Question

Year	Rp	Rm	Rf
2000	18.1832	-24.9088	5.112
2001	-3.454	-15.1017	5.051
2002	47.5573	20.784	3.816
2003	28.7035	9.4163	4.2455
2004	29.8613	8.7169	4.2182
2005	11.2167	16.3272	4.3911
2006	32.2799	14.5445	4.7022
2007	-41.0392	-36.0483	4.0232
2008	17.6082	9.7932	2.2123
2009	14.1058	16.5089	3.8368
2010	16.1978	8.0818	3.2935
2011	11.558	15.1984	1.8762
2012	42.993	27.1685	1.7574
2013	18.8682	17.2589	3.0282
2014	-1.4678	5.1932	2.1712
2015	9.2757	4.4993	2.2694
2016	8.5985	23.624	2.4443

When performing calculations in the following problems, use the numbers in the table as-is. I.e., do NOT convert 8.5985 to 8.5985% (or 0.085985). Just use plain 8.5985.

1. Compute the Sortino Ratio of the portfolio using a minimal acceptable return of R M A = 3 . To calculate DDp :

1. Compute R p − R M A each year.
2. n = number of years R p − R M A < 0 .
3. DD p = square root of 1/ n− 1 ∑ ( R p − R M A )^2 for the years when R p − R M A < 0

Answer 1

Solution: Minimal acceptable return (RMA) = 3

The difference between the Rp and minimal acceptable return (RMA) is calculated as follows

Rp - RMA is negative for 3 years as shown in the above figure.

Hence, n = 3

The square of these highlighted deviations is calculated as follows:

Sum of square of these deviations = 41.654116 + 1939.451137 + 19.961236884 = 2001.066489

On dividing the square value by n -1 = 3-1, we get: 20001.066489/2 = 1000.533

The DDp is calculated as square root of 1000.533 = sqrt(1000.533) = 31.63121

Sortino ratio is calculated as follows:

Standard deviation of the downside = DDp = 31.63121

The excess return for the year (Rp - Rf) is calculated for each year as follows:

The average of these excess returns = 11.91750588

Thus, Sortino ratio = Average Excess return/DDp

= 11.91750588/31.63121 = 0.376764186 = 0.377