Objective: This paper investigates the structural divergence between the distribution of annual investment returns (CAGR) and the resulting long-term accumulation of capital (Final Wealth). We seek to determine if the extreme concentration of wealth creation observed in various empirical studies—most notably the Bessembinder "4% Rule"—if it is a statistical possibility within an efficient, random market, or if it necessitates the existence of serial correlation (ρ) as a proxy for market inefficiency and investor skill.
Methodology: We employed Monte Carlo simulations (n=100,000) over 20-year horizons to model wealth outcomes under varying degrees of volatility (σ) and serial correlation (ρ). We specifically tested the "Random Walk Hypothesis" to see if a purely efficient market could replicate the lopsided wealth distributions found in various studies or persistent excessive returns observed in the University of Michigan’s longitudinal studies of the top 10% of investors and Bessembinder’s analysis of global equity markets.
Key Findings
1. The CAGR-Wealth Divergence: While 20-year CAGR distributions remain largely symmetrical, Final Wealth follows a log-normal distribution with positive skewness that "explodes" in the presence of serial correlation. At σ=0.15 and ρ=0.9, Wealth Skewness reaches 140.10.
2. The Rejection of Randomness: Simulations show that in a purely efficient random walk (ρ=0), the top 5% of stocks account for only for 30% of total wealth. This mathematically contradicts empirical data showing that 4% of stocks create 100% of net wealth, proving that market prices must possess structural persistence (correlation/momentum).
3. Skill as Persistence: Linking our findings to the Michigan Study, we demonstrate that the persistent outperformance of the top 10% of investors is only possible if their return streams are positively correlated. This correlation allows skilled participants to capture the non-random "Right Tail" of the market.
Conclusion: The extreme positive skewness of wealth is not an accident of luck, but a mathematical footprint of non-randomness. We conclude that successful active management, particularly in high-volatility segments, is the intentional exploitation of serial correlation. For an investor targeting higher return, wealth skewness acts as a "Success Multiplier," where the rewards for persistent outperformance are not linear, but exponential.
International Journal of Research in Finance and Management
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