Jul 2, 2012

Volatile Assets

Why we know less about bonds than we thought

Based on the research of

Torben Andersen

Luca Benzoni

There are per­haps few finan­cial instru­ments more fun­da­men­tal than bonds. 

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Every­one from cor­po­ra­tions to trea­suries to munic­i­pal gov­ern­ments issues bonds. Those same orga­ni­za­tions, along with oth­er par­tic­i­pants like cen­tral banks, also buy bonds, using those pur­chas­es to do every­thing from prop­ping up flag­ging economies to bal­anc­ing out an invest­ment port­fo­lio. Even indi­vid­u­als buy bonds — trea­suries, sav­ings bonds, munic­i­pal bonds, and so on. The entire mod­ern econ­o­my hinges on the smooth trans­fer of cap­i­tal from lenders to bor­row­ers, and bonds play a crit­i­cal role in that.

The smooth­ness of that process depends large­ly on whether investors think the rate of return appro­pri­ate­ly reflects the bond’s under­ly­ing risk. Bonds may be rel­a­tive­ly sta­ble assets com­pared to more volatile ones like stocks — and tend to earn low­er returns as a result — but they still face a mea­sure of uncer­tain­ty. Under­stand­ing that uncer­tain­ty is impor­tant for a smooth­ly func­tion­ing bond market.

Aca­d­e­mics have been study­ing bond yield volatil­i­ty for decades, and they have devel­oped a wide­ly accept­ed bench­mark that can be direct­ly linked to the cross-sec­tion of yields — an econ­o­mist would say the volatil­i­ty is spanned by the yields.” But it turns out that may not be cor­rect, call­ing into ques­tion our under­stand­ing of risk in a very impor­tant part of our finan­cial markets.

There are near­ly $37 tril­lion worth of fixed income secu­ri­ties out there that are direct­ly linked to trea­sury bonds and close­ly relat­ed assets,” says Tor­ben Ander­sen, a pro­fes­sor of finance at the Kel­logg School of Man­age­ment. Ander­sen and his col­league Luca Ben­zoni, a senior econ­o­mist at the Fed­er­al Reserve Bank of Chica­go, recent­ly used a trove of high-fre­quen­cy bond trad­ing data to deter­mine if the long-stand­ing aca­d­e­m­ic mod­el could ade­quate­ly describe the risk seen in many bonds. It could not.

When we looked at the struc­ture of the volatil­i­ties we extract­ed from the high-fre­quen­cy data, they were clear­ly not spanned or linked to the under­ly­ing bond yields in the pre­scribed fash­ion,” Ander­sen says. They were behav­ing fun­da­men­tal­ly differently.”

A Straight­for­ward Ques­tion
Ander­sen and Ben­zoni test­ed the old mod­el by tak­ing ask­ing a very straight­for­ward ques­tion: Did the mod­el actu­al­ly do as it pur­ports to? Can a cross-sec­tion of bonds actu­al­ly span volatil­i­ty? Though straight­for­ward, the ques­tion is not a sim­ple one to answer. In fact, pre­vi­ous­ly, it was thought to be unan­swer­able. The rea­son it hadn’t been test­ed seri­ous­ly before is that peo­ple were most­ly think­ing of these volatil­i­ties as unob­serv­able,” Ander­sen says. How do you test things that are not direct­ly observable?”

For­tu­nate­ly, Ander­sen had devel­oped a tech­nique a few years ago for mea­sur­ing yield volatil­i­ties in high-fre­quen­cy data, some­thing that had been very dif­fi­cult to do. By apply­ing that met­ric to a very detailed data set — Gov­PX, which con­tains intra­day yields and trade data from near­ly every major Trea­sury secu­ri­ties bro­ker — he and Ben­zoni were able to see that volatil­i­ty was not, in fact, spanned by yields.

