Continuous returns, also known as logarithmic returns, represent the periodic rate of return on an investment assuming constant compounding over an infinite number of periods. In crypto investing, this metric offers a mathematically convenient and analytically useful way to model price movements, especially for assets exhibiting frequent price fluctuations. Unlike discrete returns, continuous returns are additive over multiple periods, simplifying multi-period return calculations.
Mechanism
The calculation of continuous returns employs the natural logarithm of the ratio of the ending price to the beginning price over a specified interval. This mathematical framework provides a symmetrical distribution of returns, which aligns more closely with standard statistical assumptions for many financial models, including options pricing. Systems processing continuous returns typically rely on high-frequency data to accurately capture intra-period compounding effects, essential for precise risk and performance measurement in volatile crypto markets.
Methodology
Financial analysts and quantitative strategists use continuous returns to perform various statistical analyses, including variance and covariance calculations, to assess risk and diversification benefits. This methodology is particularly valuable for portfolio optimization models and for comparing investment performance across different time horizons. Furthermore, continuous returns are fundamental in advanced quantitative trading strategies that model asset price dynamics as continuous-time stochastic processes, such as those applied in derivative pricing for crypto options.
The Kelly Criterion is a universal capital allocation system for maximizing geometric growth, adaptable to any instrument via its underlying logarithmic utility function.
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