'Intrinsic bubbles' (i.e., bubbles which are related only to fundament
als) are considered in a simple asset pricing model where fundamentals
follow an Ornstein-Uhlenbeck process. It is shown that such bubbles i
mply an explosive path for the expectation of the asset price. It is a
lso shown that the conditional variance of the asset price diverges in
finite time. Intrinsic bubbles therefore imply highly nonstationary b
ehaviour for the asset price even when the underlying fundamental to w
hich they are related is stationary.