  We study the asymptotic behavior of the difference $\Delta \rho ^{X,
Y}_\alpha := \rho _\alpha (X + Y) - \rho _\alpha (X)$ as $\alpha \rightarrow
1$, where $\rho_\alpha $ is a risk measure equipped with a confidence level
parameter $0 < \alpha < 1$, and where $X$ and $Y$ are non-negative random
variables whose tail probability functions are regularly varying. The case
where $\rho _\alpha $ is the value-at-risk (VaR) at $\alpha $, is treated in
Kato (2017). This paper investigates the case where $\rho _\alpha $ is a
spectral risk measure that converges to the worst-case risk measure as $\alpha
\rightarrow 1$. 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 Kato (2017), 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 $Y$, $\Delta \rho ^{X, Y}_\alpha $ does not increase monotonically
with $\alpha$ and takes a maximum at a confidence level strictly less than $1$.
