What are index models?
They build on the fact that positive covariance among security returns arise from common economic forces that affect the fortunes of most firms and decompose into system wide versus firm-specific sources
What are advantages of the single index model?
- A lot less computation and estimation is required than in Markowitz
- Helps with specialization of analysts into industries
What is the disadvantage of the single index model?
The hidden assumption to separate total risk into a single macro factor plus idiosyncratic risk
How is the total risk of the portfolio based?
- Systematic component
- Non-Systematic component
What is the first step of portfolio construction using the single-index model?
Preparation of the input list:
1. Choose an index that captures your factor
2. Use statistical analysis to estimate for n assets
3. Compute the expected returns of each security without any contribution from security analysis
4. Use security analysis to develop security-specific alphas and thus forecasts of the expected return for each security
What is the second step of constructing a single-index model?
Splitting the funds invested into a passive market index and a active portfolio
What is the Treynor-Black procedure?
- Compute the initial position for each asset in the active portfolio
- Scale those initial positions to force portfolio weights to sum to 1
- Compute the alpha of the active portfolio
- Compute the idiosyncratic risk of the active portfolio
- Compute the beta of the active portfolio
- Compute the initial position of the active portfolio
7 Adjust intitial position in the active portfolio - Get final weights in the passive portfolio and securities for optimal risky portfolio
- Compute the expected excess return of the optimal risky portfolio
- Compute the variance of the optimal risky portfolio
What is the third step of building a single-index model?
Constructing the optimal complete portfolio by mixing a risk-free asset with the optimal risky portfolio
