ii
De laração
No e: Diogo Maia Ma ues
E de eço elet ó i o: diogo aia a ues @g ail. o Telefo e:
Nú e o Bilhete Ide tidade:
Título Disse taç o: á d a i odel o ash holdi gs O ie tado : P ofesso Douto á tu Rod igues
Desig aç o do Mest ado: Mest ado e Fi a ças
É áUTORI)áDá á REPRODUÇÃO INTEGRáL DESTá TESE/TRáBáLHO áPENáS PáRá EFEITOS DE INVESTIGáÇÃO, MEDIáNTE DECLáRáÇÃO ESCRITá DO INTERESSáDO, QUE á TáL SE COMPROMETE;
U i e sidade do Mi ho, de á il de
ássi atu a: ______________________________________ Diogo Maia Ma ues
iii
Agrade i e tos
T o i po ta te o o ual ue u a das segui tes pa tes, esta p gi a o de e p esso os eus ais si e os ag ade i e tos a todos, ue e o fia a , apoia a e a o pa ha a a i ha ida es ola . Nesta lista de pessoas, i luo, pais ue uito se esfo ça a pa a eu pode al a ça este pata a a ad i o, fa ília e a igos ue se p e e ajuda a e oti a a . Realço ta , o papel dete i a te do P ofesso Douto á tu Rod igues, eu o ie tado , ue a o pa hou todo o p o esso, dispo i ilizou ate ial e ealizou sugestões ue, ajuda a a esol e e alo iza o t a alho.
i
Resu o
Esta disse taç o p ete de dese ol e u odelo di i o ujo o jeti o p i ipal a alisa os efeitos dos i postos o í el óti o de ai a, asea do-se o odelo dese ol ido po Huggo ie et al. , o ual o side a do ue as de isões de gest o ao í el do i esti e to, fi a ia e to e políti a de di ide dos t i pa to so e o es o. Este odelo suge e ue o i pa to dos i postos o í el óti o de ai a o li ea , dado ue depe de do í el de esultados e do í el das dep e iações da e p esa. Deste odelo esulta ue os i postos faze eduzi o í el óti o de ai a ape as ua do as dep e iações s o supe io es aos esultados.
A stra t
This disse tatio de elops a d a i odel o ash holdi gs, ai i g to a al se the effe t of ta es i the opti al le el of ash holdi gs, ased i a d a i odel de eloped Huggo ie et al. , hi h o side s a age e t de isio s i te s of i est e t, fi a i g a d di ide d poli . This odel suggests that the i pa t of ta es i opti al le el of ash holdi gs is o -li ea . It depe ds o the le el of ea i gs a d dep e iatio s of a fi . It is sho that ta es edu e the opti al le el of ash he the dep e iatio s a e highe tha the ea i gs.
Ta le of Contents
De la ação ... ii Ag ade i e tos ... iii Resu o ... i A st a t ... . I t odu tio ... . Lite atu e Re ie ... . . Cash Holdi g Theo ... . . Cash Holdi gs E pi i al E ide e ... . . D a i Models of Cash Holdi gs ... . Methodolog ... . Results ... . . Co pa ati e “tati s ... . . . Ta get ash holdi gs a e de easi g ith age osts ... . . . Ta get ash holdi gs a e de easi g ith p ofita ilit u ... . . . Ta get ash holdi gs a e de easi g ith i o e ta ... . Co lusio ... Bi liog aph ... Appe di ... A. Elasti it ... B. P oofs of the Methodolog ... C. P oofs of the Results ... C. . Mo oto i it of Volatilit a d P ofita ilit ... C. . Mo oto i it of Ta es ...
. Introdu tion
I a o ld he e the apital a kets a e pe fe t, the p o le of i te al apital a age e t does ot o u , e ause the fi ould aise as u h apital as it a ts, ithout osts. Ho e e , i a eal o ld the e a e a ket i pe fe tio s, su h as as et of i fo atio a d t a sa tio s osts, hi h e ui e the fi to a age its ash ese es. Ke es a gued that fi s should ai tai e ess li uidit to take ad a tage of p ofita le futu e i est e t oppo tu ities, a d a a to uffe pote tial ope ati g losses. Re e tl , oti ated i ease of o po atio s’ ash holdi g i the U“A Ditt a et al., , so e studies ha e ee de eloped odels a d e pla atio s fo fi s a age thei i te al apital a d pa out poli Dé a ps et al., ; Hugo ie et al., ; Ki et al.,
; Mo elle et al., ; Opple et al., .
This disse tatio de elops a d a i odel of ash a age e t, i est e t a d fi a i g de isio s. Its ai o je ti e is to e plai a d sho ho the di ide d ou da ha ges he ta i o e ha ges. Additio all , it ill e sho , ho the diffe e t pa a ete s of the odel affe t this di ide d ou da . Fo this pu pose, t o ki ds of ash holdi g osts a e assu ed. O e is elated to lo ash etu a d a othe to age osts, as p oposed Je se . It ill e assu ed that the fi is fi a iall o st ai ed. “o, etai i g ash i gs e efits to the fi , e ause the e a e osts sa i gs i elatio to the fi ’s uses of the i te al apital, to fi a e its i est e ts o o pe sate its ope atio al losses, i stead of e te al fi a i g. Additio all , i te al apital allo s the fi to take ad a tage of p ofita le futu e i est e t oppo tu ities.
