Logafkast

Logafkast is a term used in finance to denote the logarithmic return of an asset, particularly in Scandinavian usage. It is defined as the natural logarithm of the price relative over a period: r_t = ln(P_t / P_{t-1}) = ln(P_t) − ln(P_{t-1}). When dividends or other distributions are not accounted for, logafkast is calculated from price data alone; for total-return analysis, price data are supplemented with cash flows.

Calculation and interpretation are straightforward: the logafkast for a period represents the continuously compounded rate of return. An example is P_t = 110 and P_{t-1} = 100, giving r_t = ln(110/100) ≈ 0.0953, or about 9.53%. This differs slightly from the arithmetic return r_arith = (P_t − P_{t-1}) / P_{t-1} = 0.10, illustrating the subtle distinction between log and simple percentage measures.

Logafkast has several notable properties. It is additive over successive periods: the sum of logafkast across consecutive intervals equals the logafkast over the combined period. This makes logafkast convenient for statistical modeling and for theoretical work, such as models assuming normally distributed logarithmic returns and for processes like geometric Brownian motion used in option pricing.

Applications and considerations. Logafkast is widely used in portfolio theory, econometrics, and risk management because it aligns with continuous compounding and often stabilizes variance in empirical studies. However, it is less intuitive for investors seeking a straightforward percentage change, and it requires nonzero prices and, when applicable, properly adjusted total-return data to include dividends and other cash flows.