L6 - Single Index Model

Question 1

What are the parameters of an n-asset portfolio?

Answer 1

• n expected returns E[ri]
• n return standard deviations σi
• n(n-1)/2 correlations (or covariances)

Question 2

What is the single-index model?

Answer 2

• Macroeconomic factors include –> interest rates, inflation, business cycles
  
  • things that will effect the whole economy

Question 3

What are the important properties of the error term?

Answer 3

Question 4

How do you derive the variance of the Single Index model?

Answer 4

• Also called the total risk
• Total risk = Systematic risk + Firm–specific risk

Question 5

What are the risks we can derive from the SIM model?

Answer 5

• Equation 1 is the Single Index Model
  *

Question 6

How do you calculate the Correlation between to securities?

Answer 6

• The decrease in the dimensionality of the estimation is a big advantage of the SIM model
• Relationship (2) allows for the specialisation of effort in security analysis. How?
• However, this comes at a cost. The model assumes that the correlation across assets depends only on one factor.
  
  • the market factor
    
    • Disadvantage -> assume covariance between error terms of the securities (firm-specific risk) is 0, what if this isn’t the case? if positive we would be underestimating the correlation between the two securities (thus believe there is more a diversification benefit from investing in both ) thus giving them a higher weight in your portfolio, feeding in risk into the portfolio (variance we estimate is lower than it actually is)
    • This doesn’t occur under the mean-variance model when we know the correlation and covariance between the two securities
• It ignores other sources of uncertainty such as industry events, events that may affect many firms within an industry without substantially affecting the broad macroeconomy.
• The returns for any pair of assets co-vary only because they separately and independently covary with the market index (What does this imply when comparing HP with IBM?)

Question 7

What does the SIM model look like for a portfolio on n stocks?

Answer 7

• w = 1/n if the assets are equally-weighted in the portfolio

Question 8

How to use the SIM model to construct an optimal portfolio?

Answer 8