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Omega Ratio

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Risk Metrics Series

On the StatMAP, the omega ratio risk met­ric is a use­ful risk/return trade-off mea­sure­ment for tail risk.

Put sim­ply, Omega is the ratio of an investment’s gains rel­a­tive to its loss­es. It gives you an idea of whether an investment’s return will be met or exceed­ed.

Keat­ing and Shad­wick devel­oped the omega ratio and named their met­ric after the last let­ter in the Greek alpha­bet: omega.  The idea was that omega would be the last met­ric any­one would ever need. While I don’t think there is an end-all, be-all risk met­ric, omega does offer unique insight into how out­lier events impact an investment’s return dis­tri­b­u­tion.

Calculating the Omega Ratio

To think about this visu­al­ly, let’s first look at the dis­tri­b­u­tion of returns for the S&P 500 for 2016. In the graph below, we see a dis­tri­b­u­tion of the 12 month­ly returns sort­ed from worst to first. The worst return in 2016 was -4.96%, the best was 6.78%. Three months were neg­a­tive, one was very close to zero, and eight months were pos­i­tive.

S&P Omega Ratio Year 2016- Omega Ratio - Swan Blog

Source: Zephyr StyleAD­VI­SOR

This graph might not be too inter­est­ing if one only looks at a sin­gle year. It’s chunky and doesn’t seem to tell you too much. How­ev­er, if you were to expand the time hori­zon to some­thing larg­er like 20 years, the pic­ture becomes much more infor­ma­tive.

S&P Omega Ratio- July 1007 - June 2017 - Omega Ratio - Swan Blog

Source: Zephyr StyleAD­VI­SOR

The worst one-month return over the last 20 years was -16.79% and the best was 10.93%. Returns were pos­i­tive (green area) 63.3% of the time where­as returns were neg­a­tive (red area) 36.7% of the time. Rough­ly 74% of the returns fell some­where between -5% and +5%. This graph gives us an excel­lent idea of what the over­all dis­tri­b­u­tion of returns looks like.

The omega ratio is derived from this graph. The green area, the gains, rep­re­sents the count and scale of month­ly returns that fall above a min­i­mum accept­ed return (MAR), in this case set to 0%. Ide­al­ly, this green area would be quite large. The red area, on the oth­er hand, rep­re­sents the count and scale of obser­va­tions that fall below the MAR, the loss­es. One would hope this area to be as small as pos­si­ble. Omega is cal­cu­lat­ed by divid­ing the good, green area by the bad, red area[1].

 

Evaluating Omega

What should be appar­ent by look­ing at the omega ratio graph is the impact of out­lier events on the cal­cu­la­tion of omega. If there are numer­ous obser­va­tions well below (or above) the MAR, they will equate to large amounts of real estate. Con­verse­ly, if most of the month­ly obser­va­tions fall some­where close to the MAR, they won’t gen­er­ate a lot of area to be mea­sured. There­fore, omega is an excel­lent met­ric for deter­min­ing the impact of extreme, out­lier events.

Since omega is a ratio with a “good” num­ber in the numer­a­tor and a “bad” mea­sure in the denom­i­na­tor, an ana­lyst would hope to see large omega num­bers. And just like the pain index or pain ratio, there is not an absolute val­ue that one can use as a ref­er­ence point to deter­mine whether an omega is good or bad. The omega ratio would need to be com­pared against that of a bench­mark or a group of peers.

 

Upside Omega and Downside Omega

If there is one draw­back to omega, it is that it rolls the “good” (the green area) togeth­er with the “bad” (the red area) to form a sin­gle num­ber. But what if one only wants to ana­lyze the down­side risk or upside poten­tial in iso­la­tion? Omega doesn’t account for that. After all, it’s pos­si­ble that Man­ag­er A has a very small green area and a very small red area and Man­ag­er X has very large green and red areas and at the end of the day, the omegas are rough­ly the same. This sit­u­a­tion is dis­played in the chart below.

Fund Comparison Omega Ratio - Swan Blog

Source: Zephyr StyleAD­VI­SOR

One refine­ment to the con­cept of omega is to sim­ply look at the two halves inde­pen­dent­ly and not roll them up into a sin­gle ratio[1]. This is called upside omega and down­side omega. Obvi­ous­ly, one hopes upside omega is large, sig­ni­fy­ing 1) many obser­va­tions above the MAR, 2) extreme obser­va­tions above the MAR, or 3) both. Con­verse­ly, one hopes down­side omega is small for the same rea­sons.

