Single index model

Question 1

The quality of the … … determines the success of models

Answer 1

The quality of the input list determines the success of models, because it provides for more accurate predictions.

Question 2

Why is it easier to transfer to a single index model?

Answer 2

It is easier to transfer to a single index model because the SIM requires a smaller number of estimates.

Question 3

What is alpha?

Answer 3

Alpha is the excess return of a security when the expected return of the market is equal to zero:

Question 4

What is beta?

Answer 4

Beta is the security’s sensitivity to the index, often quantified as it’s movement resulting from a 1% move in the market

Question 5

What is e?

Answer 5

e is the random, firm-specific component of the return.

Question 6

What is the key property of e?

Answer 6

ei = 0

Question 7

BiE(Rm) is known as the … … premium because it derives from the …

Answer 7

BiE(Rm) is known as the systematic risk premium because it derives from the risk premium that characterises the entire market.

Question 8

Alpha is a … premium

Answer 8

Alpha is a non-market premium, as it is asset-specific

Question 9

Total risk is … risk + … risk

Answer 9

Total risk is systematic risk + Firm specific risk

Question 10

Covariance between two securities is due to…

Answer 10

Covariance between two securities is due to the systematic risk that affects both of them

Question 11

How can we formulaically calculate the correlation between returns of asset I and j, using their correlation to the market?

Answer 11

We can use the respective correlations of asset I and j to the market to compute their correlation between each other, by multiplying the two market correlations:

Question 12

What is the formula for the amount of single index model estimates and where does this come from?

Answer 12

The formula for the amount of estimates required in the single index model is 3n+2, and this comes from the fact that for the model we need:
N estimates of alpha 
N estimates of beta 
N estimates of e 
1 estimate of E(rm)
1 estimate of Var(M)

Question 13

What is a costly assumption of the index model?

Answer 13

A costly assumption of index models, is that the main determinant of return of an asset is the movement of the market and it’s sensitivity to it. It, for example, ignores the influence of industry events.

Question 14

What are industry events?

Answer 14

Industry events are events that affect many firms within specific sectors, without substantially affecting the broad macroeconomy

Question 15

The portfolio alpha is the … … of asset betas

Answer 15

The portfolio Alpha is the weighted average of asset alphas

Question 16

The portfolio beta is the … … of asset betas

Answer 16

The portfolio beta is the weighted average of asset betas

Question 17

Non-systematic risk is removed by …

Answer 17

Non-systematic risk is removed by diversification. If any two asset returns are less than perfectly correlated, then there will be a benefit to be gained from diversification between them.

Question 18

The risk of the broad market index is almost entirely …

Answer 18

The risk of the broad market index is almost entirely systematic

Question 19

In the single index model, the optimal portfolio is a combination of the … and … portfolio, denoted by … and …

Answer 19

In the single index model, the optimal portfolio is a combination of the Active and passive portfolio, which are denoted by A (active) and P (Passive).

Question 20

The full Markowitz model is better in principle, but:

Answer 20

• The full covariance model requires estimation of thousands of terms
• Cumulative estimation error may result in a model that is actually inferior
• The single index model is practical and decentralises macro and security analysis