From this formula, it is clear that calculation of an incremental VaR, i.e. the effect of a new position to the existing portfolio VaR requires us to compute the VaR of the updated portfolio as well as the VaR of an existing portfolio. However, there is a shortcut. In particular, we...
Show that var(x+y) = var(x) + var(y) + 2 cov(x,y). Variance: A second-order central moment is called the measure of dispersion is known as a variance. In the question, we will use the expected formula of variance to prove the result. ...
Suppose that {eq}\displaystyle E(X) = 5,\ Var(X) = 5,\ E(Y) = 4,\ Var(Y) = 4 {/eq}, and {eq}Cov (X,\ Y) = 1 {/eq}. a. What is Correlation of {eq}(X,\ Y) {/eq}? b. What is {eq}...
建立长期均衡模型 ## Call:## lm(formula = PPI ~ CPI, data = data)### Residuals:## Min 1Q Median 3Q Max## -3.6930 -0.5071 -0.0322 0.4637 3.2085### Coefficients:## Estimate Std. Error t value Pr(>|t|)## (Intercept) -0.03678 0.06428 -0.572 0.568## CPI 0.54389 0.10176 5.345 2.61...
% Here we distribute the lagged y data into the Z matrix so it is % conformable with a beta_t matrix of coefficients. Z = zeros((t-tau-p)*M,K); for i = 1:t-tau-p ztemp = eye(M); for j = 1:p xtemp = ylag(i,(j-1)*M+1:j*M); ...
(v,z,w,backend='GPU')returntorch.view_as_complex(r)defconvert_data(*tensors,device='cuda'):""" Prepare tensors for backwards pass """tensors=tuple(t.to(device)fortintensors)fortintensors:ift.is_leaf:t.requires_grad=Truet.retain_grad()returntensorsdefdata(B,N,L):w=torch.randn(B...
We will say that the continuous functionU:X∞→Rrepresents “⪰” if for all(x0,x1,x2,…),(y0,y1,y2,…)∈X∞ (x0,x1,x2,…)⪰(y0,y1,y2,…)⇔U(x0,x1,x2,…)≥U(y0,y1,y2,…). A functionUsatisfying the above condition is said to bea utility function. In the pr...
Beyond this limit, formula\left(1\right)does no longer applies, because when the posterior probability reduces to the prior, the empirical test, whose outcome is synthetized byp, should be considered non-informative. Coordinates displayed on the top curve in Fig.4reveal that setting the threshold...
Var(Y)=Var(E(Y|X))+E(Var(Y|X)) This formula is known as the law of total variance. It is important to mention that the termsE(Y|X)andVar(Y|X)are functions of the random variable X. To find the values ofE(Y...
and Y.L.; writing—review and editing, X.Z. and D.W. All authors have read and agreed to the published version of the manuscript. Funding This work was support by the Scientific and Technological Innovation Ability Foundation of the Beijing Academy of Agricultural and Forestry Sciences (KJCX...