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How Some Managers Walk the Line

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Analyzing Linear Regressions of Active & Passive Funds

In a recent Swan blog post, we explored how the active-vs-pas­sive debate miss­es the point by fail­ing to dis­cuss what investors care about most: absolute per­for­mance and risk man­age­ment. In this post, we will dive deep­er by ana­lyz­ing the broad market’s impact on a vari­ety of man­ag­er types.

The tech­nique we will use for this analy­sis is referred to as lin­ear regres­sion. It’s called a lin­ear regres­sion because you lit­er­al­ly draw a straight line through a scat­ter­plot of a manager’s returns and the bench­mark. The goal of the lin­ear regres­sion is to get a line that best fits the data. Alpha, beta, and R-squared (R2) are gen­er­at­ed via a lin­ear regres­sion.

From a sta­tis­ti­cal stand­point, this is a well-estab­lished tech­nique. But from an invest­ing stand­point, does it real­ly make any sense to track that line of best fit? If the mar­ket is down -30%, -40%, or -50%, shouldn’t the investor try to be as far away from that mar­ket line as pos­si­ble?

To explore this fur­ther, we ana­lyze the impact of sys­tem­at­ic risk on four types of strate­gies, name­ly:

  1. A pure pas­sive man­ag­er, rep­re­sent­ed by Van­guard 500 Index
  2. A tra­di­tion­al active man­ag­er, rep­re­sent­ed by Growth Fund of Amer­i­ca
  3. A fac­tor-dri­ven/s­mart beta strat­e­gy, rep­re­sent­ed by DFA US Large Cap Val­ue
  4. A hedged equi­ty approach, rep­re­sent­ed by Swan’s Defined Risk Strat­e­gy

The Passive Manager: Vanguard 500 Index

Below we see a lin­ear regres­sion for the Van­guard 500 fund (VFINX) from Jan­u­ary 1998 to Decem­ber 2016 using annu­al returns. There are no sur­pris­es here. Its plot points are imme­di­ate­ly rec­og­niz­able. The -37.02% return was 2008, the +32.18% return was 2013, et cetera. The returns of the pas­sive fund track the S&P 500 index as close­ly as pos­si­ble; the fund is doing exact­ly what it should be doing. But the prob­lem is when the mar­ket tanks, the fund tracks it down in lock-step. In essence, it IS the mar­ket.

Vanguard 500 Index Linear Regressions - Swan Blog

Essen­tial­ly, the equa­tion for the regres­sion is the cap­i­tal asset pric­ing mod­el. The 0.999 coef­fi­cient is the slope of the line, also known as beta. The y-inter­cept of -0.0009 is the alpha, which is slight­ly neg­a­tive due to fees. We see the R2 as a per­fect 1 (or 100%) mean­ing the 100% of the vari­ance of returns in the fund is explained by the vari­ance of returns in the bench­mark.


The Traditional Active Manager: Growth Fund of America

Let us now look at a tra­di­tion­al active man­ag­er. In this case, we are look­ing at one of the most pop­u­lar funds in exis­tence, the Growth Fund of Amer­i­ca (AGTHX). Again, we will use the time frame Jan­u­ary 1998 to Decem­ber 2016 and annu­al returns.

American Funds Growth Fund of America - Linear Regressions - Swan Blog

Unlike the Van­guard index fund, the straight red line of the S&P 500 does not per­fect­ly fit this data. How­ev­er, it isn’t very dif­fi­cult to draw the blue dot­ted line through the scat­ter­plot and come up with a solu­tion that cap­tures 86.43% of the vari­ance of returns. We see Growth Fund’s beta being slight­ly above 1.0 as the coef­fi­cient is 1.064 and we see a pos­i­tive alpha, even after tak­ing into account fees. But see­ing how close­ly the indi­vid­ual dots hug the red line of the S&P 500, we can con­clude that sys­tem­at­ic risk is the pri­ma­ry dri­ver of per­for­mance.


The Factor-Driven Strategy: DFA US Large Cap Value

What about a fac­tor-dri­ven, “smart beta” strat­e­gy, like DFA US Large Val­ue (DFLVX)? Even though this is clas­si­fied as a large cap val­ue fund, the major­i­ty of its returns can be explained by the S&P 500 (red line). There is slight­ly more dis­per­sion from the best fit line than we saw with Growth Fund of Amer­i­ca, and there is pos­i­tive alpha in this regres­sion. But it is still safe to say by look­ing at the blue dot­ted line that the DFA fund has a lin­ear rela­tion­ship with S&P 500 mar­ket, for bet­ter or worse.

