APPENDIX 8.B
US-E3 Descriptor Definitions
This appendix gives the detailed definitions of the descriptors that underlie
the risk indexes in US-E3. The method of combining these descriptors into
risk indexes is proprietary to BARRA.
Volatility
1.BTSG: Beta times sigma. This is computed as , where βis the his-
torical beta and σεis the historical residual standard deviation. If βis nega-
tive, then the descriptor is set equal to zero.
2.DASTD: Daily standard deviation. This is computed as:
where rtis the return over day t, wtis the weight for day t, Tis the number
of days of historical returns data used to compute this descriptor (we set
this to 65 days), and Ndaysis the number of trading days in a month (we set
this to 23).
3.HILO: Ratio of high price to low price over the last month. This is cal-
culated as:
where PHand PLare the maximum price and minimum price attained over
the last one month.
4.LPRI: Log of stock price. This is the log of the stock price at the end of
last month.
5.CMRA: Cumulative range. Let Ztbe defined as:
where ri,sis the return on stock Iin month s, and rf,sis the risk-free rate for
month s. In other words, Ztis the cumulative return of the stock over the
Zr rtis
st
fs
st
=+−+
==∑∑log(^11 ,,) log( )
11logP
PH
L
Nwrdays t t
tT
2= 1∑
βσε