Pain Ratio vs. Standard Deviation

In a pre­vi­ous post we dis­cussed the pain index as a bet­ter mea­sure of risk. Now we’ll explore the con­cept fur­ther, to con­sid­er return as well as risk, using the pain ratio.

The pain index mea­sures the depth, dura­tion, and fre­quen­cy of loss­es for an invest­ment.

But what about the upside?  If there is one draw­back of the pain index, it is it only mea­sures risk, not return. If one want­ed to have the low­est pos­si­ble pain index of 0.0% and nev­er lose a cent, one would keep all of their mon­ey in a FDIC insured sav­ings account.

How­ev­er, most investors accept the fact that some risk must be under­tak­en in order to gen­er­ate any decent amount of return.

The grand­fa­ther of risk/return mea­sures is the Sharpe ratio. Devel­oped by Nobel lau­re­ate William Sharpe, the Sharpe ratio attempts to mea­sure the trade-off between return and risk (as mea­sured by volatil­i­ty).

• The numer­a­tor of the Sharpe ratio is an investment’s excess return over the risk-free rate. One would hope this num­ber is pos­i­tive.
• The denom­i­na­tor of the Sharpe ratio is a mea­sure of risk. Sharpe used stan­dard devi­a­tion as his mea­sure of risk.

By tak­ing a mea­sure of return and divid­ing it by a mea­sure of risk, Sharpe was able to quan­ti­fy an investment’s “bang for the buck”, a very use­ful bit of infor­ma­tion.

There are many vari­a­tions to the basic return-divid­ed-by risk con­cept, like Sharpe ratio, Treynor ratio, Sorti­no ratio, infor­ma­tion ratio and many oth­ers. The pain ratio fol­lows in the­se foot­steps. Devel­oped by Dr. Thomas Beck­er and Aaron Moore of Zephyr Asso­ciates, the pain ratio takes advan­tage of the inno­va­tions of the pain index.

The math­e­mat­ic equa­tion for the pain ratio is:

Pain Ratio = (AnnRtn(r_1,..,r₂) -(AnnRtn(c₁,..,c₂) / Pain Index(r_1,..,r₂)

where:

r₁,..,r₂ = man­ager return series

c₁,..,c₂ = cash equiv­a­lent return series

The Pain Ratio for Swan DRS and S&P 500

In the above graphs we see the two com­po­nents of the pain ratio.

The upper graph rep­re­sents the numer­a­tor, the excess return over the risk free rate. The risk-free rate is in yel­low while the Swan DRS is the blue line and the S&P 500 index is the dark red line. The graph illus­trates the rolling three-year return dif­fer­en­tial ver­sus the risk-free rate.

The bot­tom graph is the denom­i­na­tor of the equa­tion. The pain ratio uses the pain index as its mea­sure of risk. The graph illus­trates the depth, dura­tion, and fre­quen­cy of loss­es. Once again the DRS is in blue and the S&P 500 Index in dark red.

Work­ing through the num­bers, we can see that the Swan DRS risk/return trade-off is much supe­ri­or to the S&P 500 Index. Swan wins on both mea­sures- the return has been high­er and the risk low­er. The pain ratio is 2.66 for the DRS vs. 0.35 for the S&P 500 Index dur­ing the peri­od July 1997 to April 2016.

It is impor­tant to remem­ber that when ana­lyz­ing the pain ratio, the high­er the val­ue the bet­ter.

The pain ratio high­lights the strengths of the Swan DRS. The vast major­i­ty of Swan DRS’s hold­ings are in broad mar­ket ETFs, giv­ing the strat­e­gy upside poten­tial. Typ­i­cal­ly 10–15% of the DRS’s hold­ings are in hedges to pro­tect on the down­side. The trade-off between return and risk are well illus­trat­ed in the pain ratio.

Click to learn more about Swan’s DRS invest­ment approach and how this approach has fared in the past. For more infor­ma­tion please con­tact Swan at 970–382-8901.

About the author: Marc 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 Dis­clo­sures:

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 non­qual­i­fied 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®). 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.  This analy­sis is not a guar­an­tee or indi­ca­tion of future per­for­mance. 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 vis­it swanglobalinvestments.com.  119-SGI-052016