In spite of the importance of having a figure for the domestic average Cost of Capital to base the estimates of the discount rates used in a number of long-term investments, the fact is that Portugal does not yet know with confidence its own value. Part of the answer might be attached to the number of profound impacts that affected and disturbed its Capital Markets during the Twentieth Century, in particular the break introduced by the Carnation Revolution in 1974. This paper translates both a test to the methodology necessary to make such an estimate under the Portuguese constraints, and also a first estimate of such a figure. From the daily data available for the quotations of shares listed in the Lisbon Stock Exchange, a time series of a comprehensive index is constructed covering on a weekly basis (Wednesdays) a time sample of 31.5 years, from January 1978 to June 2009. It also constitutes the first part of a 3-year project intended to study the entire Twentieth Century and to produce an estimate for the Cost of Capital comparable to the values included in the 2002 book “The Triumph of the Optimists” authored by Dimson, March and Staunton. Although the output parallels traditional UK and USA figures, the Portuguese estimate for the Equity Return Premium is around 8%.