Portfolio Selection

Weighted Average of the expected returns of both assets

Forming portfolios can reduce risk

• The Variance of the portfolio is:
  $$\sigma_p^2 = \sum_{k=1}^{n} w_k^2 \sigma_k^2 + 2 \sum_{k=1}^{n-1} \sum_{i=k+1}^{n} w_k w_i \sigma_k,_j$$

• Common to many assets
• Not diversifiable
• Needs to be compensated for
• Is the only thing investors care about

• Specific to individual assets
• Is diversifiable
• Can be eliminated by forming portfolios

Portfolio minimizing risk for a given expected return

• The portfolio frontier
• Higher
• Lower

Two sub-portfolios:

• One of the only
• One of only

• When a risk-free asset is available, are linear combination of the and the
• It is the property