The odel p oposed i this disse tatio is ased i the pa out poli odel p oposed DeA gelo et al. . Whe ash ea hes a e tai le el, the est poli is fo the fi to sta t dist i uti g di ide ds. The odel ill i lude ta es, hi h affe t a sto hasti ash flo , as ell as dep e iatio s. Usi g the ethodolog p oposed Hugo ie et al. , the odel sho s that the le el of ash holdi gs de eases ith ta es, o l he the a ual dep e iatio of a fi is highe tha its ea i gs. It is i po ta t highlight that the opposite
situatio is e ified. I pa allel ith Dé a ps et al. . I sho that the le el of ash holdi gs de eases he the age osts e o e o e se e e.
The disse tatio p o eeds as follo s. “e tio p ese ts the lite atu e de isio s. “e tio the d a i odel. “e tio sho s ho the se e al fa to s affe t the opti al ash le el. “e tio o lude.
. Literature Re ie
. . Cash Holdi g Theo
“e e al autho s ha e o du ted studies a out a opti al le el of ash holdi gs. A opti al le el of ash holdi gs follo s f o a t ade-off et ee e efits - as a i i izatio of t a sa tio fi a ial osts, u de taki g i est e t oppo tu ities i ase of a ket f i tio s - a d osts asso iated to ash holdi gs. E pi i al e ide e sho s that a gi al e efits ha e a egati e slope, asso iated ith a de easi g utilit of a additio al u it of ash to o e the ope ati g osts. The a gi al osts a e o sta t, asso iated ith oppo tu it osts, lo e etu of ash a d age osts that happe he the i te ests of the sha eholde s diffe f o the i te ests of the de tholde s.
Figure - The opti al le el of ash holdi gs is gi e the i terse tio of the argi al ost ur e of ei g short of ash a d the argi al ost ur e of holdi g ash, Mollere et al. , p. .
If the e is a pe fe t apital a ket, this t ade-off ould e easil sol ed, e ause the e a e o t a sa tio osts, hi h i plies that the p o le of holdi g ash does ot a ise, a d fi s ould dist i ute all thei p ofits to the sha eholde s.
The e a e so e theo eti al pape s hi h fi d a ia les that e plai a d justif ha ges i the opti al le el of ash holdi gs. Ma ket i pe fe tio s, su h as as et of i fo atio o t a sa tio osts, i pl that the fi should ha e a dete i ed a ou t of ash. The la k of i fo atio ould lead to the o pa ies u de e aluatio i gi g osts to itself.
Fi a ial o st ai ts usuall o u i le e ed fi s, hi h akes the osts of aisi g fu ds highe , fo i g the fi to ut di ide d pa e ts to i ease the le el of ash holdi gs. Fu the o e, age osts also o u i these fi s, aki g it e pe si e to hold ash
ese es, e ause it is assu ed that ash is ot used i a o e t a e . Ke es
a gued that fi s should ai tai e ess li uidit to take ad a tage of p ofita le futu e i est e t oppo tu ities, hi h ep ese t a alte ati e a of fi a i g he outside fu ds a e u a aila le spe ulati e oti e . Also, fi s should ai tai e ess li uidit to
uffe pote tial ope ati g losses p e autio a oti e .
Li uidit is a a to ai tai fi a ial fle i ilit , hi h is see as a ke to sustai eal ope atio s of fi s a d a ke to a age thei de t apa it . C edit li es a e also a a of li uidit hi h ould egati el affe t the di ide d ou da of the fi , he it has a ess to this asset. Most studies sho that the igge the fi ’s e posu e le el of u e tai t
ega di g i te al a d e te al fa to s, the highe the le el of li uidit should e .
A o di g to DeA gelo et al. , fi s dist i ute di ide ds he thei ash ese es ea h a ta get le el. B o t ast, e e uit is issued as the fi u s out of ash. It is assu ed that the osts of issui g e uit a e al a s so lo as to gua a tee that it is p efe a le to issue e uit , as a a of fi a i g, tha li uidati g the fi .
. . Cash Holdi gs E pi i al E ide e
Mille et al. a d Ki et al. assu ed that the e is a opti al le el of ash holdi g. Ople et al. do ot assu e a opti al le el, ased o the a gu e t that othi g ha ges i a o po atio if it has o e o e dolla of ash fi a ed o e o e dolla of de t . I othe o ds, the e is o opti al a ou t of ash, e ause ash is si pl egati e de t , Ople et al. , p. . M e s & Majluf , i thei o t i utio to the pe ki g o de theo , sho ed that e te al fu di g has a highe ost tha ash holdi gs,
a d that aisi g e uit is o e e pe si e tha a othe sou e of fi a i g. Je se has the i e se idea. He lai s that e essi e a ou t of ash should e paid out o fi a e all positi e NPV p oje ts, to i i ize the age osts, as the autho elie es that the age osts a e ge e ated e essi e ash flo .
