  We study the ratio between the variances of work output and heat input,
$\eta^{(2)}$, for a class of four-stroke heat engines which covers various
typical cycles. Recent studies on the upper and lower bounds of $\eta^{(2)}$
are based on the quasistatic limit and the linear response regime,
respectively. We extend these relations to the finite-time regime within the
endoreversible approximation. We consider the ratio $\eta_{\text{MP}}^{(2)}$ at
maximum power and find that the square of the Curzon-Ahlborn efficiency,
$\eta_{\text{CA}}^2$, gives a good estimate of $\eta_{\text{MP}}^{(2)}$ for the
class of heat engines considered, i.e., $\eta_{\text{MP}}^{(2)} \simeq
\eta_{\text{CA}}^2$. This resembles the situation where the Curzon-Ahlborn
efficiency gives a good estimate of the efficiency at maximum power for various
kinds of finite-time heat engines. Taking an overdamped Brownian particle in a
harmonic potential as an example, we can realize such endoreversible small heat
engines and give an expression of the cumulants of work output and heat input.
The approximate relation $\eta_{\text{MP}}^{(2)} \simeq \eta_{\text{CA}}^2$ is
verified by numerical simulations. This relation also suggests a trade-off
between the efficiency and the stability of finite-time heat engines at maximum
power.