 

Compare Omega Ratios for a Better Understanding

The omega ratio can help advi­sors under­stand how well an invest­ment strat­e­gy or alter­na­tive approach mit­i­gates tail risk. Advi­sors will want to com­pare the omega ratios of a few funds to prop­er­ly assess this.

Using the Defined Risk Strat­e­gy (DRS) as an exam­ple, the DRS Select Com­pos­ite has his­tor­i­cal­ly done a good job mit­i­gat­ing loss­es. How­ev­er, there is a cost to this: The price of pro­tect­ing on the down­side is to give up some of the returns on the upside. The graph below illus­trates this trade-off.

DRS & S&P Omega Ratios - July 1007 - June 2017 - Omega Ratio - Swan Blog

Source: Zephyr StyleAD­VI­SOR. The S&P 500 Index is an unman­aged index and can­not be invest­ed into direct­ly. Past per­for­mance is no guar­an­tee of future results. DRS results are from the DRS Select Com­pos­ite, net of all fees, from July 7, 1997 to June 30, 2017.

The S-graph for the DRS Select Com­pos­ite is nar­row­er than the S-graph for the S&P 500. The area encap­su­lat­ed by the count and scale of returns less than 0% (i.e., the down­side omega) is small­er than that of the S&P 500—a good thing. How­ev­er, the trade-off is the upside omega area, rep­re­sent­ing the count and scale of returns greater than 0%, which is less than that of the S&P 500.

It has always been Swan’s phi­los­o­phy that pro­tect­ing against loss­es is more impor­tant than cap­tur­ing all of the upside gains. The graphs below illus­trate how the DRS Select Composite’s his­to­ry reflects this bias between the months of July 7, 1997 and June 30, 2017.

Tail Risk Outliers - Omega Ratio - Swan Blog

Source: Zephyr StyleAD­VI­SOR, Swan Glob­al Invest­ments. The Bar­clays U.S. Aggre­gate Bond Index and the S&P 500 Index are unman­aged indices and can­not be invest­ed into direct­ly. DRS results are from the DRS Select Com­pos­ite, net of all fees, from July 7, 1997 to June 30, 2017. Past per­for­mance is no guar­an­tee of future results. Struc­tures men­tioned may not be avail­able with­in your Broker/Dealer.

You can quan­ti­fy this trade-off by divid­ing the upside omega by the down­side omega to get the over­all omega ratio. For the DRS, the omega is 2.09, where­as the omega for the S&P 500 is 1.49. As stat­ed ear­li­er, one would hope to have larg­er omega num­bers; this means the ratio between the good and bad areas of the dis­tri­b­u­tion is skewed more to the pos­i­tive with the DRS.

The omega ratio for the DRS is slight­ly less than that of the hedge fund index, 2.09 ver­sus 2.13. The DRS has more upside omega (1.38 vs 1.04) but also more down­side area (0.66 vs 0.49). At the end of the day, the trade-off between upside and down­side is rough­ly equal between the two.

 

Mitigating Tail Risk

While omega won’t be the one and only risk met­ric to eval­u­ate invest­ments with, omega pro­vides insight into how out­lier events affect the dis­tri­b­u­tion of a giv­en investment—an impor­tant attribute for those who want to pro­tect invest­ment port­fo­lios from major mar­ket events. Advi­sors can use this met­ric when com­par­ing funds’ his­tor­i­cal expe­ri­ences in avoid­ing or min­i­miz­ing the impact of “black swan” events.

 

About the Author

Marc Odo, Marc Odo, CFA®, CAIA®, CIPM®, CFP®, Director of Investment Solutions - Swan Global Investments

Marc Odo, CFA®, CAIA®, CIPM®, CFP®, Direc­tor of Investor Solu­tions, is respon­si­ble for help­ing clients and prospects gain a detailed under­stand­ing of Swan’s Defined Risk Strat­e­gy, includ­ing how it fits into an over­all invest­ment strat­e­gy. For­mer­ly, Marc was the Direc­tor of Research for 11 years at Zephyr Asso­ciates.

 

 

 

Notes and Disclosures

[1] Omega was devel­oped by Con Keat­ing and William Shad­wick in 2002. http://www.isda.org/c_and_a/pdf/GammaPub.pdf

[2] Break­ing out omega into its sep­a­rate com­po­nents was not part of the orig­i­nal Keat­ing and Shad­wick paper. It was an enhance­ment brought about by Zephyr Asso­ciates.