Lite atu e a out the pa out poli sho s that, o e the ea s, di ide ds e e the ost o o a to edist i ute the e essi e ash. No ada s, it is e ide t, see Figu e , a sig ifi a t i ease of sha es epu hases is oti ated fi a ial fle i ilit gi e the Ve aele , . This as oti ated ta ad a tage of sha es epu hases hi h a e ta ed o a apital gai elati g to di ide ds hi h a e ta ed as o di a i o e , ei g the apital gai lo e tha the o di a i o e. A othe a to use the e essi e ash is to i ease the et o ki g apital, hi h is see as a su stitute of ash.
Figure - Distri utio of fir s pa out ethod for a sa ple of USA fir s. REPO is the e pe diture o the pur hase of o o a d preferred sto ks; DIV is total dollar a ou t of di ide ds de lared o o o sto k; MV is the arket alue of o o sto k; Alle et al. , p. .
The pa out poli a also e used to i ease i te al fu ds, he the fi is fi a iall o st ai ed. This a e do e i easi g the etai ed ea i gs utti g di ide d pa e ts, Fazza i et al., , a d pa i g di ide ds he fi s ha e highe ash ala es, Ople et al., . The efo e, it is e pe ted that fi s ith highe effe ti e ta ates hold lo e ash ala es, e ause a highe ta ate ould o espo d to a highe ta shield, that
ep ese ts a highe oppo tu it osts of holdi g ash, Bigelli et al. .
Addittio all , Beuseli k et al. usi g data f o ulti atio al Eu opea o po atio s, sho ed that o pa ies o posed su sidia fi s eed o e le els of li uidit . A stud
pe fo ed Ditt a et al. fou d e ide e that fi s hi h ha e highe Resea h a d De elop e t R&D te d to hold o e ash. A stud pe fo ed Ople et al.
sho ed that fi s ith o e g o th oppo tu ities a d iskie ash flo s te d to hold o e ash. Lastl , Mikkelso & Pa t h p o ed that fi s holdi g a la ge pe e tage of ash do ot u de pe fo i elatio to othe fi s f o thei i dust , hi h p o es that the
osts asso iated ith ash holdi g do ot i flue e the esults sig ifi a tl .
. . D a i Models of Cash Holdi gs
Molle e et al. de eloped a ash holdi g fu tio ased o a oligopolisti a ket odel of a si gle p odu t, i hi h the goal of ea h fi is to a i ize the p ese t alue of futu es di ide ds. To ea h the opti al le el of ash, the ash holdi g fu tio is opti ized depe di g o the p ofit fu tio of ea h fi , the i te ests of ash holdi gs, the fi a i g a ou t aised, the di ide d poli a d the issua e osts elated to fi a i g. The o lude that the opti al le el of ash should o e all ope ati g losses ithout ha i g to issue e uit . Fu the o e, he li uid assets a e ot suffi ie t, the fi should i ease fi a i g to a g eate a ou t, ea i g i i d that, fo ea h u it aised the fi , the lo est the issua e ost ill e. The ai o lusio is that the le el of ash holdi g is st o gl affe ted o petitio a d fi a i g o st ai s.
Hugo ie et al. defi e a a ie afte hi h aisi g ash holdi gs ill ot e efit the fi . To fi d this a ie , the assu e that the a gi al ost of holdi g ash is o sta t, a d the a gi al e efit of holdi g ash is de easi g, hi h esults i a opti al le el of ash. To a i ize sha eholde ’s ealth, the de eloped t o odels, o e i hi h it is possi le to e pa d the p oje t a d a othe hi h is ot possi le to e pa d. Th ough the opti izatio of these t o odels, the o luded the follo i g. Whe the le el of ash holdi gs is elo the opti al poi t, the fi should etai its ea i gs u til it ea hes the opti al le el ut, if at the sa e ti e, the fi has a i est e t oppo tu it , the p oje t should e fi a ed ith e te al fu ds. Whe the le el of ash holdi g is a o e opti al,
the fi should dist i ute the ea i gs. Ne e theless, if the fi has a i est e t oppo tu it , the p oje t should e fi a ed ith ash fu ds.
Dé a ps et al. i thei o t i utio to the lite atu e elated to the ta get le el of ash holdi gs, de eloped a odel hi h a i izes the alue of the fi i elatio to opti al e uit issua e, o side i g fi a i g a d age osts. This auses the fi alue to ha e a i easi g a d o a e fu tio of the le el of ash ese es, hi h o fi s the theo that a gi al e efits of holdi g ash is a de easi g a d o e fu tio of the le el of ash ese es. The o luded that the a gi al alue of ash fo sha eholde s i eases ith issua e osts, the ta get le el of ash i eases ith the olatilit of ash flo s a d the ag itude of issua e osts. I additio , the de eloped sto k p i e d a i s that de i e f o the opti al le el of ash. The also p edi ted that the e is a egati e elatio ship et ee the a gi al alue of ash a d the sto k p i e, efle ti g the fa t that o e o e u it of ash de eases the p o a ilit of issue e uit a d, o se ue tl , ust i u i less issua e osts. Fu the o e, the sho that, he age osts e o e o e se e e, the olatilit of sto k etu s i eases, hi h leads to a i ease of e te al fi a i g osts, fo i g the fi to ai tai the ash ese es le el.
