It is widely accepted that no obvious serial correlation exists, nor can exist in a perfect market, in the pattern of changes away from the trend in equity share prices; for, if it did, arbitrageurs would step in and make money by buying when positive changes were anticipated, and vice versa. Yet in the UK at least, such correlation does appear to exist in the prices of another, arguably equally important set of assets, namely housing. This note shows, on the basis of the leading UK house price indices, the evidence that this is so, and discusses how this pattern can continue without being arbitraged away. The tentative conclusion is that there are likely to be some individuals and firms who will be able to profit from the situation.