  For products $P_N$ of $N$ random matrices of size $d \times d$, there is a
natural notion of finite $N$ Lyapunov exponents $\{\mu_i\}_{i=1}^d$. In the
case of standard Gaussian random matrices with real, complex or real quaternion
elements, and extended to the general variance case for $\mu_1$, methods known
for the computation of $\lim_{N \to \infty} \langle \mu_i \rangle$ are used to
compute the large $N$ form of the variances of the exponents. Analogous
calculations are performed in the case that the matrices making up $P_N$ are
products of sub-blocks of random unitary matrices with Haar measure.
Furthermore, we make some remarks relating to the coincidence of the Lyapunov
exponents and the stability exponents relating to the eigenvalues of $P_N$.
