Question

1. Your client has a portfolio with the return information for the past 6 years. Your client indicates that the minimum acceptable return threshold is 5%. Please calculate the Sortino ratio.

Year	Portfolio
1	6
2	15
3	12
4	9
5	-2
6	2

Answer 1

Rf is not given in the question

we are assuming rf of 5%

Sortino Ratio = Rp - Rf / downside deviation

Step 1 - Calculation of downside deviation

Portfolio return above minimum acceptable return threshold will not be considered for downside deviation

Year	Return X	X-Mean	(X-Mean)^2
1	6	-1	Return Above 5%
2	15	8	Return Above 5%
3	12	5	Return Above 5%
4	9	2	Return Above 5%
5	-2	-9	81
6	2	-5	25
Mean	7		106

downside deviaion = sqrt (106 / Number of observaion)

downside deviaion = sqrt (106 / 6)

downside deviaion = 4.203

sortino ratio = 7-5 / 4.203 = 0.4758