Search results
Results from the WOW.Com Content Network
In many cases the geometric mean is the best measure to determine the average growth rate of some quantity. (For example, if in one year sales increases by 80% and the next year by 25%, the end result is the same as that of a constant growth rate of 50%, since the geometric mean of 1.80 and 1.25 is 1.50.)
Exponential growth is a process that increases quantity over time at an ever-increasing rate. It occurs when the instantaneous rate of change (that is, the derivative) of a quantity with respect to time is proportional to the quantity itself. Described as a function, a quantity undergoing exponential growth is an exponential function of time ...
Compound annual growth rate ( CAGR) is a business, economics and investing term representing the mean annualized growth rate for compounding values over a given time period. [1] [2] CAGR smoothes the effect of volatility of periodic values that can render arithmetic means less meaningful. It is particularly useful to compare growth rates of ...
In logistic populations however, the intrinsic growth rate, also known as intrinsic rate of increase (r) is the relevant growth constant. Since generations of reproduction in a geometric population do not overlap (e.g. reproduce once a year) but do in an exponential population, geometric and exponential populations are usually considered to be ...
Using the Kelly criterion and based on the odds in the experiment (ignoring the cap of $250 and the finite duration of the test), the right approach would be to bet 20% of one's bankroll on each toss of the coin, which works out to a 2.034% average gain each round. This is a geometric mean, not the arithmetic rate of 4% (r = 0.2 x (0.6 - 0.4 ...
The economic growth-rates of countries are commonly compared using the ratio of the GDP to population (per-capita income). The "rate of economic growth" refers to the geometric annual rate of growth in GDP between the first and the last year over a period of time. This growth rate represents the trend in the average level of GDP over the period ...
Similar to the r > 0 case, the r < 0 convergence rate = ar 2m / (s - s m-1) = 1 - r 2, which is the same as the convergence rate of a non-alternating geometric series if its terms were similarly paired. Therefore, the convergence rate does not depend upon n or m and, perhaps more surprising, does not depend upon the sign of the common ratio.
The geometric average return is equivalent to the cumulative return over the whole n periods, converted into a rate of return per period. Where the individual sub-periods are each equal (say, 1 year), and there is reinvestment of returns, the annualized cumulative return is the geometric average rate of return.