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Zephyr K-ratio

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Risk Metrics Series

The objec­tive of this ongo­ing edu­ca­tion­al series of blog posts is to sort through, explain, and orga­nize all of the var­i­ous per­for­mance met­rics that are avail­able to the finan­cial ana­lyst, but most investors real­ly want just two things:

  1. They want their wealth to appre­ci­ate at a rapid rate
  2. They do not want to devi­ate from that path of wealth appre­ci­a­tion

Luck­i­ly, there’s a ratio for that: Zephyr K-Ratio[1]. This ratio mea­sures the con­sis­ten­cy of wealth cre­ation over time.


The Steeper the Slope, The Faster the Climb

Let’s begin with an illus­tra­tion to help under­stand this new met­ric.

Below we see a cumu­la­tive return graph for the S&P 500 over the last 20 years[2]. Super­im­posed over the actu­al data is a straight, best-fit line.

K-ratio S&P 500 - Zephyr K-Ratio - Swan Blog

Source: Zephyr StyleAD­VI­SOR, Swan Glob­al Invest­ments.


The slope of the line is the return mea­sure, so the steep­er the slope of that line, the bet­ter. A steep­er slope indi­cates a more rapid pace of wealth appre­ci­a­tion.

Obvi­ous­ly in real life the path of wealth appre­ci­a­tion is not a straight line. There are many ups and downs along the way. How­ev­er, a straight line of wealth appre­ci­a­tion can be thought of as an ide­al. If an invest­ment offered a con­sis­tent rate of

wealth appre­ci­a­tion with no devi­a­tions on a month-to-month or year-to-year basis, it would like­ly find an enthu­si­as­tic pool of investors.


Calculating & Evaluating the Zephyr K-Ratio

The K-ratio is the slope of the best-fit line that mea­sures cap­i­tal appre­ci­a­tion divid­ed by the stan­dard error of the mean, which it uses as its mea­sure of risk.

The stan­dard error of the mean is sub­tly but impor­tant­ly dif­fer­ent than the stan­dard devi­a­tion used in most per­for­mance and risk sta­tis­tics. While stan­dard devi­a­tion mea­sures how much indi­vid­ual obser­va­tions of data tend to be dis­persed from the mean val­ue, stan­dard error of the mean is a test of the mean itself—it is a way to indi­cate how pre­cise or accu­rate a mean val­ue is.

Using the stan­dard error of the mean as a mea­sure of risk allows us to see just how close­ly an actu­al return pat­tern match­es that ide­al­ized straight line. The small­er the stan­dard error of the mean, the clos­er the actu­al return series is to the ide­al­ized straight line. Con­verse­ly, a large stan­dard error of the mean indi­cates that the actu­al path the invest­ment takes mean­ders far and wide off the straight line.

With this ratio, the larg­er the num­ber the bet­ter, and a com­par­i­son to peers is nec­es­sary to deter­mine whether a num­ber is “good” or “bad.”


K-Ratio Addresses a Standard Deviation Flaw

As an added ben­e­fit, the K-ratio address­es one of the long-stand­ing com­plaints regard­ing the use of stan­dard devi­a­tion as a risk mea­sure: it does not and can­not take into account the tim­ing of bad returns. If there are a dozen very bad month­ly returns over the span of ten years, stan­dard devi­a­tion can­not tell whether those bad months were ran­dom­ly scat­tered through­out a decade or if they were all clus­tered in a small peri­od of time. Any­one who remem­bers the dark days of late 2008/early 2009 can recall that some of the worst months in mem­o­ry were tight­ly clus­tered with­in a few quar­ters.

The stan­dard error of the mean and the K-ratio rem­e­dy this. A finan­cial cri­sis push­es the invest­ment from the ide­al­ized straight line, so you can clear­ly see where that clus­ter of bad months hap­pened.


The Zephyr K-Ratio in Action: A Comparison

For the K-ratio to have mean­ing, it must be com­pared to oth­er invest­ments’ K-Ratios. Using the Defined Risk Strat­e­gy (DRS) as an exam­ple, we com­pare the K-Ratio for the DRS Select Com­pos­ite to the S&P 500.

