Lecture Overview:

• Portfolio Theory
  • Risk preferences and risk aversion
  • One & Two risky assets
    • Benefits of portfolio diversification
  • Many risk assets
• One risky assets and risk-free asset
  • Capital allocation line (CAL)
  • Complete portfolio
• Many risky assets and a risk-free asset
  • Optimal CAL
  • Optimal risky portfolio
  • Optimal complete portfolio
• Capital Market Line (CML)

Risk Preferences and Risk Aversion

We assume investors are risk adverse, they don’t like risk.

<aside> ➡️ Trade-off between Risk = $\sigma$, and Return = $E(r)$

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Benefits of Diversification

• Market risk → Systematic/non-diversifiable risk
• Firm-specific risk → Non-systematic Risk, risk related to certain firms/industries
  • Can be eliminated by diversification

Two Risky Assets

• A portfolio of two risky assets, A and B.
• Expected returns: $E(r_A)~and~E(r_B)$
• Risks: $\sigma_A~ and~\sigma_B$
• Weights: $1=w_a+w_B$, can be negative if short selling.
• Correlation between A and B: $\rho_{AB}$, affected the portfolio risk