. Methodolog
I this odel, it is o side ed that age ts a e isk- eut al, hose ash flo s a e dis ou ted at a o sta t ate . It is assu ed a fi is su je t to a ta ate a d elo gs to a pe fe t o petitio a ket, he e the p i e, the ope ati g osts a d the ua tit of output sold is gi e the a ket at a ti e > . The a e age of ope ati g ash flo is de oted ,a d it is e posed to sto hasti sho ks gi e a B o ia otio p o ess . The efo e, a fi is e posed to pote tial ope ati g losses that a e o e ed, eithe usi g ash ese es o issui g e e uit . Net ash flo Π also o side s the ta shield of the fi , he e is the alue of dep e iatio . The efo e, the e olutio of the et ash flo is gi e :
= . − + . + . .
Whe a fi has a positi e et ash flo , a age e t to etai s ea i gs i side the fi , de oted at a ti e t > . It is assu ed that the e is a ost of holdi g ash ith a etu , hi h is lo e tha . The diffe e e et ee oth a e i te p eted as a a ost of ash . A othe a to aise fu ds is to fi d fi a i g th ough outside i esto s. No etheless, the e a e so e apital suppl f i tio s, su h as: the ti e to se u e outside fu di g a d the u e tai t elated to apital suppl , hi h akes fi di g i esto s o e o pli ated. Hugo ie et al. i thei o t i utio to d a i ash holdi g odels, aptu ed these apital suppl f i tio s, th ough the pa a ete , hi h ep ese ts the a i al ate of i esto s, assu i g that a fi fi ds i esto s a o di g to Poisso p o ess. This i plies that he = , the fi a ot aise fu ds i apital a kets a d ust fi a e itself o l ith i te al fu ds. Whe → ∞, the e a e o f i tio s i apital a kets, hi h i plies that the fi a issue fu ds i sta ta eousl f o the apital a kets a d does ot eed ash ese es. Due to the u e tai t of apital a kets, e i esto s, du i g the egotiatio of the te s of a e issua e, use thei a gai i g po e
, to aptu e su plus f o efi a i g.
The su plus is gi e :
. = + − −
Go pe s et al. sho that the su plus aptu ed e i esto s de eases ith the apital suppl , hi h ea s, the la ge the , the s alle the .
I this a , the d a i s of the fi ’s ash ese es a e gi e :
C = . + . − + . + . . − + .
he e ep ese ts the pa outs to sha eholde s a d Poisso p o ess at a ti e . Fu the o e, it is sho that ash ese es g o ith i te est ea ed o ash holdi gs, et ope ati g ash flo a d ith outside fi a i g. O the othe ha d, the de ease ith pa outs to sha eholde s. As a age e t seeks to a i ize the alue of the fi hoosi g ot o l the fi ’s i est e t poli ut also its pa out poli , fi a i g a d li uidatio poli ies, it is assu ed that , , a d a e e oge ousl dete i ed.
To a i ize the fi alue, it is e essa to fi d the le el of ash that a i izes the e efits fo the fi . It is assu ed that the a gi al e efit of holdi g ash is de easi g a d that the a gi al ost of ash holdi gs is o sta t. The e is a le el of ash uffe ∗
he e the a gi al ost a d e efit a e e ualized. “o, a o e this le el, it is opti al to sta t pa i g di ide ds, a d so the follo i g ou da o ditio applies:
lim⟶ ∗ ∗ =
This ea s that, if the a gi al alue of ash is g eate tha o e, it is opti al to etai ash. Whe the a gi al alue of ash de eases u til it ea hes o e, it is opti al to sta t pa i g di ide ds. The alue- a i izi g pa out t igge is dete i ed the high- o ta t
o ditio :
Co side i g the egio fo hi h it is opti al to etai ea i gs , ∗ , the fi alue
o plies ith the follo i g o di a diffe e tial e uatio ODE :
+ . + . − + . + . ∗ − ∗+ − =
The left-ha d side of the e uatio is the e pe ted ha ge i the fi alue i the egio he e the fi etai s ea i gs. The fi st te aptu es the effe ts of ash sa i gs o fi alue, the se o d o e aptu es the effe ts of ash flo olatilit a d the thi d o e efle ts the effe t of apital suppl . The ight-ha d side ep ese ts the e ui ed ate of etu to i est i the fi .
Whe the le el of ash i the fi is g eate tha the opti al le el, a fi should dist i ute all ash holdi gs a o e ∗ th ough di ide ds, a d the alue of the fi is gi e :
∗ + − ∗
It is also assu ed that a fi a a a do its assets at a ti e dist i uti g all its ash. O the othe ha d, a fi a e fo ed to li uidatio , if its ash uffe ea hes ze o follo i g a se ies of egati e sho ks. Fo the fi to e a ti e fo a lo g pe iod, it is o side ed that the li uidatio alue of assets is gi e = . , he e φ ∈ [ , ] ep ese ts
the ta gi ilit of the assets at ti e of li uidatio . “o, the alue- at hi g o ditio he the ash uffe ea hes ze o is:
= .
Usi g ou da o ditio s a d , follo i g Hugo ie et al. , I sol e the ODE o tai i g the e p essio , hi h sho s the et alue of a fi fi a iall o st ai ed fo all le els of ash holdi gs.
