Parametric portfolio optimization by Brandt 2009

[paulyan]

Hi schnellinga,

I think that you misunderstand the original model.
Below is your code for the PPS function.

def PPS(x, wb, nt, excess, size, value, rr):
    w1= wb + nt * (x[0] * excess)
    w2= wb + nt * (x[1]* size)
    w3= wb + nt * (x[2]* value)
    wret = (w1*excess + w2*size + w3*value).sum() 
    ut = ((1 + wret) ** (1 - rr)) / (1 - rr)
    u = -(ut.mean())
    return u

Below is the original one.

# original one
def PPS(x, wb, nt, ret, m12, mktcap, rr):
    wi = wb + nt * (x[0] * m12 + x[1] * mktcap)
    wret = (wi * ret).sum(axis=1)
    ut = ((1 + wret) ** (1 - rr)) / (1 - rr)
    u = -(ut.mean())
    return u

According to the original model, there are two parameters: 12month returns (for the momentum strategy)
and size (for the size effect). Because of this, there are two coefficients : x[0] and x[1]. If looking at the
original input data sets, you will find two associated columns: adjusted closing price and mktcap, shown below.

df.head()
Out[317]:

Moderator Note:
Output tags also work well for input

Output:
           symbol   adjusted      close  shares_held  year  month  \
Date                                                                
2008-01-01   MSFT  25.413656  32.599998     92220260  2008      1   
2008-02-01   MSFT  21.286415  27.200001     92220260  2008      2   
2008-03-01   MSFT  22.209873  28.379999     92220260  2008      3   
2008-04-01   MSFT  22.319431  28.520000     92220260  2008      4   
2008-05-01   MSFT  22.244507  28.320000     92220260  2008      5   

                  mktcap  day  
Date                           
2008-01-01  3.006380e+09    1  
2008-02-01  2.508391e+09    1  
2008-03-01  2.617211e+09    1  
2008-04-01  2.630122e+09    1  
2008-05-01  2.611678e+09    1  

For your input data set, i.e., the Fama-French monthly data set, there is no market cap, shown below.

>>>ff_factors.head()
Out[318]: 

Output:
            Mkt-RF     SMB     HML
1926-07-31  0.0296 -0.0238 -0.0273
1926-08-31  0.0264 -0.0147  0.0414
1926-09-30  0.0036 -0.0139  0.0012
1926-10-31 -0.0324 -0.0013  0.0065
1926-11-30  0.0253 -0.0016 -0.0038

Because of this, you can test the results for just one parameter: 12-month returns.
However, in your PPS function, you use 3, x[0], x[1], and x[2], instead of one.

Hope that this would help.
Best,
Paul

Larz60+ write Jul-27-2022, 03:10 AM:
Please post all code, output and errors (it it's entirety) between their respective tags. Refer to BBCode help topic on how to post. Use the "Preview Post" button to make sure the code is presented as you expect before hitting the "Post Reply/Thread" button.
Fixed for you this time, please use bbcode tags on future posts