I'm trying to obtain a parallel shift in my efficient frontier based on the Merton 1972-parameters. As i think a picture tells you more than 1000 words here is what i tried:
The setting of my problem is the following:
Std.and Mean vector:
To derive an analytical solution for the efficient frontier (as i don't want to numerically search every time i try something) i obtained the following frontier:
I try to shift this efficient frontier to the right (e.g. increasing the volatility of all combinations of assets). Here is an illustration. The two green frontiers are what i get if i use the original market setting and if i shift the volatility of the efficient frontier by a fixed shift (here by 5% to illustrate my problem).
The blue line is the analytical frontier that i hope to get after changing the covariance matrix (after recalculating my Merton 1972-Parameters given the changed covariance matrix) such that it matches with the shifted efficient frontier (the right one in green).
I tried to shift the volatility-vector but this changed the curvature and the position of the blue efficient frontier but doesn't match the right green one.
My question is therfore: How can i manipulate the covariance matrix such that my blue efficient frontier matches the right green frontier?
Please let me know if something is not clear, i will provide details then. As always i appreciate your help and suggestions. Thomas
EDIT: I played around a bit and here is one thought: Minimizing the sum of squared differences by manipulating my Merton parameters gets me somehow close.
Any better ideas? :-/