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William P. Bengen is a retired financial adviser who first articulated the 4% withdrawal rate ("Four percent rule") as a rule of thumb for withdrawal rates from retirement savings; [1] it is eponymously known as the "Bengen rule". [2] The rule was later further popularized by the Trinity study (1998
Other authors have made similar studies using backtested and simulated market data, and other withdrawal systems and strategies. The Trinity study and others of its kind have been sharply criticized, e.g., by Scott et al. (2008), [2] not on their data or conclusions, but on what they see as an irrational and economically inefficient withdrawal strategy: "This rule and its variants finance a ...
In statistics, the 68–95–99.7 rule, also known as the empirical rule, and sometimes abbreviated 3sr, is a shorthand used to remember the percentage of values that lie within an interval estimate in a normal distribution: approximately 68%, 95%, and 99.7% of the values lie within one, two, and three standard deviations of the mean, respectively.
Dollar cost averaging: If an individual invested $500 per month into the stock market for 40 years at a 10% annual return rate, they would have an ending balance of over $2.5 million. Dollar cost averaging (DCA) is an investment strategy that aims to apply value investing principles to regular investment.
An early reference to the rule is in the Summa de arithmetica (Venice, 1494. Fol. 181, n. 44) of Luca Pacioli (1445–1514). He presents the rule in a discussion regarding the estimation of the doubling time of an investment, but does not derive or explain the rule, and it is thus assumed that the rule predates Pacioli by some time.
The following arguments are presented more completely in Chapter 1 of Barro and Sala-i-Martin [3] and in texts such as Abel et al.. [4]Let k be the capital/labour ratio (i.e., capital per capita), y be the resulting per capita output (= ()), and s be the savings rate.
For example, Konijn shows that for N = 59, the 95 percent confidence interval for the mean m is (m − Cs, m + Cs) where C = 4.447 × 1.006 = 4.47 (this is 2.28 times larger than the value found on the assumption of normality showing the loss on precision resulting from ignorance of the precise nature of the distribution).
[citation needed] One author uses the terminology of the "Rule of Average Conditional Probabilities", [4] while another refers to it as the "continuous law of alternatives" in the continuous case. [5] This result is given by Grimmett and Welsh [6] as the partition theorem, a name that they also give to the related law of total expectation.