPM)

• The capital asset pricing model defines the
  relationship between risk and return
• E(RA) Rf ?A(E(RM) Rf)
• If we know an assets systematic risk, we can use
  the CAPM to determine its expected return
• This is true whether we are talking about
  financial assets or physical assets

13
The Security Market Line

• There is a linear relationship between a stocks
  beta and its expected return (See figure on next
  slide). The security market line (SML) is graphed
  as the line through the risk-free investment and
  the market.
• According to the CAPM, if the expected return and
  beta for individual securities are plotted, they
  should all fall along the SML.

14
SML
15
Estimating Beta from Historical Returns

• Beta corresponds to the slope of the best-fitting
  line (Characteristic Line) in the plot of the
  securitys excess returns versus the market
  excess return.

16
Total vs Systematic Risk

• Consider the following information
• Standard Deviation Beta
• Security C 20 1.25
• Security K 30 0.95
• Which security has more total risk?
• Which security has more systematic risk?
• Which security should have the higher expected
  return?