In the Model table you can view and edit current parameters of the analytical model The financial market model which assumes that all assets collectively follow a random walk in continuous time. This means that distribution of logarithmic returns is normal, returns are serially uncorrelated, and variance of returns grows linearly with a time interval under consideration.. Here you also can find information related to the selected factor-based asset pricing model A regression model which imposes additional structure on the parameters of the Analytical model. This is achieved by imposing conditions on regression coefficients. The one-factor case corresponds to CAPM. Fama-French 3-factor model is another commonly used asset pricing model.. Analytical model parameters vector Mu Vector parameter of the Analytical model. Asset Mu can be viewed as the expected simple annual rate of return in the asset, as opposed to the expected geometric rate of return, measured by the expected growth rate. and the covariance matrix Symmetric matrix containing covariances between portfolio components annual returns. Its diagonal elements are equal to squared volatilities of corresponding assets., are calculated in the parameters estimation procedure. Fields related to the asset-pricing model are filled during portfolio construction (if you previously selected at least one factor An asset which plays the role of an independent variable in the context of Factor-based asset pricing models. in the Portfolio Construction dialog).
Below you can find the detailed description of the fields in the MODEL table. Fields available for editing are market with green.
Sample Statistics here you can find parameters of the historical sample contained in the LogReturns table as well as current estimates of vector Mu and volatilities.
Start Date the first date in the historical sample for the selected portfolio component
End Date the last date in the historical sample for the selected portfolio component
Number of Observations sample size for the selected portfolio component
Mu this field contains assets Mu Vector parameter of the Analytical model. Asset Mu can be viewed as the expected simple annual rate of return in the asset, as opposed to the expected geometric rate of return, measured by the expected growth rate.
Volatility this field contains assets volatilities The most common measure of risk. Defined as annualized standard deviation of returns.
Factor Model Statistics contains fields related to portfolio multi-factor analysis. For further details see Factor-based asset pricing models section in Theory Help.
In the text below the term "asset Meaning of this term depends on the context. As a rule, it denotes any portfolio component. But in the context of Factor-based asset pricing models the term "asset" stands for a dependent variable as opposed to Factor, which stands for an independent variable. In the latter case the more explicit term "ordinary asset" is used sometimes." stands for a dependent variable of the linear regression equation.
Instantaneous Alpha contains free terms of the linear regression equation. Asset pricing models assume that these values are equal to zero.
t-Statistics for Instantaneous Alpha t-statistics is used to test the hypothesis that linear regression coefficients are equal to zero. Here t-statistics is used to check that the corresponding instantaneous alpha is zero. If t-statistics value exceeds 3, then there is a high (more then 99%) probability that the corresponding instantaneous alpha is non-zero.
Standard Error of Forecast contains standard deviations of the regression residuals.
R^2 contains determination coefficients statistics which takes values between 0 and 1. The more it is close to 1, the higher is the explanation power of the current asset pricing model against the corresponding asset.
Assets Mu, implied by the Model contains values of Mu Vector parameter of the Analytical model. Asset Mu can be viewed as the expected simple annual rate of return in the asset, as opposed to the expected geometric rate of return, measured by the expected growth rate. implied by the assumptions of the current asset pricing model.
Betas contains matrix of betas (sensitivity coefficients) of the portfolio components against each of factors.
t-Statistics for Betas t-statistics is used to test the hypothesis that linear regression coefficients are equal to zero. Here t-statistics is used to check that the corresponding beta is zero. If t-statistics value exceeds 3, then there is a high (more then 99%) probability that the corresponding beta is non-zero.
For further details see Factor-based asset pricing models section of Theory Help.
Matrices
Covariance Matrix contains the covariance matrix Symmetric matrix containing covariances between portfolio components annual returns. Its diagonal elements are equal to squared volatilities of corresponding assets. of portfolio components. Since the covariance matrix is necessarily symmetrical, you can edit only its lower part. elements which lie below
Volatility Matrix contains the volatility matrix Upper triangular matrix such that its square is equal to the Covariance matrix. Computed from the covariance matrix using Cholessky decomposition. Used in the equations of the Analytical model. of portfolio components (don't mix it up with the volatilities vector). From the formal point of view, the volatility matrix is defined as a lower triangular matrix such that its square is equal to the covariance matrix. The volatility matrix is resulted form the covariance matrix using the Cholesky decomposition.
Correlation Matrix contains the correlation matrix Symmetric matrix containing correlations between portfolio components returns. Its diagonal elements are equal to 1. of portfolio components.
Covariance Matrix implied by the Model contains the covariance matrix calculated under the assumptions of the selected asset pricing model A regression model which imposes additional structure on the parameters of the Analytical model. This is achieved by imposing conditions on regression coefficients. The one-factor case corresponds to CAPM. Fama-French 3-factor model is another commonly used asset pricing model..
To unambiguously define the analytical model you need to set Mu vector and the covariance matrix. When setting the covariance matrix you have the following options:
Set the covariance matrix itself.
Set the volatility matrix Upper triangular matrix such that its square is equal to the Covariance matrix. Computed from the covariance matrix using Cholessky decomposition. Used in the equations of the Analytical model..
Set the correlation matrix Symmetric matrix containing correlations between portfolio components returns. Its diagonal elements are equal to 1. and the volatility The most common measure of risk. Defined as annualized standard deviation of returns. vector.
Important! When changing any of these fields all others are recalculated automatically. For instance, if you change the volatility matrix, then the covariance matrix, correlation matrix, and volatility vector will be immediately recalculated.
To switch between Statistics Tables, Covariance Matrix, Volatility Matrix, Correlation Matrix and (possibly) Model-implied Covariance Matrix you should use the corresponding buttons at the top of the window.
If running SmartFolio under Excel 2007, then incell databars and icons are used to better visualize data in the table. You can turn on/off this by repeatedly clicking the Data Bars On/Off button. Below are some notes on conditional formatting:
Orange bars correspond to naturally nonnegative statistics such as risk measures. However, in some cases such statistics can become negative, as in the case of Contribution to Portfolio Risk.
Statistics that relate to measures of return are shown with Green for positive values and Red for negative ones.
All other statistics including matrix values are shown with Blue and Red respectively.
4 rating icons are used to indicate the significance levels of some statistics in the Factor Model Statistics subtables according to the following rules:
Icon with 1 filled column - t-value between 0 and 1
Icon with 2 filled columns - t-value between 1 and 2
Icon with 3 filled columns - t-value between 2 and 3
Icon with 4 filled columns - t-value above 3
