What inherent limitations exist when using the Capital Asset Pricing Model (CAPM) to determine required rate of return for illiquid assets such as private equity?

The Capital Asset Pricing Model (CAPM) has several limitations when applied to illiquid assets like private equity. First, CAPM relies on a well-defined market portfolio to determine an asset's beta, which measures its systematic risk relative to the market. For private equity, a truly representative market portfolio is difficult to construct because private equity investments are not publicly traded and historical data is limited and often stale. Second, CAPM assumes that assets are easily tradable and priced in an efficient market. Illiquidity violates this assumption because private equity investments are difficult to buy or sell quickly without significantly affecting their price. This illiquidity adds a risk premium not fully captured by CAPM. Third, obtaining reliable historical return data for private equity is challenging. Valuations are often based on appraisals rather than market transactions, which can smooth out returns and underestimate volatility, leading to an inaccurate beta calculation. Fourth, CAPM assumes that investors can borrow and lend at the risk-free rate, which is often not the case for private equity investments, particularly for smaller investors. Finally, CAPM primarily focuses on systematic risk, neglecting idiosyncratic or firm-specific risks which are substantial in private equity. Due to these limitations, alternative models like the Fama-French three-factor model or multifactor models that incorporate liquidity premiums are often considered more appropriate for valuing illiquid assets.