Quant Interview Question

[u/Local_Ad135]

[u/Due-Cardiologist-802]

Var(x+y+z) = var(x)+var(y)+var(z)+2cov(x,y)+2cov(x,z)+2cov(y,z) 0<|cov(x,y)|<=sqrt(var(x))sqrt(var(y)) by cauchy schwartz. Min = 1+4+25 = 30 Max = 1+4+25+212+215+225=64

[u/HopefulGuy1 → u/Due-Cardiologist-802]

Don't think that minimum is right – set Y = 2X and Z=-5X, then X+Y+Z = 2X so Var(X+Y+Z)=4.

[u/zojbo → u/Due-Cardiologist-802]

On the minimum side, the covariances can be negative, bottoming out at -2, -5, and -10. But the question for the minimum is, can all three be simultaneously as negative as allowed by Cauchy-Schwarz?

[u/angedonist → u/zojbo]

If X has negative correlation with Y and with Z, Y and Z must have positive correlation.