The DRS Select Com­pos­ite looks strong when ana­lyzed in terms of con­sis­ten­cy of wealth cre­ation in con­trast to the S&P 500. First of all, the slope of the best-fit line is steep­er than that of the S&P 500, mean­ing the DRS Select Com­pos­ite does a bet­ter job of cre­at­ing wealth.

K-ratio S&P 500 & DRS Select Composite - Zephy K-Ratio - Swan Blog

Source: Zephyr StyleAD­VI­SOR, Swan Glob­al Invest­ments. All S&P 500 data based on his­tor­i­cal per­for­mance of the S&P Total Return Index. All his­tor­i­cal per­for­mance of the Swan DRS Select Com­pos­ite is net of fees. Pri­or per­for­mance is not a guar­an­tee of future results.


Sec­ond­ly, and more impor­tant­ly, the actu­al data line tends to hug the ide­al­ized best-fit line much more close­ly than the S&P 500 fits its ide­al line. This is the con­sis­ten­cy part of the equa­tion.

A strong return met­ric divid­ed by a small­er risk met­ric will cer­tain­ly lead to bet­ter over­all ratios. That is what we see with the K-ratio metric—the DRS win­ning on both the wealth cre­ation and con­sis­ten­cy fronts.


Defined Risk Strategy: Smooth & Consistent Wealth Creation

The DRS was devised with this goal in mind: to pro­vide a nice, smooth, con­stant rate of wealth cre­ation. The K-ratio illus­trates how well the strat­e­gy was able to achieve that goal.

Consistency of Wealth Creation - Zephyr K-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.

The DRS Select Composite’s K-ratio is 119.23, much bet­ter than the S&P 500’s 22.73. The S&P 500’s K-ratio shows that the two big bear mar­kets in 2000-02 and 2007-09 had a big impact on an investor’s path of wealth cre­ation. The bal­anced 60/40 mix and the hedge fund index did bet­ter than the S&P 500 with K-ratios of 45.86 and 58.00, respec­tive­ly, but are well short of the DRS Select Composite’s K-ratio of 119.23.

An invest­ment made sole­ly in a S&P 500 prod­uct would have been knocked severe­ly off course by those crises. Of course, any­one who had been through those peri­ods remem­bers those events, but the K-ratio allows us to quan­ti­fy the impact of those events on one’s wealth cre­ation.


About the Author:

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




Important Notes and Disclosures:

[1] The K-ratio was first pro­posed by Lars Kest­ner in 1996. The Zephyr K-ratio is a vari­a­tion of the K-ratio that removes an ele­ment of the for­mu­la that incor­po­rates the num­ber of data points used in the cal­cu­la­tion.

[2] Because this is a cumu­la­tive return graph, it takes into account the com­pound­ing of wealth. In order to super­im­pose a best-fit line over a com­pound­ing series, the graph must first be con­vert­ed to a log scale.

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. The 60/40 bench­mark is a blend­ed com­pos­ite, weight­ed 60% in the afore­men­tioned S&P 500 Index and 40% in the Bar­clays US Aggre­gate Bond Index to rep­re­sent bal­anced port­fo­lios. The Bar­clays US Aggre­gate Bond Index is a broad-based flag­ship bench­mark that mea­sures the invest­ment grade, US dol­lar-denom­i­nat­ed, fixed-rate tax­able bond mar­ket. The index includes Trea­suries, gov­ern­ment-relat­ed and cor­po­rate secu­ri­ties, MBS (agency fixed-rate and hybrid ARM pass-throughs), ABS and CMBS (agency and non-agency). HFRI Fund Weight­ed Com­pos­ite Index: The HFRI Fund Weight­ed Com­pos­ite Index is a glob­al, equal-weight­ed index of over 2,000 sin­gle-man­ag­er funds that report to HFR Data­base. Con­stituent funds report month­ly net of all fees per­for­mance in US Dol­lar and have a min­i­mum of $50 Mil­lion under man­age­ment or a twelve (12) month track record of active per­for­mance. The HFRI Fund Weight­ed Com­pos­ite Index does not include Funds of Hedge Funds.

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.com191-SGI-051018

By |2018-10-02T10:56:36+00:00May 10th, 2018|Blog|Comments Off on Zephyr K-ratio