pandas, melt, unmelt preserve index

You need preserve index values by reset_index and parameter id_vars:

df2 = pd.melt(df.reset_index(), id_vars="index",value_vars=['asset1','asset2'])
print (df2)
    index variable  value
0  coper1   asset1      1
1  coper2   asset1      3
2  coper3   asset1      5
3  coper1   asset2      2
4  coper2   asset2      4
5  coper3   asset2      6

Then pivot working nice:

print(df2.pivot(index='index',columns="variable", values="value"))
variable  asset1  asset2
index                   
coper1         1       2
coper2         3       4
coper3         5       6

Another possible solution with stack:

df2 = df.stack().reset_index()
df2.columns = list('abc')
print (df2)
        a       b  c
0  coper1  asset1  1
1  coper1  asset2  2
2  coper2  asset1  3
3  coper2  asset2  4
4  coper3  asset1  5
5  coper3  asset2  6

print(df2.pivot(index='a',columns="b", values="c"))
b       asset1  asset2
a                     
coper1       1       2
coper2       3       4
coper3       5       6