ODE as o tai ed f o Ito’s Le a
All p oofs should e see i Appe di B a d i Hugo ie , J., Mala ud, “., Mo elle , E. . Capital suppl u e tai t , ash holdi gs, a d i est e t. Re ie of Fi a ial Studies, , - - “e tio . a d Appe di B.
π C + L C . . − . + H C . V ∗ − H C . π ∗ , < ∗ ∗ + − ∗ , > ∗ he e, = + ∗ − ∗+ + . − + . + − = ∗∗ .. −− ∗∗ .. = ∗ .. −− ∗.. ith = − + ; ; − . + . −. + . = − + ; ; − . + . −. + .
The alue of a fi at the opti al le el of ash holdi g is o tai ed he e o es
∗. Whose alue is gi e :
∗ = . ∗+ − + .
With this ethodolog , the alue of the fi is a o a e a d a i easi g fu tio of , hi h ea s that the a gi al alue of ash ese es is g eate tha o e u til ∗. Whe
the a gi al alue of ash e o es o e, the fi sta ts to pa its di ide ds.
I Appe di B, it is sho that the e is a u i ue solutio a d t i e o ti uousl diffe e tia le fo fo the e ti e a ge of .
The e a e t o spe ifi ases i this odel. Fi st, he the e a e o a osts of ash = ut the e a e apital suppl f i tio s, the est poli fo the fi is to hold as u h ash as possi le. “e o d, he the e a e o apital suppl f i tio s , ut the e a e a osts of ash, it i plies that a fi should ot hold fu ds, e ause it ould aise fu ds as it
a ts a d the e a e osts asso iated to holdi g ash.
Figure - Fir Value he a raise depe di g the a ess to apital arkets. The para eters are: = . ,
= . , = . , = %, = . % = %.
. Results
. . Co pa ati e Stati s
As it as sho , the opti al le el of ash holdi gs is dete i ed ala i g a gi al osts ith a gi al e efits of holdi g ash. Fo e a ple, a ha ge i p ofita ilit , oti ated a ash flo sho k , o a ha ge i the ta le el , o a ha ge i the dep e iatio of the fi , o a ha ge i apital suppl f i tio s , o a ha ge i age
osts , ill lead to a ha ge i a gi al e efit of holdi g ash, hi h o se ue tl ill affe t the ta get le el of ash. I this se tio , it ill e sho a d easu ed hat the effe ts of a ha ge of a a ia le i the ta get le el of ash a e.
I o de to pe fo this a al sis, a ase- ase has ee defi ed, he e the ha a te isti s of the fi , su h as dep e iatio , a e age a d olatilit of ash flo a e e ual to . u its of ash UN , hi h a e affe ted a ta ate of %. Just like i Hugo ie et al.
e te al fa to s a e assu ed ash holdi g’s ate of etu of . % a d dis ou t ate WACC of %. I this fi st a al sis t o ases a e a al sed. The fi st, he the fi a ot aise fu ds = a d the se o d, he the fi aises fu ds i pe iods of si o ths,
hi h i plies = .
I Figu e , it is possi le to see, as i Dé a ps et al. , that the alue of the fi is a i easi g a d o a e fu tio of the ash. I Figu e the a gi al e efit of the fi is a de easi g a d o e fu tio , hi h e e goes elo o e.
Figure - Margi al Be efit of Cash Fir Value he a raise depe di g the a ess to apital arkets. The para eters
are: = . , = . , = . , = %, = . % = %.
Mo elle et al. p o ed that, the highe the fi a ial o st ai of a fi , the highe the le el of ash holdi gs, o side i g the p e autio a oti e. Ta le , sho s fo diffe e t le els of hat is the opti al le el of ash a d espe ti e elasti it i elatio to the ase- ase. It is possi le to e if that the odel is a o da e to this theo . If the a i al ate of i esto s is see as a easu e of fi a ial o st ai s. We a o se a le that the e is a highe e efit fo a fi i holdi g ash, aki g the opti al le el of ash holdi gs highe . This a e see g aphi all ith a o e e t of a gi al e efit to the ight-ha d side, hi h t a slates i a lo e alue of the fi .
The sa e esult a e see i Figu e , hi h elates to the opti al le el of ash ith the a i al ate of i esto s. Figu e a d Ta le allo a additio al a al sis, elati el to the di e sio of i pa t. Based o Ta le , it is possi le to o lude that the i pa t of the ta get le el of ash is highe he the a i al ate of i esto s i eases f o to , tha
This ethod is used i all ta les - “ee Appe di A
∗ ∗,
. - .
.
. - .
Ta le - Opti al alue of ash holdi g o sideri g differe t le els of arri al rate of i estors. The para eters are: = . , = . , = . , = %, = . % = %.
f o to , hi h i plies a elasti it of - . a d - . , espe ti el . This ea s that, outside fi a i g is o e i po ta t fo fi s i fi a ial o st ai t, tha fo fi s
hi h a e ot.
. . . Target ash holdi gs are de reasi g ith age
osts
Age osts o e f o a aste of ash i i effi ie t p oje ts o u justified e pe ses hi h ge e ate p i ate e efits. Je se p o ed that a fi hi h holds highe le els of
ash, astes o e o e i i effi ie t p oje ts. He e, it is e pe ted that he the age osts i ease, the opti al le el of ash should de ease, to i i ize the aste of ash. This is sho i figu e , hi h elates the opti al le el of ash to age osts.
