Valuing Bitcoin

Valuing  Bitcoin     Summary:  I  use  a  very  simple  model  of  transaction  value,  bitcoin  velocity  and  the   number   of   bitcoins   in   use   to   derive   a   fair   value   for   a   bitcoin   today.   Rather   than   trying   to   analyse   in   detail   the   likelihood   of   and   means   by   which   bitcoin   may   become   more   widely   adopted,   I   use   a   scenario   analysis   that   allows   us   to   take   a   ‘finger   in   the   air’   approach   to   estimating   the   likelihood   of   Bitcoin’s   success   or   failure.   Taking   this   approach   we   can   back-­‐calculate   to   work   out   what   is   implied   in   the   current   valuation   of   bitcoins   in   terms   of   likelihood   of   adoption,   or   other   key   variables.       This   is   primarily   a   simplified   framework   to   help   elucidate   the   fundamentals   that   drive  the  value  of  bitcoins.  The  assumptions  herein  are  very  ‘back  of  the  envelope’   and  are  principally  for  exposition.         1.  First  principles     The  value  of  a  single  bitcoin  is  related  to  the  value  and  velocity  of  transactions   made  using  bitcoin,  and  the  volume  of  bitcoins  in  use.     The   value   of   transactions   made   with   bitcoin.   Let’s   say   we   assume   that   bitcoin   will  succeed  in  becoming  the  payment  choice  for  US$100bn  of  transactions  per   year.   Let’s   also   first   assume   that   this   US$100bn   takes   the   form   of   one   single   transaction  –  say  to  buy  all  of  the  outstanding  stock  of  Facebook.  In  order  for  this   to   be   possible,   the   entire   market   value   of   Bitcoin   would   need   to   be   at   least   US$100bn.  For  argument’s  sake,  let’s  say  someone  managed  to  accumulate  all  of   the   bitcoins   in   existence   (ca.12.5   million   today)   and   used   them   to   make   this   transaction,   then   we   can   infer   that   the   value   of   a   single   bitcoin,   when   this   transaction  happens,  is  $8,000.       The   velocity   of   transactions   made   with   bitcoin.   Let’s   take   the   same   example   above,   but   this   time   let’s   assume   that   rather   than   one   transaction,   it   takes   the   form   of   two   transactions   –   let’s   say   to   buy   ‘whataspp’   and   ‘wechat’,   for   the   equivalent   of   US$50bn   each.   Let’s   further   assume   that   the   seller   of   whatsapp,   uses   the   US$50bn   of   bitcoins   he   has   received,   to   buy   wechat.   How   much   does   Bitcoin   need   to   be   worth   to   facilitate   this   series   of   transactions?   Hopefully   one   can   see   that   at   the   very   least,   it   needs   to   be   worth   $4,000,   half   of   the   example   above,   because   the   same   bitcoins   could   be   used   twice.   Therefore,   the   same   ‘value’   of   transactions   has   been   facilitated,   US$100bn,   but   depending   on   the   number   of   times   the   same   bitcoin   can   be   used   the   implied   value   of   bitcoin   can   differ.       The  volume  of  bitcoins  in  use.  The  previous  two  examples  have  assumed  that  the   whole   outstanding   stock   of   bitcoins   is   being   used   to   facilitate   the   transactions.   This  is  unlikely  to  be  true.  It  is  very  likely  that  a  good  number  of  bitcoins  have   been  ‘lost’  –  ie.,  stuck  on  hard  drives  thrown  into  landfills,  etc.  Let’s  assume  there   are  2.5  million  lost  bitcoins  –  the  value  in  our  first  example  would  then  have  to   be  US$10,000.  Moreover,  clearly  a  lot  of  people  today  hold  bitcoins  as  a  store  of  

