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The return, or the holding period return, can be calculated over a single period.The single period may last any length of time. The overall period may, however, instead be divided into contiguous subperiods. This means that there is more than one time period, each sub-period beginning at the point in time where the previous one ended. In such a case, where there are
Example of the optimal Kelly betting fraction, versus expected return of other fractional bets. In probability theory, the Kelly criterion (or Kelly strategy or Kelly bet) is a formula for sizing a sequence of bets by maximizing the long-term expected value of the logarithm of wealth, which is equivalent to maximizing the long-term expected geometric growth rate.
The modified Dietz method [1] [2] [3] is a measure of the ex post (i.e. historical) performance of an investment portfolio in the presence of external flows. (External flows are movements of value such as transfers of cash, securities or other instruments in or out of the portfolio, with no equal simultaneous movement of value in the opposite direction, and which are not income from the ...
In probability theory, a log-normal (or lognormal) distribution is a continuous probability distribution of a random variable whose logarithm is normally distributed. Thus, if the random variable X is log-normally distributed, then Y = ln( X ) has a normal distribution.
The logarithm keys (LOG for base 10 and LN for base e) on a TI-83 Plus graphing calculator Logarithms are easy to compute in some cases, such as log 10 (1000) = 3 . In general, logarithms can be calculated using power series or the arithmetic–geometric mean , or be retrieved from a precalculated logarithm table that provides a fixed precision.
The rate of return on a portfolio can be calculated indirectly as the weighted average rate of return on the various assets within the portfolio. [3] The weights are proportional to the value of the assets within the portfolio, to take into account what portion of the portfolio each individual return represents in calculating the contribution of that asset to the return on the portfolio.
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The natural logarithm of x is generally written as ln x, log e x, or sometimes, if the base e is implicit, simply log x. [2] [3] Parentheses are sometimes added for clarity, giving ln(x), log e (x), or log(x). This is done particularly when the argument to the logarithm is not a single symbol, so as to prevent ambiguity.