sd.multiperiod     package:PerformanceAnalytics     R Documentation

_c_a_l_c_u_l_a_t_e _a _m_u_l_t_i_p_e_r_i_o_d _o_r _a_n_n_u_a_l_i_z_e_d _S_t_a_n_d_a_r_d _D_e_v_i_a_t_i_o_n

_D_e_s_c_r_i_p_t_i_o_n:

     Standard Deviation of a set of observations R_{a} is given by:

     std = sqrt(var(R))

     It should follow that the variance is not a linear function of the
     number of observations.  To determine possible variance over
     multiple periods, it wouldn't make sense to multiply the
     single-period variance by the total number of periods: this could
     quickly lead to an absurd result where total variance (or risk)
     was greater than 100%.  It follows then that the total variance
     needs to demonstrate a decreasing period-to-period increase as the
     number of periods increases. Put another way, the increase in
     incremental variance per additional period needs to decrease with
     some relationship to the number of periods. The standard accepted
     practice for doing this is to apply the inverse square law. To
     normalize standard deviation across multiple periods, we multiply
     by the square root of the number of periods we wish to calculate
     over. To annualize standard deviation, we multiply by the square
     root of the number of periods per year.


                     sqrt{sigma}cdotsqrt{periods}


     Note that any multiperiod or annualized number should be viewed
     with suspicion if the number of observations is small.

_U_s_a_g_e:

         sd.multiperiod(x, scale = NA)
         sd.annualized(x, scale = NA)
         StdDev.annualized(R, scale = NA)

_A_r_g_u_m_e_n_t_s:

    x, R: an xts, vector, matrix, data frame, timeSeries or zoo object
          of asset returns 

   scale: number of periods in a year (daily scale = 252, monthly scale
          = 12, quarterly scale = 4) 

_V_a_l_u_e:

     standard deviation value, scaled for multiple periods

_A_u_t_h_o_r(_s):

     Brian G. Peterson

_R_e_f_e_r_e_n_c_e_s:

     Bacon, C. _Practical Portfolio Performance Measurement and
     Attribution_. Wiley. 2004. p. 27 

_S_e_e _A_l_s_o:

     'sd' 
      <URL: http://wikipedia.org/wiki/inverse-square_law>

_E_x_a_m_p_l_e_s:

         data(edhec)
         sd.annualized(edhec)
         sd.annualized(edhec[,6,drop=FALSE])
         # now for three periods:
         sd.multiperiod(edhec[,6,drop=FALSE],scale=3)