L10 - Factor Model Flashcards
1
Q
What is the problem with the Markowitz model?
A
- Theoretically a beautiful setup
- In the real world we are faced with empirical challenges
- – The quality of input parameters needs to be high
- Example from book. Given 50 stocks we have
- – 50 estimates of expected returns
- – 50 estimates of variances
- – 1225 estimates of covariances (2500 (CVM) - 50(Var)/ 2 –> only want the triangle part
- ■ The number of estimates needed increases rapidly with the number of stocks
- ■ Bad estimates can lead to horrible portfolio allocation decisions
2
Q
What is a simplification we can use of Markowitz model?
A
- The single factor model
- Idea: Simplify the economy such that an asset’s return is characterized by:
- – Its expected return
- – Two sources of uncertainty: ■
- systemic risk-factor which is common for all assets (m)
- A risk component which is specific only to the specific asset (𝑒𝑖 )
3
Q
What is the variance and covariance of the signal Factor model?
A
4
Q
Empirically how much easier is the Single Factor model to compute than Markowitz?
A
- Parameters to estimate for 50 stocks:
- – 50 estimates of expected returns (difficult to estimate) –> time series average?
- – 50 estimates of firm-specific variances (easy to estimate) –> ARCH and GARCH models
- – 1 estimate of factor variance (easy to estimate)
- usually the US stock market
- – 50 estimates of factor loadings (How to estimate?)
COMPARE TO:
- Example from book. Given 50 stocks we have
- – 50 estimates of expected returns
- – 50 estimates of variances
- – 1225 estimates of covariances
*
5
Q
How do we choose the systemic risk factor in the single factor model?
A
- usually, pick a stock market
- also called the Index Model
6
Q
What does the variance tend to when implementing diversification into the Index model?
A
- have 1/n because it is equally weighted in the portfolio
