Lecture Summary on Capital Market Line and Market Portfolio

Key Concepts

Risk-Free Rate and Minimum Variance Frontier

• Risk-Free Rate: Considered as 5%
• Minimum Variance Frontier: Plot capital market line tangent to it
• Market Portfolio: Point of tangency with 15% expected return and 20% standard deviation

Market Price of Risk

• Formula: (Expected Return on Market - Risk-Free Rate) / Standard Deviation of Market
• Calculation: (0.15 - 0.05) / 0.2 = 0.5
• Interpretation: For each unit of risk, expected return increases by 0.5 units (probabilistically, not deterministically)

Portfolio Weightings

Basics

1. 100% in Risk-Free Asset
   • Expected Return: 5%
   • Std. Deviation: 0%
2. 100% in Market Portfolio
   • Expected Return: 15%
   • Std. Deviation: 20%

Mixed Weightings

• Intermediate calculations using given market price of risk
• Example: 50/50 mix would have 10% expected return and 10% standard deviation
• Formula use: Verify using exact weightings like 75/25

Leverage and Borrowing

Leveraging with Different Weights

• 25% Leverage: Borrowing at risk-free rate
  • Expected Return: 17.5%
  • Std. Deviation: 25%
• 50% Leverage: Borrowing at risk-free rate
  • Expected Return: 20%
  • Std. Deviation: 30%
• 100% Leverage: Borrowing at risk-free rate
  • Expected Return: 25%
  • Std. Deviation: 40%

Lending and Borrowing at Different Rates

Borrowing at Higher Rate (e.g., 7%)

• Slope of Capital Market Line gets flatter
• Expected Return Calculation: (Expected Return - Borrowing Rate) / Market Std. Deviation
• Example: Borrow 75%
  • Expected Return: 21%
  • Std. Deviation: 35%
• Comparison: Same risk but lower returns due to higher cost of borrowing

Recap

• Using Two Assets: Simplified investment strategy using market portfolio and risk-free rate
• Adjustments: Based on individual risk tolerance through leverage and borrowing
• Cost of Borrowing: Higher borrowing rates reduce returns without affecting market volatility