Figure – Se siti it of opti al ash holdi g to age osts. The para eters are: = . , = . , = . ,
= %, = . %, = .
Figure - Se siti it of opti al ash holdi g to arri al rate of i estors. The para eters are: = . , = . ,
= . % = . %
= . %
As it as e plai ed efo e, i this odel, age osts a e al ulated th ough the diffe e e et ee the dis ou t ate a d the etu ate of ash flo s. “o, to pe fo a a al sis, hi h easu es the di e sio of the ha ge i elatio to a ha ge i age
osts, t o diffe e t i pa ts o age osts e e assu ed: egati e i pa t = . % , a d positi e i pa t = . % , oti ated a i te al fa to , o hi h the ase- ase is = . % .
A o di g to Figu e , Figu e a d Ta le , e a o lude that, o the o e ha d, the i ease of age osts has a egati e i pa t o ta get ash holdi g a d o the othe ha d, a de ease of age osts has a highe i pa t o the ta get le el of ash holdi g tha a i ease of the sa e ate, ep ese ti g a elasti it of - . a d - . ,
espe ti el .
I te al a age e t i p o e e ts ould e o side ed.
= − ∗ ∗
,
. % . - .
. % .
. % . - .
Ta le - Opti al alue of ash holdi g o sideri g differe t le els of age osts. The para eters are: = . ,
= . , = . , = %, = . % = .
Figure - Fir Value for differe t le els of age osts. The para eters are: = . , = . , = . , = %,
. . . Target ash holdi gs are i reasi g ith ash flo olatilit σ
Assu i g that the olatilit of the fi i eases, oti ated a isk i est e t, it is e pe ted that the di ide d ou da of the fi i eases, i o de to se u e so e ope ati g losses . Figu e , hi h sho s the i pa t of i easi g olatilit i ta get ash holdi g, is i li e ith the theo , oti g a slight o e it .
Figure - Se siti it of opti al ash holdi g to olatilit . The para eters are: = . , = ,
= . , = %, = . % = %.
P e autio a oti e p oposed Ke es .
Figure - Margi al Be efit of Cash for differe t le els of age osts. The para eters are: = . , = . , = . ,
The esults p e iousl p ese ted a e also sho i usi g Ta le , a d also i Appe di C. hi h sho s the opti al le el of ash holdi g, fo lo e σ = . , ediu σ = . a d high σ = . . Cal ulati g the elasti it et ee the ase- ase a d t o othe ases, it is possi le to o lude the slight o e it of the fu tio , as ell as the i pa t of olatilit ei g igge i the lo to ediu a ge. I this a ge, a i ease i pp of olatilit , i plies a i ease of . pp i the ta get ash holdi g; he eas i the ediu to high a ge of olatilit , a i ease of pp i plies a i ease of . pp i opti al le el of ash. This esult is ei fo ed i Appe di C. , hi h e plai the o oto i it of olatilit .
A additio al a al sis ould e see i Figu e a d Figu e , a al si g the i pa t that a ha ge i olatilit auses o the fi alue. The p ese t the fi alue a d the a gi al e efit of ash, espe ti el , fo lo , ediu a d high le els of olatilit . We a o se a le a do a d o e e t of the fi alue, as ell as a de ease of o a it , hi h ea s that, ith the i ease of olatilit , o e o e u it of holdi g ash ill e o e o e e efi ial to the fi . Pe fo i g a o pa ati e a al sis of all ases p ese ted i this disse tatio , the i ease of olatilit , hi h has a highe i pa t i the opti al ash holdi g, p ese ts highe alue i elasti it i elatio to ase ase .
Pe e tual Poi t A solut alues. ∗ ∗ , = . . = . . . = . . .
Ta le - Opti al alue of ash holdi g o sideri g differe t le els of olatilit . The para eters are: = . , = ,
= . = .
= .
Figure - Fir Value for differe t le els of olatilit . The para eters are: = . , = , = . , = %,
= . % = %.
Figure - Margi al Be efit of Cash for differe t le els of olatilit . The para eters are: = . , = ,
= . , = %, = . % = %.
. . . Target ash holdi gs are de reasi g ith profita ilit u
Assu i g that the p ofita ilit of the fi de eases, oti ated e te al fa to s, it is e pe ted that the di ide d ou da of the fi i eases, as a esult of a highe p o a ilit of ope ati g losses. I the ase of a fi hose p ofita ilit is e lo , i elatio to othe fi s ith the sa e ha a te isti s, a d pe the p e autio a easo , the fi should a u ulate o e ash. This esult a e see i Figu e , hi h sho s the i pa t of a i ease of p ofita ilit i ta get ash holdi g.
= . = . = .
Figure - Se siti it of opti al ash holdi g to profita ilit . The para eters are: = . , = , = . , =
%, = . % = %.
“o, to a al se this h pothesis, a d late a al se the effe t of a p ofita ilit ha ge i the i pa t of ta es at ta get ash le el, th ee s e a ios e e o side ed: a pessi isti s e a io, he e the a e age of ash flo de eases de i i g f o a e te al fa to = . ; a d a opti isti s e a io, he e = . a d the ase ase = . . I a opti isti s e a io, the odel sho s that the e is a i ease of the fi alue, as ell as a i easi g of a gi al e efit. I a pessi isti s e a io, the e is a edu tio of the fi alue.
