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

Sam, Rainsy (2026): From Volatility to Time: Toward a New Theory of Risk Based on Capital Recovery.

Abstract

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.

• Item Type: MPRA Paper
• Language: English
• Keywords: Potential Payback Period (PPP); Risk Theory; Capital Recovery; Time-Based Risk; SIRR; Asset Valuation; Expected Returns
• Subjects: D - Microeconomics > D8 - Information, Knowledge, and Uncertainty > D81 - Criteria for Decision-Making under Risk and Uncertainty; E - Macroeconomics and Monetary Economics > E4 - Money and Interest Rates > E43 - Interest Rates: Determination, Term Structure, and Effects; G - Financial Economics > G1 - General Financial Markets > G10 - General; G - Financial Economics > G1 - General Financial Markets > G11 - Portfolio Choice ; Investment Decisions; G - Financial Economics > G1 - General Financial Markets > G12 - Asset Pricing ; Trading Volume ; Bond Interest Rates

References

[1] Markowitz, H. (1952). Portfolio Selection. Journal of Finance. [2] Sharpe, W. F. (1964). Capital Asset Prices: A Theory of Market Equilibrium under Conditions of Risk. Journal of Finance. [3] Campbell, J. Y., & Shiller, R. J. (1988). The Dividend-Price Ratio and Expectations of Future Dividends and Discount Factors. Review of Financial Studies. [4] Fama, E. F., & French, K. R. (1988). Dividend Yields and Expected Stock Returns. Journal of Financial Economics. [5] Cochrane, J. H. (2011). Discount Rates. Journal of Finance. [6] Sam, R. (2025). The Potential Payback Period (PPP) and Return-Based Valuation. SSRN Working Paper / www.stockinternalrateofreturn.com