Pre-print, Working paper: Precautionary saving was first modelled by Leland (1968), Sandmo (1970) and Drèze & Modigliani (1972), and then later by Kimball (1993). The measure of savers' prudence in reaction to an exogenous income risk has been the subject of a large empirical literature, which has yet to reach a consensus. One approach uses simulation methods to calibrate theoretical models on real data, and concludes that about half of all saving is precautionary, while econometric work on the same problem produces much lower figures for the share of precautionary saving of between 1% and 20%. The main goal of this paper is to quantify the extent of precautionary saving by French savers who face risks regarding their future income. The empirical analysis is based on data from the INSEE "Patrimoine 2004" survey. The measures of income risk are subjective, and reported directly by the respondent with respect to the next five years. These cover the risk of job loss and other potential income movements. We find only a modest degree of precautionary saving in this French sample. While the results depend to an extent on the type of wealth under consideration, the measure of the risks faced, and the estimation method, the share of precautionary saving only rarely exceeds 10%.