1. The exact definition of the mod function depends on the programming language. I would guess gtr1 is Floating-point Truncated similar to C fmod.

Using a different random number generator can show if there is a problem. The hash function takes a parameter from 1e-25 to 1e25:

from Excel: param0=10^(50*(RAND()-0.5))
Junk: hash(aprc,dspo(1),param0)

The random number generators using hash and mod have similar SDcg.

        Screen         yrs  Depth  SDcg  SDpop
Dartboard2023c80hash2  66     80   0.42    30
Dartboard2023c80hash4  66     80   0.45    32
Dartboard2023c80hash1  66     80   0.45    33
Dartboard2023c80hash3  66     80   0.46    33
 
Dartboard2023c80mod4   66     80   0.43    31
Dartboard2023c80mod1   66     80   0.46    33
Dartboard2023c80mod3   66     80   0.46    33
Dartboard2023c80mod2   66     80   0.48    35

https://gtr1.net/2013/?~Dartboard2023c80hash1:h253...
https://gtr1.net/2013/?~Dartboard2023c80hash2:h253...
https://gtr1.net/2013/?~Dartboard2023c80hash3:h253...
https://gtr1.net/2013/?~Dartboard2023c80hash4:h253...
https://gtr1.net/2013/?~Dartboard2023c80mod1:h253n...
https://gtr1.net/2013/?~Dartboard2023c80mod2:h253n...
https://gtr1.net/2013/?~Dartboard2023c80mod3:h253n...
https://gtr1.net/2013/?~Dartboard2023c80mod4:h253n...

The gtr1 glossary says: "the function mod first divides the investment's corresponding value in the field referenced by field_ref by divisor_num and truncates the resulting quotient to an integer; the product of divisor_num and the integral quotient is then subtracted from the investment's value in field_ref and the resulting difference (remainder) is assigned to the investment's value in the calling field."

The highest aprc in the S&P 1500 gtr1 data is now NVR $5235. The highest dspo is 24482. I checked the gtr1 numbers for a stock with a high aprc and high dspo, and the calculation looks correct. The 0.0003 difference is small compared to the 0 to 153 range of RandomA.

RandomA: mod(linear(1,dspo(1),23,aprc,97,trm(1,17)),153)

  ticker   dspo:1    aprc      trm:1,17    wgtSum   [RandomA]
   LMT     20960    475.50     0.993621   31992.88   15.8809
 
  manual    calc     check
           dspo:1  23*aprc   97*trm:1,17   wgtSum
 wgtSum:   20960   10936.50     96.38     31992.88
quotient             209         153        31977
remainder                                 15.8812

Mechanical Investing FAQ

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