Final_1.pdf
RAINING ON THE PARADE If you ever happen to make a presentation involving data analysis, here is a situation that you might enco ...
model and the y-axis is the AIC value. Note that the AIC value registers a minimum at four parameters. This is three AR paramete ...
Modeling Stock Prices The model that is most commonly assumed for stock price movement is called a log-normal process; that is, ...
Time Series 31 FIGURE 2.6A GE Series. 10 30 50 70 90 3.05 3.10 3.15 3.20 3.25 3.30 FIGURE 2.6B Returns. 0 Returns 0.08 2 4 6 8 1 ...
zero. If anything, the variance of the normal distribution two time steps away increases, and the plausible range of values that ...
FURTHER READING MATERIAL Time Series Diebold, Francis X. Elements of Forecasting. (Cincinnati, Ohio: South Western Col- lege Pub ...
APPENDIX Lag 1 Correlation in a MA(1) Series The variance of ytcan be calculated using the preceding formulas as Therefore, unli ...
The correlation is therefore Conditions under Which the Maximum Likelihood Is Equivalent to Minimizing Sum of Squares The substi ...
Examining the expression for logarithm of the likelihood, we see that the only variable term is. Note that this is the sum of sq ...
37 CHAPTER 3 Factor Models Introduction Factormodels are models that are used to explain the risk/return character- istics of as ...
Thus in the CAPM model there is a single explanatory factor and exposure value; namely, the market return and beta. A natural ex ...
ratio, the price/book ratio, attributes relating to the capital structure of the firm like debt/equity ratios, and the like. Eve ...
and therefore greater risk. This approach to measuring risk as the second moment of the return distributions was originally prop ...
var(r) = eVeT+ var(re) (3.7) whereVis the covariance matrix and eis the factor exposure vector. Also note from Equation 3.7 that ...
covariance matrix with the factor exposures and specific variances is suffi- cient for us to deduce the vector of expected facto ...
that the matrix has a square root; that is, V=B^2 for some B, where V,Bare matrices. Consider the situation where we are require ...
Nevertheless, in the absence of any information whatsoever, the covari- ance matrix serves as a critical piece of information to ...
portfolio is also along the same lines. If we are able to evaluate the net fac- tor exposure for the portfolio, then we can trea ...
(3.12) or ep=hX (3.13) That is, the exposure of a portfolio is given by the matrix product of the holdings vector and the exposu ...
(3.19) The formula to evaluate the variance may be easily adapted to evaluate the covariance between two portfolios. We will lea ...
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