Figure - Fir for differe t le els of profita ilit . The para eters are: = . , = , = . , = %,
Figure - Margi al Be efit of Cash for differe t le els of profita ilit . The para eters are: = . , = , = . ,
= %, = . % = %.
These esults a e su a ised i Ta le , hi h ep ese ts the opti al ash holdi gs fo the ase- ase, opti isti a d pessi isti s e a ios. We a o lude that, the i pa t of a i ease i p ofita ilit is highe i a opti isti s e a io tha i a pessi isti s e a io. This esult de i es f o the fa t that the e is a igge effo t fo a fi hi h has a lo e p ofita ilit holdi g a highe le el of ash, tha fo a fi hi h has highe p ofita ilit . Co se ue tl , the eed of holdi g ash is ha ful to fi s hi h ha e lo e le els of p ofita ilit , e ause, e o d the lo e p ofita ilit , these fi s ust hold highe le els of ash, hi h a e asso iated to a lo e ash etu a d a i ease i age osts . This esult is ei fo ed i Appe di C. , hi h e plai the o oto i it of p ofita ilit .
Ta le - Opti al alue of ash holdi g o sideri g differe t le els of profita ilit . The para eters are: = . ,
= , = . , = %, = . % = %. As as said Je se . ∗ ∗ , = . . - . = . . = . . - .
. . . Target ash holdi gs are de reasi g ith i o e ta
Bigelli et al. lai that the di ide d ou da is a de easi g fu tio of ta es i o e. This as e plai ed the ta shield, that ep ese ts a ash-i -flo fo the fi . Thus, pe the p e autio a oti e, the fi a de ease its ta get le el of ash ese e. We ill p o e that the elatio et ee a i ease of ta es a d di ide d ou da is ot a li ea fu tio , it depe ds o fi ’s dep e iatio a d fi ’s p ofita ilit . This is e plai ed the i pa t that a i ease of ta es auses i fi ’s p ofita ilit . As it as e plai ed efo e, a i ease i ta es i plies that the ash-out-flo ill e highe , hi h e ui e a highe opti al le el of ash. Fu the o e, a i ease of ta es auses a i ease i the ta sa i gs, hi h leads the opti al le el of ash to e lo e . Fi all , e o lude that the i pa t of the di ide d ou da , esulti g f o a i ease of ta es, depe ds o the a ou t of the p ofita ilit a d dep e iatio alue of the fi . This esult is p o ed i Appe di C. , hi h e plai the o oto i it of ta es.
Usi g the ase- ase, opti isti a d pessi isti s e a ios i te s of p ofita ilit , it is possi le to o lude, that the i pa t of a ha ge i ta es ould ha e th ee diffe e t effe ts o ta get ash holdi g, Figu e . If the ase ase is assu ed a ha ge i ta does ot affe t the ta get le el of ash, e ause the i pa t of ta i p ofita ilit a d dep e iatio a e e ual, so the effe t is ull. If the opti isti s e a io is assu ed a ha ge i ta auses a de ease of ta get ash le el, e ause the i pa t of ta i p ofita ilit is highe tha i dep e iatio , esulti g i a ash-out-flo . If the pessi isti s e a io is assu ed a ha ge i ta ould ause a i ease of ta get ash le el, e ause the i pa t of ta i dep e iatio is highe tha i p ofita ilit , esulti g i a ash-i -flo .
Figure - Se siti it of opti al ash holdi g to Ta es. The para eters are: = . , = , = . , = . ,
. Con lusion
This disse tatio p oposes a d a i odel of i est e t, fi a i g, a d ash a age e t de isio s, ai i g to e plai o po ate poli ies of ash holdi gs, di ide d pa e ts, e te al fi a i g, p ofita ilit a d dep e iatio of a fi . This odel o side s a fi fi a iall o st ai ed deali g ith age osts, a agi g the i te al apital. The ai o je ti e of the odel is to theo eti all e plai ho a ha ge of diffe e t a ia les affe t the ta get le el of ash. We assu e that this odel has a eak ess, hi h is, odel is a theo eti al fo ulatio hi h i te ds to do so e a al sis a out it. It does ot allo fi s to o pute its opti al le el of ash.
The ai esult of this disse tatio is elated to the i pa t of ta es i the le el of ash holdi gs. All othe s elatio ships a e a o di g to theo Dé a ps et al. . The effe t of ta es o t adi ts the lite atu e, as it as sho ed. The i pa t i a ta get le el of ash aused a ha ge i the ta ate is ot li ea , depe di g o the fi ’s p ofita ilit a d fi ’s dep e iatio . Co side i g a positi e sho k i a ta ate, the opti al le el of ash o l de eases i fi s i hi h the a ual dep e iatio is highe tha the a ual p ofit of the fi . Additio all , this odel allo ed to o lude that the olatilit is the a ia le hi h has a highe i pa t i the opti al le el of ash.
Bi liograph
Alle , F., Mi hael , R. . Pa out poli . Ha d ook of the E o o i s of Fi a e, , -.
