DownsideDeviation    package:PerformanceAnalytics    R Documentation

_f_u_n_c_t_i_o_n _f_o_r _d_o_w_n_s_i_d_e _r_i_s_k _o_f _t_h_e _r_e_t_u_r_n _d_i_s_t_r_i_b_u_t_i_o_n

_D_e_s_c_r_i_p_t_i_o_n:

     Downside deviation is an alternative measure of dounside risk.

_U_s_a_g_e:

     DownsideDeviation(Ra, MAR = 0)

_A_r_g_u_m_e_n_t_s:

      Ra: a vector, matrix, data frame, timeSeries or zoo object of
          asset returns 

     MAR: Minimum Acceptable Return, in the same periodicity as your
          returns 

_D_e_t_a_i_l_s:

     Downside deviation, similar to semi deviation, eliminates positive
     returns when calculating risk.  Instead of using the mean return
     or zero, it uses the Minimum Acceptable Return as proposed by
     Sharpe (which may be the mean historical return or zero).

     To calculate it, we take the subset of returns that are less than
     the target (or Minimum Acceptable Returns (MAR)) returns and take
     the differences of those to the target.  We sum the squares and
     divide by the total number of returns to get a below-target
     semi-variance.


 DownsideDeviation(R , MAR)= delta_{MAR} = sqrt{ frac{sum^{n}_{t=1}(R_{t} - MAR)^{2}}{n} }


     This is also useful for calculating semi-deviation or semivariance
     by setting

     MAR = mean(x)

     Sortino recommends calculating downside deviation utilizing a
     continuous fitted distribution rather than the discrete
     distribution of observations.  This would have significant
     utility, especially in cases of a small number of observations. He
     recommends using a lognormal distribution, or a fitted
     distribution based on a relevant style index, to construct the
     returns below the MAR to increase the confidence in the final
     result.  Hopefully, in the future, we'll add a fitted option to
     this function, and would be happy to accept a contribution of this
     nature.

_V_a_l_u_e:

_N_o_t_e:

_A_u_t_h_o_r(_s):

     Peter Carl

_R_e_f_e_r_e_n_c_e_s:

     Sortino, F. and Price, L. Performance Measurement in a Downside
     Risk Framework. _Journal of Investing_. Fall 1994, 59-65. 

     Plantinga, A., van der Meer, R. and Sortino, F. The Impact of
     Downside Risk on Risk-Adjusted Performance of Mutual Funds in the
     Euronext Markets. July 19, 2001. Available at SSRN: <URL:
     http://ssrn.com/abstract=277352>  

     <URL: http://www.sortino.com/htm/performance.htm> see especially
     end note 10

_S_e_e _A_l_s_o:

_E_x_a_m_p_l_e_s:

     data(edhec)
     head(edhec[,6,drop=FALSE])
     sd(edhec[,6])
     DownsideDeviation(edhec[,6])  # MAR 0%
     DownsideDeviation(edhec[,6], MAR = .04/12) #MAR 4%
     DownsideDeviation(edhec[,6], MAR = mean(edhec[,6])) #MAR = mean return, calculate semivariance

