We propose a new valuation method for private equity investments. First, we construct a cash-flow replicating portfolio for the private investment, applying Machine Learning techniques on cash-flows on various listed equity and fixed income instruments. The second step values the replicating portfolio using a flexible asset pricing model that accurately prices the systematic risk in bonds of different maturities and a broad cross-section of equity factors. The method delivers a measure of the risk-adjusted profit earned on a PE investment and a time series for the expected return on PE fund categories. We apply the method to buyout, venture capital, real estate, and infrastructure funds, among others. Accounting for horizon-dependent risk and exposure to a broad cross-section of equity factors results in negative average risk-adjusted profits. Substantial cross-sectional variation and persistence in performance suggests some funds outperform. We also find declining expected returns on PE funds in the later part of the sample.