We study the asymptotic behavior of the difference ∆ρα<sup>X,Y</sup> := ρα(X Y )−ρα(X) as α → 1, where ρα is a risk measure equipped with a confidence level parameter 0 < α < 1, and where X and Y are non-negative random variables whose tail probability functions are regularly varying. The case where ρα is the value-at-risk (VaR) at α, is treated in [20]. This paper investigates the case where ρα is a spectral risk measure that converges to the worst-case risk measure as α → 1. We give the asymptotic behavior of the difference between the marginal risk contribution and the Euler contribution of Y to the portfolio X Y . Similarly to [20], our results depend primarily on the relative magnitudes of the thicknesses of the tails of X and Y . We also conducted a numerical experiment, finding that when the tail of X is sufficiently thicker than that of Y , ∆ρα <sup>X,Y</sup> does not increase monotonically with α and takes a maximum at a confidence level strictly less than 1