value,   or   perhaps   more   accurately,   as   a   speculative   investment.   The   number   of   bitcoins  genuinely  in  circulation,  therefore  falls  still  further.         2.  Arriving  at  a  formula  to  determine  the  value  of  a  bitcoin     Using   the   basic   principles   outlined   above,   we   can   generate   a   simple   formula   to   describe  the  value  of  a  bitcoin  as  such:     1  btc  =  T/V/U     Where  T  =  transaction  value   V  =  velocity   U  =  no.  of  bitcoins  in  use     This   is   obviously   a   simplification,   so   we   need   to   explore   each   aspect   in   greater   detail  to  understand  how  to  use  it  properly.     2.1  Transaction  value  (T)     How  do  we  determine  transaction  value  in  the  real  economy?  The  obvious  place   to  look  is  GDP,  the  most  widely  used  measure  of  economic  activity.  It  measures   the   value   of   all   final   goods   and   services   consumed   in   an   economy.     Does   this   equate  to  the  value  of  transactions  in  the  economy?  No  –  because  before  a  good   is   finally   consumed   there   are   typically   many   other   transactions   going   on   to   facilitate  its  transformation  from  raw  material,  to  intermediate  good,  to  finished   good,  to  consumption  by  end  consumer.  The  advantage  of  GDP,  however,  is  that   it   is   relatively   easy   to   measure.   Estimating   the   value   of   all   transactions,   on   the   other  hand,  is  very  hard  and  is  a  problem  economist  have  recognized  for  a  long   time.   That   is   not   to   say   there   aren’t   estimates:   a   September   2013   white   paper   by   Mastercard   estimated   the   total   value   of   transactions   globally   in   2011   as   $592   trillion,  compared  to  global  consumer  payments  /  GDP  of  $63  trillion.  This  may   well   be   a   good   ballpark   figure,   however   for   our   purposes   we   can   probably   just   stick   to   measures   of   GDP.   Why?   Because,   faced   with   this   measurement   issue,   economists  have  worked  around  it  to  base  their  analyses  on  GDP,  and  therefore   as  we  try  to  compare  bitcoin  value  versus,  say,  the  USD,  it  makes  sense  to  use  the   framework  most  commonly  used.       It   is   important   to   understand,   however,   that   because   of   this   framework   only   bitcoin   transactions   that   are   used   in   the   final   consumption   of   goods   and   services   count   towards   our   measure   of   ‘T’.   Trading   of   bitcoins,   or   international   remittances,  for  instance,  do  not  count.       2.2  Velocity  (V)     Given   the   difficulty   in   measuring   the   value   and   volume   of   transactions   in   an   economy,   it   is   quite   difficult   to   measure   velocity   directly,   in   an   accurate   or   meaningful   way.   To   get   round   this   problem   economists   take   a   different   approach,  which  is  quite  useful  for  our  purposes.  Rather  than  measure  velocity   (V),  we  measure  the  ratio  (k)  of  all  cash  balances  in  the  economy  (coins,  notes,  

bank  deposits  –  M1  money)  to  a  measure  of  transaction  volume,  in  this  case  GDP.   By  means  of  illustration,  this  ratio  for  the  US  today  is  about  14%.  This  means  that   to  support  the  USA’s  GDP  of  $16  trillion,  roughly  $2.3  trillion  needs,  at  any  one   time,   to   be   sat   in   bank   accounts,   in   people’s   wallets   or   under   the   mattress.   Put   simply  this  measures  how  much  people  and  businesses  like  to  keep  on  hand  for   everyday   consumption.   The   rest   of   their   savings   can   go   into   non-­‐cash   savings   vehicles,  like  a  house,  or  the  stock  market.       The  velocity  of  money  V  can  be  seen  as  the  inverse  of  k  –  i.e,  each  dollar  of  that   $2.3  trillion  would  need  to  be  spent  around  7  times  in  the  year  to  generate  the   $16  trillion  in  GDP.  This  in  reality  is  a  simplification,  but  we  can  work  with  it  to   come  up  with  comparable  assumptions  for  bitcoin.     2.3  Bitcoins  in  Use  /  Money  supply  (U)     In  order  to  work  out  the  velocity  of  money  in  the  US  economy,  economists  need   to   know   the   money   supply.   Figuring   out   the   money   supply   in   fiat   currencies   is   more  complex  than  for  bitcoin  –  this  is  because  there  are  different  types  of  fiat   money   –   it   can   be   in   the   form   of   coins   and   notes,   or   in   basic   bank   current   accounts,   savings   accounts,   fixed   deposits,   etc.   In   the   example   above   we   calculated   the   velocity   of   M1   money   –   that   is   coins,   notes   and   demand   deposit   bank  accounts.       Bitcoin   is   just   bitcoin,   and   we   know   there   have   been   ca.   12.5m   bitcoins   mined.   That   being   said,   it   is   not   so   straightforward   to   determine   bitcoins   ‘in   use’.   For   one,   there   are   all   the   lost   coins.   In   the   analysis   herein   I   have   assumed   2.5m   have   been   lost   (or,   more   accurately,   private   keys   lost).   There   is   also   the   question   of   how   to   treat   those   bitcoins   that   are   being   held   for   investment   purposes.   M1   is   sort   of   a   measure   of   ‘ready   cash’   –   a   description   that   does   not   really   apply   to   most   bitcoins.   In   reality,   most   bitcoin   holders   probably   treat   some   portion   of   their  stockpile  as  ‘ready  cash’,  and  the  rest  as  investment.  It  is  this  ‘ready  cash’   proportion  that  is  of  interest  in  calculating  U.       3.  Estimating  a  value  for  bitcoin     With   the   above   analysis   in   place,   it   is   easy   to   start   understanding   the   implications  for  the  value  of  bitcoin.  For  example,  if  the  US  were  to  switch  to  a   pure  bitcoin  economy  today,  and  the  velocity  of  bitcoin  was  the  same  as  for  the   dollar,  then  we  can  say  the  value  of  a  single  bitcoin  would  need  to  be:     Btc  =  T/V/U  =  16  trillion  /  7  /  12.5  million  =  $183,000     3.1  The  value  of  bitcoin  based  on  today’s  usage     Estimating  T,  V  and  U:     T.   It   is   quite   hard   to   estimate   what   T   is   today.   We   know   the   total   transaction   value   from   the   blockchain,   but   most   of   this   is   exchanging   bitcoin   for   other  