Swan Glob­al Invest­ments, LLC is a SEC reg­is­tered Invest­ment Advi­sor that spe­cial­izes in man­ag­ing mon­ey using the pro­pri­etary Defined Risk Strat­e­gy (“DRS”). SEC reg­is­tra­tion does not denote any spe­cial train­ing or qual­i­fi­ca­tion con­ferred by the SEC. Swan offers and man­ages the DRS for investors includ­ing indi­vid­u­als, insti­tu­tions and oth­er invest­ment advi­sor firms. Any his­tor­i­cal num­bers, awards and recog­ni­tions pre­sent­ed are based on the per­for­mance of a (GIPS®) com­pos­ite, Swan’s DRS Select Com­pos­ite, which includes non-qual­i­fied dis­cre­tionary accounts invest­ed in since incep­tion, July 1997, and are net of fees and expens­es. Swan claims com­pli­ance with the Glob­al Invest­ment Per­for­mance Stan­dards (GIPS®). The Swan Defined Risk Strat­e­gy Select Com­pos­ite demon­strates the per­for­mance of non-qual­i­fied assets man­aged by Swan Glob­al Invest­ments, LLC since incep­tion. It includes dis­cre­tionary indi­vid­ual accounts whose account hold­ers seek the upside poten­tial of own­ing stock, and the desire to elim­i­nate most of the risk asso­ci­at­ed with own­ing stock. The Com­pos­ite relies on LEAPS and oth­er options to man­age this risk. Indi­vid­ual accounts own S&P 500 exchange trad­ed funds and LEAPS asso­ci­at­ed with the exchange trad­ed funds as well as mul­ti­ple oth­er option spreads that rep­re­sent oth­er indices that are wide­ly trad­ed. The Defined Risk Strat­e­gy was designed to pro­tect investors from sub­stan­tial mar­ket declines, pro­vide income in flat or chop­py mar­kets, and to ben­e­fit from mar­ket appre­ci­a­tion. Stock and options are the pri­ma­ry com­po­nents of the strat­e­gy.

All Swan prod­ucts uti­lize the Defined Risk Strat­e­gy (“DRS”), but may vary by asset class, reg­u­la­to­ry offer­ing type, etc. Accord­ing­ly, all Swan DRS prod­uct offer­ings will have dif­fer­ent per­for­mance results due to offer­ing dif­fer­ences and com­par­ing results among the Swan prod­ucts and com­pos­ites may be of lim­it­ed use. All data used here­in; includ­ing the sta­tis­ti­cal infor­ma­tion, ver­i­fi­ca­tion and per­for­mance reports are avail­able upon request. The S&P 500 Index is a mar­ket cap weight­ed index of 500 wide­ly held stocks often used as a proxy for the over­all U.S. equi­ty mar­ket. Index­es are unman­aged and have no fees or expens­es. An invest­ment can­not be made direct­ly in an index. Swan’s invest­ments may con­sist of secu­ri­ties which vary sig­nif­i­cant­ly from those in the bench­mark index­es list­ed above and per­for­mance cal­cu­la­tion meth­ods may not be entire­ly com­pa­ra­ble. Accord­ing­ly, com­par­ing results shown to those of such index­es may be of lim­it­ed use. The adviser’s depen­dence on its DRS process and judg­ments about the attrac­tive­ness, val­ue and poten­tial appre­ci­a­tion of par­tic­u­lar ETFs and options in which the advis­er invests or writes may prove to be incor­rect and may not pro­duce the desired results. There is no guar­an­tee any invest­ment or the DRS will meet its objec­tives. All invest­ments involve the risk of poten­tial invest­ment loss­es as well as the poten­tial for invest­ment gains. Pri­or per­for­mance is not a guar­an­tee of future results and there can be no assur­ance, and investors should not assume, that future per­for­mance will be com­pa­ra­ble to past per­for­mance. All invest­ment strate­gies have the poten­tial for prof­it or loss. Fur­ther infor­ma­tion is avail­able upon request by con­tact­ing the com­pa­ny direct­ly at 970–382-8901 or www.swanglobalinvestments.com178-SGI-042718

By | 2018-05-03T15:18:48+00:00 April 26th, 2018|Blog|Comments Off on Omega Ratio