Incremental VaR and VaR with background risk: traps and misinterpretations
نویسنده
چکیده
In recent ...nancial literature the Incremental Value-at-Risk (IVaR), i.e., the incremental e¤ect on VaR of adding a new instrument to the existing portfolio, has become a standard tool for making portfolio-hedging decisions. Since, calculating the exact IVaR value could be computationally very costly, approximate formulas have been developed. According to the most commonly used formula, IVaR is approximately equal to the current VaR multiplied by the beta coe¢cient of the candidate asset. A spontaneous question arises: could the beta sign be a qualitative indicator of a pro...table (non-pro...table) trade? Fallacy of this conjecture is proved. These results seem to cast shadows on the above approximate formula reliability even for small changes in portfolio composition. Then, VaR sensitivity to an exogenous undiversi...able zero-mean random perturbation (background-risk) is tested and hedging decision rules set out. Finally, a new multidimensional notion of VaR is proposed.
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