Modern Finance DownsideDeviation

Home › Finance › Finance › DownsideDeviation

DownsideDeviation

Returns the annualized shortfall of returns below a target, ignoring gains.

Syntax

DownsideDeviation( periodReturns( ), targetPerPeriod, frequency )

Examples

#import "std/money"
using money

'' Only the SHORTFALL against a target counts -- upside volatility is
'' ignored, which is what makes it the right denominator for Sortino.
''
'' IT IS NOT StdDev OF THE BELOW-TARGET VALUES: it measures deviation
'' from the TARGET, not from their mean, and divides by the FULL
'' observation count so that rarely being below target is rewarded.
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 DownsideDeviation( r( ), 0.0, RETURN_MONTHLY ).Value( )    '' 0.03122498999199199

'' It is smaller than total volatility whenever there is upside.
dim as boolean smaller = ( DownsideDeviation( r( ), 0.0, RETURN_MONTHLY ).Value( ) < _
                           Volatility( r( ), RETURN_MONTHLY ).Value( ) )
print smaller                            '' true

'' A series never below target has exactly zero downside deviation.
dim as float64 up_( 0 to 3 ) = { 0.01, 0.02, 0.01, 0.03 }
print DownsideDeviation( up_( ), 0.0, RETURN_MONTHLY ).Value( )   '' 0

---

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