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The Impact of Volatility Drag on Investment Returns

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In a pre­vi­ous ‘Math Mat­ters’ blog post titled, “The Impor­tance of Avoid­ing Large Loss­es,” we dis­cussed the impacts of large loss­es on port­fo­lios and wealth cre­ation. Cer­tain­ly any­one who lived through the Dot-com crash of 2000-02 or the finan­cial cri­sis of 2007-09 is well aware of the dam­age that loss­es of 30%, 40% or 50% can have on a port­fo­lio. What many peo­ple don’t know, how­ev­er, is the impact that volatil­i­ty drag has on the long-term suc­cess of an invest­ment plan.

If bear mar­kets can be described as a rare but cat­a­stroph­ic flood for a port­fo­lio, then every­day volatil­i­ty can be seen as water dam­age slow­ly that erodes away the foun­da­tions of your house (invest­ment returns).

Increasing Volatility can Create a Drag on Investment Returns | Swan Blog

Source: Swan Glob­al Invest­ments

Invest­ment returns are often stat­ed as long-term aver­ages. The prob­lem with aver­ages, how­ev­er, is that aver­ages mask details. The day-to-day or month-to-month expe­ri­ence of an investor might be rad­i­cal­ly dif­fer­ent from the long-term aver­ages. What hap­pens in-between might have a large impact on the final wealth of an investor.

Again, we start with a sim­ple illus­tra­tion. If one were asked which of the fol­low­ing three sce­nar­ios would yield the best ten-year results, one might be tempt­ed to choose the last of these three options:

  1. Up 10% one year, down 5% the next, repeat­ed for ten years
  2. Up 25% one year, down 20% the next, repeat­ed for ten years
  3. Up 40% one year, down 35% the next, repeat­ed for ten years

In fact, the oppo­site is true. After a decade:

  • Sce­nario A, with its most mod­est gains and loss­es, per­forms best and is the only sce­nario that is prof­itable;
  • Sce­nario B breaks even and;
  • Sce­nario C los­es mon­ey.

This phe­nom­e­non is known as volatil­i­ty drag. Also called vari­ance drain, volatil­i­ty drag was detailed in a 1995 paper by Tom Mess­more titled “Vari­ance Drain — Is your return leak­ing down the vari­ance drain?”. Mess­more observed that the more vari­able a giv­en asset’s return is, the greater the dif­fer­ence between the arith­metic and geo­met­ric returns.

  • Arith­metic mean is the aver­age of a set of numer­i­cal val­ues, cal­cu­lat­ed by adding togeth­er and divid­ing by the num­ber of terms in the set (Source: Wikipedia).
  • Geo­met­ric mean is defined as the val­ue of a set of num­bers by using the prod­uct of their val­ues, as opposed to the arith­metic mean which uses their sum (Source: Wikipedia).

Formula for Volatility Drag or “Variance Drain”

Formula for Variance Drain or Volatility Drag | Swan Blog

This for­mu­la shows that the vari­ance of returns “drains” the arith­metic aver­age returns to pro­duce the small­er, real­ized, com­pound returns (Source: Deck­er, Robert: The Vari­ance Drain and Jensen’s Inequal­i­ty).

Why does this mat­ter for investors? 

It ties back to our pre­vi­ous posts on com­pound­ing returns and min­i­miz­ing loss­es.

In order to opti­mal­ly take advan­tage of the pow­er of com­pound­ing, investors must avoid large loss­es and recov­er­ies requir­ing expo­nen­tial growth. In addi­tion, investors must also avoid the neg­a­tive pow­er of com­pound­ing by seek­ing to low­er volatil­i­ty and vari­ance drain as best as pos­si­ble.

The table below shows dif­fer­ent sce­nar­ios with the same arith­metic annu­al return (i.e. 10%) but cou­pled with dif­fer­ent lev­els of volatil­i­ty.

 

Increased Volatility can Cause Negative Geometric Returns - Swan Blog

Source: Tyton Cap­i­tal Advi­sors, “Low Charges And High Volatil­i­ty: How To Erase Your Returns”

Gen­er­al­ly speak­ing, there are two rules of thumb to remem­ber when it comes to volatil­i­ty drag.

  1. The high­er the lev­el of volatil­i­ty, the more detri­men­tal the impact of volatil­i­ty drag, as evi­denced in the table above.
  2. The longer the time peri­od, the big­ger the neg­a­tive impact will be.

This sit­u­a­tion is also explored in a post on volatil­i­ty we recent­ly wrote for ETFTrends.com. In addi­tion, the greater the volatil­i­ty, the more unlike­ly it is that an investor will be able to “stay the course” and stick with an invest­ment or strat­e­gy.

We can see how these fac­tors all tie togeth­er in their math­e­mat­i­cal appli­ca­tion with­in an investor’s port­fo­lio: com­pound­ing, avoid­ing large loss­es, and now volatil­i­ty. Com­pound­ing, whether neg­a­tive or pos­i­tive, is the com­mon thread through­out all of them. As a recap, the four key math­e­mat­i­cal prin­ci­ples out­lined in “Math Mat­ters” are:

  1. The impor­tance and pow­er of com­pound­ing
  2. The val­ue of avoid­ing large loss­es to returns
  3. The impor­tance of vari­ance drain
  4. The val­ue of a non-nor­mal dis­tri­b­u­tion of returns

The last blog post in this ‘Math Mat­ters’ series will dis­cuss the chang­ing the shape of dis­tri­b­u­tion of returns.

 

 

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

 

 

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By | 2017-08-08T12:04:43+00:00 September 27th, 2016|Blog|Comments Off on Volatility is a Drag

About the Author:

As Director of Investment Solutions, Marc 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.