A dual-risk theory of valuation separating market-based discounting from expectational distortion

This paper develops a dual-risk valuation theory that extends the classical discounted cash flow model by adding an analytically distinct source of risk: expectational risk. We model expectational risk through the valuation ratio K, which measures systematic distortion in projected cash flows (expectational distortion), and study its interaction with the benchmark discount rate c (market-based discounting). The objective is to embed ex-ante alpha into valuation as a structural quantity rather than treat it as an ex-post residual. Methodologically, we build an analytical framework that defines the gain of capital g = f (c, K) and the effective cost of capital cef as the internal rate that reconciles distorted expectations with fair value. We derive closed-form conditions under which discounting ceases to be equivalent to expected return, characterize the horizon behavior of cef , and establish asymptotic results for the per-period equivalent of g, denoted γ. The main findings show that K and c jointly determine valuation outcomes, with g providing a forward-looking measure of ex-ante alpha whenever systematic distortion persists. We prove conditions where cef ̸ = c, identify regimes in which short and medium horizons are most sensitive to K, and show that γ → 0 as the horizon lengthens, which clarifies when the expectational distortion captured by K becomes irrelevant for intrinsic value. These results reframe alpha as a structural feature of biased expectations and separate the two risk primitives: market opportunity cost (market risk) and expectational distortion (expectational risk). The framework generalizes DCF to incorporate systematic errors in cash-flow projections and yields practical guidance for enterprise valuation.