EMPIRICAL COPULAS FOR A DIVERSIFICATION SCHEME (PART 2)

How does the algorithm work when the matter is: DIVERSIFICATION?

Easy, You should learn some basic rules about HEDGING & DIVERSIFICATION. On the one hand, if your lead asset needs a hedge, try to look for an asset with a CORRELATION quite near to 1 or -1. On the other hand, if you want to invest the same money in two or more assets or anymore cash will be invested in assets different to your current portfolio standings, try to look for an asset with a CORRELATION near to 0. Hence, volatilities values by themselves are NOT CRUCIAL FIGURES.

A huge difference arising here are the shares percentages or weights of each asset. While when hedging, the hedge ratio is deployed and the position (either long or short) comes defined by the direction of the related correlation value; such a scheme does not apply when you are solved to diversify.

The latter situation demmands OPTIMIZATION or a predefined total return/total risk ratio to find out the weights of each element belonging to the ensemble. The position to be held comes defined by THE RELATIVE STRENGHT INDEX.

In the real world you wil never find a couple of assets with a perfect CORRELATION. But the indifference or neutral zone is given by the following interval: ]-0.5;0.5[

Hopefully, this example will explain COPULAS for a DIVERSIFICATION PROCESS.

An investor holds a portfolio labeled: Emerging Market Index (EMI), the investment pool has solved to diversify by entering a short position in a portfolio labeled: Technological Market Index (TMI) The Gaussian Correlation between EMI & TMI = -0.0277737277896621. The probabilities for both indexes are in the event of a success: EMI = 0.607216494845361 & TMI = 0.579381443298969. In the event of a default: EMI = 0.392783505154639 & TMI = 0.420618556701031. The investment pool concluded with a 50/50 position in both assets.

Copula value for a succes of such an ensemble? Copula value for a default of such an ensemble? Copula value for a succes of one portfolio and a default of the remainig one?

First, lets start by building the probability space:

(0.607216494845361*0.5 *0.579381443298969*0.5) = A

( 0.392783505154639*0.5 *0.420618556701031*0.5) =B

( 0.607216494845361*0.5 *0.420618556701031*0.5) =C

( 0.392783505154639*0.5 *0.579381443298969*0.5) =D =0.25. The logics here are a bit tricky since you have a short position, both values have been calculated assuming a long postion in the couple.

For the first scenario asked: C/0.25 =0.255406525666915

For the second question asked: D/0.25 = 0.227571474120523

For the last question: A+B/0.25 = 0.517022000212562

Finally, a few warnings. If by luck you are handling 2 assets with correlation = 0 or among the neutral zone; you have got 4 scenarios with near equal chances to happen. But if you are hedging, and your 2 assets have a correlation either equal to 1 or -1, you have to build 2 scenarios only and 2 scenarios are feasable to happen!