Sortino Ratio

StatMAP

capital A variation of the Sharpe ratio, the volatility benchmark tail PRESERVATION Sortino ratio is a return-versus-risk

trade-off metric that uses downside R e tu rn deviation as its measure of risk. r i s k

sortino ratio t r ad e - o ff

How Is it Useful? What Do the Graphs Show Me? The Sortino ratio addresses a shortcoming of using The two graphs below illustrate the two halves of the standard deviation as a measure of risk in a return- Sortino ratio. The numerator is identical to the numerator versus-risk trade-off ratio. Standard deviation punishes a in the Sharpe ratio. It is the rolling excess return above and manager equally for “good” risk and “bad” risk. Downside beyond the risk-free rate, as displayed in the upper graph. deviation adjusts for this by only counting the “bad” risk The lower graph illustrates how the Sortino ratio uses and ignoring “good” observations in a return series. The downside deviations, or the “bad” occurrences in a data Sortino ratio replaces standard deviation with downside stream, as its measure of volatility risk. deviation, so it is the added return per unit of “bad” risk rather than overall risk.

What Is a Good Number? Rolling Three Year Return 40% Like most ratios, the higher the Sortino ratio, the better. 30% One would hope to see substantial excess return above 20% r n

and beyond the risk-free rate, accompanied by little u t

e 10% downside deviation. A scenario such as this would R 0% produce a large Sortino ratio. It is important to keep in -10% mind the asset class under consideration when analyzing Dec 1995 Dec 1997 Dec 1999 Dec 2001 Dec 2003 Dec 2005 Dec 2007 Dec 2009 Dec 2012 Sortino ratios. Rolling Three Year Downside Deviation

) 18% % 0

= 15% R A

What Are the Limitations? M 12% ( n o i t 9% a Since the Sortino ratio uses downside deviation as its i v e

D 6% measure of risk, any limitations of downside deviation e d i s

n 3%

carry over to the Sortino ratio. With downside deviation, w o

D 0% there must be enough “bad” observations in order for the Dec 1995 Dec 1997 Dec 1999 Dec 2001 Dec 2003 Dec 2005 Dec 2007 Dec 2009 Dec 2012 calculation to be statistically significant. Created with Zephyr StyleADVISOR. Manager returns supplied by: Morningstar, Inc.

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4 4

3 3

2 2 Sortino 1 1 0 0 Large Cap US Stocks Sortino Ratio (MAR = 0%) Sortino Ratio (MAR = 0%) Small Cap US Stocks Ratio International Stocks (Developed) Sortino Ratio: 1990s Sortino Ratio: 2000s Emerging Markets Stocks Investment Grade US Bonds 5 5 High Yield US Bonds

What Are 4 4

3 Typical Values? 3

2 One would expect to see 2 Sortino ratios change 1 significantly for most asset 1 0 classes between the two 0

decades of the 1980s and -1 Sortino Ratio (MAR = 0%) Sortino Ratio (MAR = 0%) 1990s and the “lost decade” Created with Zephyr StyleADVISOR. Manager returns supplied by: Morningstar, Inc. of the 2000s. Indeed, that January 1986 - December 2012 is the case. The numerator of the Sortino ratio was reduced in the 2000s

Common as many asset classes Sortino Ratio 1980s 1990s 2000s struggled to outperform 1/86 - 12/12 the risk-free cash rate. The Large Cap US Stocks 2.34 2.52 0.15 1.13 denominator was increased, Small Cap US Stocks 1.89 1.86 0.49 1.09 as markets exhibited more

downside deviations short International Stocks (Developed) 2.41 1.44 0.32 1.02 of the 0.0% minimum acceptable return (MAR). Emerging Markets Stocks N/A 0.93 0.76 1.24

Investment Grade US Bonds 3.69 4.85 3.41 4.33

High Yield US Bonds 3.25 3.71 1.29 2.23

Related Metrics Math Corner 2 Downside Deviation: the amount The below calculation for the Sortino ratio is not of “bad” volatility risk complicated, as it is simply a variation of the Sharpe ratio. It is up to the user to define what the Sharpe Ratio: the trade-off of breakpoint is for minimum acceptable return (MAR) return per unit of volatility risk in the calculation of downside risk. Frequently used values for MAR are the risk-free rate or a hard- target value like 0%.