KellyRatio       package:PerformanceAnalytics       R Documentation

_c_a_l_c_u_l_a_t_e _K_e_l_l_y _c_r_i_t_e_r_i_o_n _r_a_t_i_o (_l_e_v_e_r_a_g_e _o_r _b_e_t _s_i_z_e) _f_o_r _a _s_t_r_a_t_e_g_y

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

     Kelly criterion ratio (leverage or bet size) for a strategy.

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

     KellyRatio(Ra, rf = 0, method="half")

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

      Ra: a vector of returns to perform a mean over 

      rf: risk free rate, in same period as your returns 

  method: method=half will use the half-Kelly, this is the default

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

     The Kelly Criterion was identified by Bell Labs scientist John
     Kelly, and applied to blackjack and stock strategy sizing by Ed
     Thorpe.

     The Kelly ratio can be simply stated as

     bet size is the ratio of edge over odds

     mathematically, you are maximizing log-utility

     Kelly criterion says: f should equal the expected excess return of
     the strategy divided by the expected variance of the excess
     return, or


                 leverage = (mean(R)-rf)/StdDev(R)^2


     As a performance metric, the Kelly Ratio calculated
     retrospectively on a particular investment will give you a measure
     of the edge that investment has over the risk free rate.  It may
     be use as a stack ranking method to compare investments in a
     manner similar to the various ratios related to the Sharpe ratio.

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

     Kelly Ratio or Bet/Leverage Size

_N_o_t_e:

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

     Brian G. Peterson

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

     Thorp, Edward O. (1997; revised 1998). The Kelly Criterion in
     Blackjack, Sports Betting, and the Stock Market. <URL:
     http://www.bjmath.com/bjmath/thorp/paper.htm> 
      <URL: http://en.wikipedia.org/wiki/Kelly_criterion>

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

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

         data(edhec)
                                                                                                                                                                   edhec.length = dim(edhec)[1]
         start = rownames(edhec[1,])
         end = rownames(edhec[edhec.length,])

         rf.zoo = download.RiskFree(start = start, end = end)

         for (i in 1:ncol(edhec)) {print(colnames(edhec)[i]); print(KellyRatio(edhec[,i],rf=rf.zoo))}

