From Volatility to Time: Toward a New Theory of Risk Based on Capital Recovery

Traditional financial theory defines risk as the volatility of returns, a backward-looking statistical measure derived from price fluctuations. This article challenges that paradigm by proposing a forward-looking definition of risk based on the dynamics of capital recovery. Using the Potential Payback Period (PPP), we define risk as the uncertainty associated with the time required to recover invested capital. We provide both theoretical and empirical arguments supporting this redefinition. In particular, we show that the term structure of interest rates provides direct evidence that risk is fundamentally linked to time: for a given issuer, longer maturities require higher yields despite identical credit risk, reflecting greater uncertainty over longer horizons. We also formalize the relationship between recovery time and expected returns using a capital-doubling representation, establishing a direct correspondence between the PPP and implied returns. This framework leads to a unified interpretation of valuation, expected returns, and risk across asset classes, and suggests a reinterpretation of portfolio theory in terms of recovery horizons rather than volatility.