The rea­son it hadn’t been test­ed seri­ous­ly before is that peo­ple were most­ly think­ing of these volatil­i­ties as unob­serv­able,” Ander­sen says. How do you test things that are not direct­ly observable?”

The way the stan­dard mod­el is actu­al­ly set up, it’s a rel­a­tive­ly lin­ear map­ping between the expect­ed returns and cer­tain risks,” Ander­sen says. After the volatil­i­ties have moved, the yield should also have moved.” And, he adds, yields also should have moved in a con­sis­tent man­ner. What we find is, to be hon­est, that this prop­er­ty is bad­ly vio­lat­ed,” Ander­sen says. We don’t have to put too much struc­ture on to find out that this doesn’t quite work.”

There’s this unspanned sto­chas­tic volatil­i­ty fea­ture that turns out to be impor­tant for the bond mar­kets, we think.”

With the stan­dard aca­d­e­m­ic mod­el poten­tial­ly bad­ly bro­ken, Ander­sen rec­om­mends a fix. His advice is to look out­side yield cross-sec­tions for infor­ma­tion that might bet­ter char­ac­ter­ize volatil­i­ty. One such promis­ing area is macro­eco­nom­ic data that are not already rep­re­sent­ed in bond yields. These might include infla­tion not account­ed for in yield curves, expec­ta­tions about mon­e­tary pol­i­cy, or even some knowl­edge about the glob­al busi­ness cycle.

While the stan­dard mod­el is promis­ing, Ander­sen does not think there is a bul­let­proof rem­e­dy for its prob­lems. There are some recent papers that pur­port to do some of this, but I wouldn’t declare suc­cess yet,” he notes.

Advice for Port­fo­lio Man­agers
Though prac­ti­tion­ers do not direct­ly use the stan­dard aca­d­e­m­ic mod­el test­ed in this study, Ander­sen points out that it serves as a foun­da­tion for algo­rithms that are used by traders. That pos­es a prob­lem. In a per­fect world, prac­ti­tion­ers would be able to quick­ly sell an asset that is drag­ging down their port­fo­lio, but that is not always pos­si­ble. Many traders in charge of large hold­ings, Ander­sen says, are going to have a tril­lion dol­lars worth of nom­i­nal bonds with var­i­ous matu­ri­ties. It’s not that easy to get rid of a third of the portfolio.”

To com­pen­sate for that lack of agili­ty, traders assess their risk expo­sure using some vari­ant of the stan­dard aca­d­e­m­ic mod­el and then con­struct a hedg­ing strat­e­gy based on the model’s results. Yet if the algo­rithms that help traders gauge risk are flawed — as Ander­sen and Benzoni’s research sug­gests — then many hedges may not ade­quate­ly cov­er a portfolio’s risks.

Until exist­ing mod­els are over­hauled to become less reliant on yield spans and incor­po­rate more of the macro­eco­nom­ic data that Ander­sen sug­gests would be use­ful, traders should be cau­tious when build­ing a bal­anced port­fo­lio. Based on his research, Ander­sen says, I would warn against using what the mod­el would tell you would be a decent hedge.”


Relat­ed read­ing on Kel­logg Insight

The Trou­ble with VPIN: New eco­nom­ic indi­ca­tor fails to live up to its promises

The VIX, CIV, and MFIV: Mea­sur­ing up the accu­ra­cy of option-based pre­dic­tors of volatility

Banks, Bonds, and Account­ing Qual­i­ty: Poor finan­cial report­ing can deter­mine your lend­ing options

Featured Faculty

Torben Andersen

Nathan S. and Mary P. Sharp Professor of Finance, Department Chair of Finance

About the Writer

Tim De Chant was science writer and editor of Kellogg Insight between 2009 and 2012.

About the Research

Andersen, Torben, and Luca Benzoni. 2010. “Do Bonds Span Volatility Risk in the U.S. Treasury Market? A Specification Test for Affine Term Structure Models.” Journal of Finance. 65(2): 603-653.

Read the original

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