Question

Report the portfolio cumulative return and annual geometric average over the period. And explain why the portfolio does not deliver the annual geometric mean of 6% p.a. Using mean- variance framework to explain it.

The portfolio each weight is SMB 15%; HML 45%; Mom 40%.

date

SMB (return rate)

HML (return rate)

Mom (return rate)

201901	3.01%	-0.62%	-8.68%
201902	2.06	-2.84	0.79
201903	-3.13	-4.07	2.18
201904	-1.68	1.93	-2.61
201905	-1.2	-2.39	7.61
201906	0.33	-1.08	-2.23
201907	-2.07	0.14	2.68
201908	-2.41	-4.99	7.6
201909	-0.9	6.71	-6.85
201910	0.25	-2.07	0.24
201911	0.87	-1.86	-2.62
201912	0.68	1.83	-2.13

Answer 1

formulas used -:

cumulative Return =((1+C3)*(1+C4)*(1+C5)*(1+C6)*(1+C7)*(1+C8)*(1+C9)*(1+C10)*(1+C11)*(1+C12)*(1+C13)*(1+C14))-1

Geometry Mean=((1+C3)*(1+C4)*(1+C5)*(1+C6)*(1+C7)*(1+C8)*(1+C9)*(1+C10)*(1+C11)*(1+C12)*(1+C13)*(1+C14))^(1/12)-1

Portfolio return=SUMPRODUCT(C17:E17,C18:E18)

the average return of portfolio was not equal tpo six because all securities in to the portfolio were having lower retun and due to that portfolio retun can never be higher than the return on indiovidual securities