How to calculate pivot value from OHLC data

I've a pandas dataset with open, high, low, close and key column. Now I want to group the dataset by key and calculate pivot with the formula - (high + low + close) / 3. Upto this I'm able to do. But the requirement is to shift the calculated data to next group which I'm unable to code.

I'm able to group the dataset by key column and able to calculate pivot data.

import pandas as pd
data = pd.DataFrame([[110, 115, 105, 111, 1],[11, 16, 6, 12, 1],[12, 17, 7, 13, 1],[12, 16, 6, 11, 2],[9, 13, 4, 13, 2],[13, 18, 9, 12, 3],[14, 16, 10, 13, 3]], columns=["open","high","low","close","key"])
data['p'] = (data.high.groupby(data.key).transform('max') + data.low.groupby(data.key).transform('min') + data.close.groupby(data.key).transform('last')) / 3
print(data)

Currently I'm getting below output.

   open  high  low  close  key      p
0   110   115  105    111    1  44.666667
1    11    16    6     12    1  44.666667
2    12    17    7     13    1  44.666667
3    12    16    6     11    2  11.000000
4     9    13    4     13    2  11.000000
5    13    18    9     12    3  13.333333
6    14    16   10     13    3  13.333333

But after shifting value to next group the expected output should be as mentioned below.

   open  high  low  close  key      p
0   110   115  105    111    1     NaN
1    11    16    6     12    1     NaN
2    12    17    7     13    1     NaN
3    12    16    6     11    2  44.666667
4     9    13    4     13    2  44.666667
5    13    18    9     12    3  11.000000
6    14    16   10     13    3  11.000000

Instead 3 dimes groupby use GroupBy.agg with dictionary, then sum values per rows and divide 3. Last use Series.map with Series.shifted values for new column:

s = data.groupby('key').agg({'low':'min','high':'max','close':'last'}).sum(axis=1) / 3

data['s'] = data['key'].map(s.shift())
print(data)
   open  high  low  close  key          s
0   110   115  105    111    1        NaN
1    11    16    6     12    1        NaN
2    12    17    7     13    1        NaN
3    12    16    6     11    2  44.666667
4     9    13    4     13    2  44.666667
5    13    18    9     12    3  11.000000
6    14    16   10     13    3  11.000000