Inside the Optimal Risky Portfolio

1
Inside the Optimal Risky Portfolio

• New Terms
• Co-variance
• Correlation
• Diversification
• Diversification the process of adding assets to
  a portfolio in order to reduce the risk of the
  overall portfolio

2
Types of Risk

• Systematic Risk This risk is part of the
  economic system (it is systemic!). It is
  non-diversifiable and is a/k/a market risk
• Non-Systematic Risk is firm specific. It can be
  diversified away
• How can we tell if adding assets to a portfolio
  will reduce the overall risk of the portfolio?
• Covariance
• Correlation

3
Diversification and Risk An Example

• Two stock funds
• Avers A fund made up of Pizza Companies
• Zagrebs A fund made up of beef producing
  companies
• What is the expected return on each fund?

4
Diversification and Risk An Example

• What is the individual deviation, variance and
  standard deviation for each fund?

5
Diversification and Risk An Example

• What would happen if these two assets were
  combined in a single portfolio?
• What is the Variance?
• What is the Standard Deviation?

6
Diversification and Risk An Example

• How do we measure the Covariance and Correlation
  Coefficient?
• The Covariance the product of the deviations

7
Diversification and Risk An Example

• Correlation Coefficient
• Covariance
• SDA SDZ
• If the Correlation Coefficient is lt 1, the
  addition of the asset has diversification
  benefits, regardless of the other risk/return
  characteristics of the asset!

8
Three Rules for Portfolios Made Up of Two Risky
Assets!

• The rate of return on the portfolio is a weighted
  average of the returns on the component
  securities, with the investment proportions as
  weights
• rp wara wzrz
• The same holds true for the Expected rate of
  return
• Rp waE(ra) wzE(rz)
• The variance of the rate of return on the two
  risky asset portfolio is
• V (waSDa)2 (wzSDz)22(waSDa)(WzSDz)Corraz