We study the asymptotic behavior of the difference
as
, where
is a risk measure equipped with a confidence level parameter
, and where
X and
Y are non-negative random variables whose tail probability functions are regularly varying. The case where is the value-at-risk (VaR) at
α, is treated in [
1]. This paper investigates the case where
is a spectral risk measure that converges to the worst-case risk measure as
. 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 [
1], our results depend primarily on the relative magnitudes of the thicknesses of the tails of
X and
Y. Especially, we find that
is asymptotically equivalent to the expectation (expected loss) of
Y if the tail of
Y is sufficiently thinner than that of X. Moreover, we obtain the asymptotic relationship
as
, where
is a constant whose value likewise changes according to 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,
does not increase monotonically with
α and takes a maximum at a confidence level strictly less than 1.