Modern Finance Volatility

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Volatility

Returns the sample standard deviation of returns, annualized.

Syntax

Volatility( periodReturns( ), frequency )

Examples

#import "std/money"
using money

'' The SAMPLE standard deviation of the returns, annualized.
''
'' IT SCALES BY THE SQUARE ROOT of the frequency, not by the frequency --
'' variance scales with time, standard deviation with its square root.
dim as float64 r( 0 to 11 ) = { 0.02, -0.01, 0.03, 0.015, -0.025, 0.04, _
                               0.01, -0.005, 0.02, 0.03, -0.015, 0.025 }
dim as float64 b( 0 to 11 ) = { 0.018, -0.012, 0.025, 0.012, -0.02, 0.035, _
                               0.008, -0.004, 0.018, 0.028, -0.012, 0.022 }

print Volatility( r( ), RETURN_MONTHLY ).Value( )        '' 0.07088723439378913

'' Which is why monthly and quarterly differ by exactly sqrt( 3 ).
dim as float64 vm = Volatility( r( ), RETURN_MONTHLY ).Value( )
dim as float64 vq = Volatility( r( ), RETURN_QUARTERLY ).Value( )
print vm / vq                                            '' 1.732050807568877

'' A single observation has no sample variance -- n-1 is zero.
dim as float64 one_( 0 to 0 ) = { 0.02 }
print Volatility( one_( ), RETURN_MONTHLY ).Failure( ).Message( )

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Library: Finance
Category: Finance
Documented under: Nothing Becomes A Keyword
Source: pkg/std/money/finport.tiko in the tiko repository.