In this paper by placing risk assessment within the context of financial economics, we investigate a recent claim on the consistency of risk evaluations with respect to time horizons [7]. We compare the usual computations of some popular risk measures, the Value-at-Risk (VaR), the Tail-Value-at-Risk (TVaR), Wang's distortion-based risk measures [9] as well as general risk measures based upon general distortion functions, in the Black-Scholes model, using the actual probability distribution (of the underlying stock price stochastic process of portfolios where multiples asset are involved) with the computations using risk neutral probability distribution. We show that, the computations of these risk measures using actual probability distribution are not consistent, whereas they are under risk neutral probability.
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