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(R, Rf = 0, method="half")

_A_r_g_u_m_e_n_t_s:

       R: 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. 
     As such, the Kelly criterion is equal to the expected excess
     return of the strategy divided by the expected variance of the
     excess return, or


                leverage = (mean(R)-Rf=0)/StdDev(R)^2


     As a performance metric, the Kelly Ratio is calculated
     retrospectively on a particular investment as 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

_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>

_E_x_a_m_p_l_e_s:

         data(managers)
         KellyRatio(managers[,1,drop=FALSE], Rf=.04/12)
         KellyRatio(managers[,1,drop=FALSE], Rf=managers[,10,drop=FALSE])
         KellyRatio(managers[,1:6], Rf=managers[,10,drop=FALSE])