Discount factor and Frequency distribution: Difference between pages

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(DF).  
''Statistics.''
A description of the relative number of times that given outcomes have occurred, or are expected to occur, relative to the whole population.  


'''1.'''
Three important frequency distributions are the Normal distribution, Lognormal distribution, and Leptokurtic distribution, described below. All three of these types of distribution are used in practice as approximations to model the distributions of  financial variables.


Strictly, the number less than one which we multiply a future cash flow by, to work out its present value as:
''Normal distributions'' are usually the simplest approximations to work with, and are assumed by - for example - many Value at Risk analysis models and measures. A theoretical shortcoming of using normal distributions as a model is that they assume an infinitely large downside potential including negative prices; whereas many financial variables - such as asset prices - cannot in practice fall so far as to become negative.


PV = DF x future cashflow.
''Lognormal distributions'' usually describe better the theoretical range of financial variables such as traded equity prices, which theoretically have no upside limit but which cannot fall below zero.


In practice, observed financial returns are usually more closely approximated by ''leptokurtic distributions'', with a greater frequency both of very high and of very low returns, than predicted by the comparable normal distribution. So in risk analysis, if a population distribution is assumed to be normal, but is in reality leptokurtic, downside risk will be understated.


The periodic discount factor is calculated from the periodic yield as:
Other common types of frequency distribution include Binomial distributions and Poisson distributions.


DF = (1 + periodic yield)<SUP>-1</SUP>
== See also ==
 
* [[Binomial distribution]]
 
* [[Cumulative frequency distributions]]
Commonly abbreviated as DF(n,r) ''or'' DF<SUB>n</SUB>
* [[Decile]]
 
* [[Frequency curve]]
 
* [[Frequency polygon]]
where
* [[Grouped frequency distribution]]
 
* [[Histogram]]
n = number of periods, ''and''
* [[Leptokurtic frequency distribution]]
 
* [[Lognormal frequency distribution]]
r = periodic cost of capital.
* [[Normal frequency distribution]]
 
* [[Percentile]]
 
* [[Poisson distribution]]
 
* [[Probability]]
'''''Examples'''''
* [[Value at risk]]
 
For example, when the periodic cost of capital (r) = 6% and the number of periods in the total time under review (n) = 1, then:
 
Discount factor = (1+r)<sup>-n</sup>
 
= 1.06<sup>-1</sup>
 
= '''0.9434'''
 
 
 
The greater the time delay, the smaller the Discount Factor.
 
For example, when the periodic cost of capital = 6% as before, but the number of periods delay increases to 2, then:
 
Discount factor = (1+r)<sup>-n</sup>
 
= 1.06<sup>-2</sup>
 
= '''0.8890'''
 
''(A smaller figure than the 0.9434 we calculated previously for just one period's delay.)''
 
 
'''2.'''


Loosely and historically, the yield or cost of capital used for the purpose of calculating Discount Factors. 
For example the 6% rate applied in definition 1. above.
== See also ==
* [[Annuity factor]]
* [[Compounding factor]]
* [[Factors]]
* [[Present value]]

Revision as of 14:19, 23 October 2012

Statistics. A description of the relative number of times that given outcomes have occurred, or are expected to occur, relative to the whole population.

Three important frequency distributions are the Normal distribution, Lognormal distribution, and Leptokurtic distribution, described below. All three of these types of distribution are used in practice as approximations to model the distributions of financial variables.

Normal distributions are usually the simplest approximations to work with, and are assumed by - for example - many Value at Risk analysis models and measures. A theoretical shortcoming of using normal distributions as a model is that they assume an infinitely large downside potential including negative prices; whereas many financial variables - such as asset prices - cannot in practice fall so far as to become negative.

Lognormal distributions usually describe better the theoretical range of financial variables such as traded equity prices, which theoretically have no upside limit but which cannot fall below zero.

In practice, observed financial returns are usually more closely approximated by leptokurtic distributions, with a greater frequency both of very high and of very low returns, than predicted by the comparable normal distribution. So in risk analysis, if a population distribution is assumed to be normal, but is in reality leptokurtic, downside risk will be understated.

Other common types of frequency distribution include Binomial distributions and Poisson distributions.

See also