Risk budgets are frequently used to allocate the risk of a portfolio by decomposing the total portfolio risk into the risk contribution of each component position. Many approaches to portfolio allocation use ex post methods for constructing risk budgets and take the variance as a risk measure. In this paper, however, we use ex ante methods to evaluate the component contribution to conditional value-at-risk (CVaR) and allocate risk. The proposed minimum CVaR concentration portfolio draws a balance between the investor's return objectives and the diversification of risk across the portfolio. For a portfolio invested in bonds, commodities, equities and real estate, we find that over the period from January 1984 to June 2010, the minimum CVaR concentration portfolio offers an attractive compromise between the good risk-adjusted return properties of the minimum CVaR portfolio and the positive return potential and low portfolio turnover of an equally weighted portfolio.