Asset Return Modelling Flashcards
Why sometimes does the inversion of Beta^TD^-1Beta fail?
The matrix is singular meaning their determinant is equal to zero. This happens if some of the columns in Beta are linearly dependent ex: one column is the sum of the other columns.
This means multiple solutions exist so solution is not unique
Why SMB is strongly negative for small company? sm gone wrong
Possible explanations could be:
* Other factors, such as sector, which we have omitted from the analysis.
* Sampling error in the historic data.
* Some other reason why Paprika is behaving like a large company in terms
of its historic returns.
How should one compare models
Goodness of fit - sum of squared differences - smaller the better.
Also consider the methods proposed if they make sense.
If weights are inversly proportional to variance what are the entries of D^-1
1/Var(company)
What would you expect from SMB interpretation
Positive for smaller firms and negative for bigger firms - measuring size by market cap
Those with the highest or lowest values of SMB should be in the six companies used to estimate the returns
Commenting on reliability of the estimated factor loadings - small data
Unlikely to eb reliable as we are trying to estimate from just X years of annual returns - alot of sampling error expected
Why does the Fama French model use quintiles and describe how method could be changed and its effects
Fama french use top and bottom quintiles however choice of quintiles is arbitrary so no reason to think that using more shares than that would invalidate results - for example could you the extreme 3/8 of the same instead and may even be better if less sampling.
Effects: would give different factor loadings, probably higher as the factor returns would reduce with adding more moderate shares
What is the characteristic polynomial
Finding the determinant of matrix
Lamda*Identity-Matrix
To find an eigenvector what equation needs solving
(Matrix-LamdaIdentity)Vector=0
How can you verify eigenvectors are orthogonal
Calculate E^TE to see that its a diagonal matrix - will be the identity if the eigenvectors are normalised.
What matrix A solves: MatrixE=EA
A is the diagonal matrix of eigenvalues if E is the matrix of eigenvectors
How to tell if model fit has improved
Has sum of squares reduced
How can you analyse the statistical factor models loadings
Asses in terms of sector or some sort of category and see if there is a pattern. That would indicate that the first, second etc factor of the statistical factor model is capturing that characteristic.
Is there any relation between factor loadings of Statistical model and SMB and HML factors?
NO
Know the weighted sum of squares and residual sum of squares formula in relation to the trace