DFA US Large Cap Value - Linear Regressions - Swan Blog

With both Growth Fund of Amer­i­ca and DFA US Large Val­ue we see that the mar­ket risk is the pri­ma­ry dri­ver of both pos­i­tive and neg­a­tive returns. Broad­ly speak­ing, a bad year in the mar­ket equates to a bad year for the stock-pick­er or the fac­tor fund. On the flip side, a good year in the mar­ket will mean a good year for either strat­e­gy.


The Hedged Equity Approach: Swan’s Defined Risk Strategy

Final­ly, let’s turn our atten­tion to the Defined Risk Strat­e­gy. The dots of the scat­ter­plot are much “flat­ter” than the red mar­ket line, mean­ing the beta is low. The DRS lacks some of the upside of the mar­ket, but more impor­tant­ly, avoids a good por­tion of the down­side. It is pos­si­ble to draw a line through the data, but the blue, dot­ted regres­sion line doesn’t do a very good job of explain­ing the DRS’s per­for­mance. The R2 “good­ness of fit” is only 22.9%. There is pos­i­tive alpha, mean­ing there has been an excess return har­vest­ed for the amount of risk tak­en.

DRS Linear Regressions - Swan Blog

The rea­son why the DRS has such a unique regres­sion is because of its hedg­ing. Even though the mar­kets were down in 2000, 2001, 2002 and 2008, the DRS par­tic­i­pat­ed lit­tle in those bear mar­kets. There haven’t been any dou­ble-dig­it cal­en­dar year loss­es. Two of the neg­a­tive years occurred dur­ing flat years in the mar­ket when the car­ry­ing cost of the hedge wasn’t off­set by gains in the equi­ty mar­ket or pre­mi­um col­lec­tion income (2011 and 2015). There haven’t been many years of extreme­ly out­sized returns, but most of the annu­al returns fall into a rather tight range, regard­less of mar­ket con­di­tions.

This, of course, is all by design.

The DRS does not want a lin­ear rela­tion­ship to the mar­ket. The DRS seeks to par­tic­i­pate in mar­kets when they are ris­ing, but active­ly hedges against down­ward moves.

The goal of the DRS is illus­trat­ed by a tar­get return band. The tar­get return band is one of the key con­cepts or tools we use at Swan.

Target Return Band - Linear Regressions - Swan Blog

The diag­o­nal red line is the prof­it-loss dia­gram for the S&P 500. The curved gold line rep­re­sents the return pro­file of the DRS’s hedged equi­ty posi­tion: the buy-and-hold posi­tion in the mar­ket com­bined with the pro­tec­tive ele­ments of the hedge. The gold line lags the S&P 500 in up mar­kets but is still upward slop­ing. In down mar­kets, the hedged equi­ty posi­tions flat­ten out as the S&P 500 con­tin­ues to drop. The grey-blue area around the gold curve is the antic­i­pat­ed range of impact from over­lay­ing Swan’s short-term pre­mi­um col­lec­tion trades over the hedged equi­ty posi­tion. It is our goal that returns of the DRS will be with­in or above the blue shad­ed area. In 20 of 21 years, they have been.

For an in-depth dis­cus­sion of the tar­get return band please refer to the blog post, “The Tar­get Return Band.”

Van­guard, Amer­i­can and DFA were cho­sen as rep­re­sen­ta­tives for the dif­fer­ent invest­ment approach­es due to their pop­u­lar­i­ty with investors and their long track records. How­ev­er, based upon the results seen in the first sec­tion, I could have run sim­i­lar regres­sion analy­sis on just about any of the 1,451 mutu­al funds in the domes­tic equi­ty space, and the vast major­i­ty of funds would have had scat­ter­plots that looked very sim­i­lar to Amer­i­can or DFA. This is why at the out­set of this blog series, we made the claim that the deci­sion between active and pas­sive man­age­ment is not the debate we should be hav­ing. The real risk to an investor, the risk we should be focused upon, is sys­tem­at­ic risk.


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:

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®).

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 254-SGI-100917


By |2018-11-12T16:24:38+00:00October 12th, 2017|Blog|Comments Off on How Some Managers Walk the Line: Analyzing Linear Regressions of Active & Passive Funds