Beuseli k, C., Deloof, M., Va st aele , A. . Co po ate go e a e a d ash poli ies of ulti atio al o po atio s. Worki g paper, U i e sit of A t e p.
Bigelli, M., Sá hez-Vidal, J. . Cash holdi gs i p i ate fi s. Jou al of Ba ki g &
Fi a e, , - .
Cossi , D., H i ko, T. . The e efits of holdi g ash: a eal optio s app oa h. Ma agerial Fi a e, , - .
DeA gelo, H., DeA gelo, L., Stulz, R. M. . Di ide d poli a d the ea ed/ o t i uted apital i : a test of the life- le theo . Jour al of Fi a ial e o o i s, , - .
Dé a ps, J. P., Ma iotti, T., Ro het, J. C., Ville eu e, S. F ee ash flo , issua e osts, a d sto k p i es. The Jour al of Fi a e, , - .
Ditt a , A., Mah t-S ith, J. Se aes, M. I te atio al o po ate go e a e a d o po ate ash holdi gs. Jour al of Fi a ial a d Qua titati e A al sis, , – . Ditt a A, Ma th-S ith J, . Co po ate go e a e a d the alue of ash holdi gs. Jour al of Fi a ial E o o i s, , - .
Fazza i, S. M., Hu a d, R.G., Pete se , B., . Fi a i g o st ai ts a d o po ate i est e t. Brooki gs Papers o E o o i A ti it , , - .
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Mille , M. H., D. O , . A odel of the de a d fo o e fi s. Quarterl Jour al of E o o i s, , - .
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Appendi
A.
Elasti it
I o de to o pute the di e sio of the i pa t that a ha ge of a a ia le has i the ta get le el of ash, the follo defi itio as used:
∗, =
∗− ∗
∗
∗− ∗
∗
B.
P oofs of the Methodolog
To fa ilitate the a age e t’s opti izatio p o le , it as stipulated that = , hi h ea s that, the e is o a gai i g po e of e i esto s. Additio all , it as assu ed that the diffe e tial ope ato ℒ a d the su plus f o efi a i g ℱ a e defi ed as:
ℒ. = . . + . − + . + . − .
ℱ. = max + − −
To fi d , hi h de otes the alue of a fi ith o g o th optio , fou steps ill e follo ed:
i De i e the Ha ilto -Ja o i-Bell a HJB e uatio ;
ii “ho the s ooth solutio to the HJB e uatio do i ati g the fu tio alue;
iii Co je tu e a opti al poli a d de i e the o espo di g fi alue;
i “ho that the fi alue asso iated to the opti al poli of step is i deed a s ooth solutio to the HJB e uatio ;
i The HJB e uatio fo the fi alue ith o optio is gi e :
max ℒ. + ℱ. , − , − =
Whe e de otes the fi li uidatio alue.
ii The s ooth solutio to HJB a o plishes:
A , ∀
B = satisfies ℒ. + ℱ. , ∀ ∗
C , ∀
iii The opti al poli is:
D . = . . + . − + . + . − . − ∗+ −
E c = . , =
F = ∗ + − ∗, > ∗
G lim⟶ ∗ ∗ =
H lim⟶ ∗ ′ ∗ =
he e the u i ue s ooth solutio is .
i The fi alue asso iated to the opti al poli is o tai ed th ough the su stitutio of E - H i D
E uatio D tu s i to a sta da d ODE, if ∗ is fi ed. This is e pli itl sol ed ia Itô’s
fo ula, as Hugo ie et al. sho i Le a B. .
A o di g to this stud , the u i ue o ti uousl diffe e tia le solutio is:
= . + . + − ∗ . − . he e, = + ∗ − ∗+ + . − + . + − = ∗∗ .. −− ∗∗ .. = ∗ .. −− ∗.. ith = − + ; ; − . + . −. + . = − + ; ; − . + . −. + .
Additio all , the p oof of the u i ue solutio a d the fu tio is t i e diffe e tia le is sho i Le a B. of Hugo ie et al. .
C.
P oofs of the Results
I o de to sho a al ti all the esults sho ed, it as take as a efe e e the P oof B of Mo elle et al. . To esta lish the o oto i it of esults, it as e essa defi e the a d use follo i gs au ilia fu tio s.
I = − .
J = . − +
C. . Mo oto i it of Volatilit a d Profita ilit
Usi g the i pli it fu tio theo e a d the au ilia fu tio I is possi le to do the sa e a al sis, hi h Mo elle et at. did i Le a a d , he e the p o ed that ta get
ash holdi gs a e o oto e i easi g i σ a d o oto e de easi g i .
C. . Mo oto i it of Ta es
To pe fo a a al sis a out the o oto i it of ta es, it is e essa to use pa tial de i ati es, as ell as the au ilia fu tio J .
∗
= ∗× = ∗× −
Usi g the p e ious e p essio , e a o se e that the o oto i it of ta es is gi e the alue of pa a ete ’s a d , ut also depe ds o the ta get ash holdi g ei g o oto e de easi g i . “o, if the a e e ual, ta get ash holdi gs a e o oto e o sta t ith ta es. If is highe tha , ta get ash holdi gs a e o oto e i easi g ith ta es. If is highe tha , ta get ash holdi gs a e o oto e de easi g ith ta es.