currencies  or  transfers  between  accounts.  This  doesn’t  count  in  our  estimate  of   bitcoin  ‘GDP’.  We  do  know  it  must  be  quite  low  –  the  most  well  known  retailer   accepting  bitcoin,  Overstock.com,  takes  in  about  $1m  in  bitcoin  sales  per  month,   so  $12m  per  year.  Let’s  estimate,  finger  in  the  air,  that  total  real  world  goods  and   services  transactions  in  bitcoin  are  $1bn  per  year  –  this  may  well  still  be  high.       V.   It   is   very   difficult   to   estimate   velocity   for   those   bitcoins   that   are   in   use   as   ‘currency’.  It  seems  a  fair  assumption,  however,  that  the  velocity  is  slower  than   for  USD,  since  there  are  simply  not  many  bitcoiners  out  there  buying  and  selling   stuff.   Again,   with   a   finger   in   the   air,   let’s   assume   velocity   of   bitcoin   today   is   1   (compared  to  around  7  for  the  USD).       U.  we  know  there  have  been  around  12.5  million  bitcoins  ever  mined  –  but  are   they  in  use?  Certainly,  some  have  been  lost,  so  we  should  definitely  remove  them   from  our  calculation  of  U.  What  about  coins  that  are  being  used  for  speculative   investment?  Are  they  in  use,  but  just  very  slow  moving?  We  could  choose  to  look   at  it  that  way,  but  I  would  rather  assume  that  people  using  bitcoin  see  some  of   their   stockpile   as   being   ‘for   investment’,   and   some   as   for   everyday   spending.   Those  that  are  for  investment  are  really  more  like  houses  or  stocks  and  bonds,   and   therefore   not   really   part   of   U.   Over   time,   as   bitcoin   approaches   its   long   term   price   we   would   expect   that   people   would   hold   bitcoin   less   as   an   investment,   and   therefore   bitcoins   in   use   would   rise.   For   now   though   it   seems   clear   that   most   bitcoins   are   being   held   for   investment.   Again,   it   is   impossible   to   say   what   proportion,   but   I   think   it   is   high   –   say   at   least   80%.   If   we   assume   that   2.5   million   bitcoins  are  lost,  and  that  80%  are  for  investment,  that  means  that  only  2  million   are  ‘in  use’.           These   finger   in   the   air   assumptions   give   us   the   following   as   a   minimum   value   required  to  support  the  value  of  btc  transactions  in  the  economy  today:     Btc  =  T/V/U  =  1bn  /  1/  2mn  =  $500.       Of  course,  we  know  the  value  of  bitcoin  today  (ca  $422  as  of  12  April  2014),  so   we   could   back   calculate   the   value   of   an   individual   variable.   Since   the   average   value  of  bitcoin  over  the  last  year  or  so  is  in  the  $500  range,  these  assumptions   look  plausible.       The  true,  fair,  value  of  bitcoin  today,  however,  given  that  most  people  are  holding   it   as   an   investment,   is   clearly   based   on   future   expectations   of   its   adoption   and   usage.   Below,   therefore,   I   build   up   some   basic   assumptions   about   what   that   could  look  like,  to  derive  a  very  rough,  back  of  the  envelope  type  calculation  for   the  real  value  of  one  bitcoin.         3.2  Estimating  a  fair  value  for  bitcoin    

Obviously,  it  is  very  unlikely  that  bitcoin  will  replace  the  US  dollar,  so  we  need  to   arrive  at  some  sort  of  reasonable  assumptions  for  what  might  happen.     For   the   purposes   of   this   exposition,   I   will   focus   on   where   bitcoin   could   be   in   5   years   time.   This   is   a   close   enough   time   frame   to   feel   comfortable   making   some   sort  of  prediction.  Of  course,  the  full  potential  of  bitcoin  may  not  be  realized  for   10   or   20   years   or   more,   however   in   order   to   be   conservative   and   to   keep   the   assumptions  at  a  level  where  people  can  have  a  good  gut  feel  for  whether  they   are  realistic  or  not,  let’s  stick  to  5  years.       I’m  going  to  use  three  scenarios:   1. Crash  and  burn  –  where  bitcoin  is  dead  in  5  years  –  no  one  is  using  it   at  all  –  it  just  didn’t  live  up  to  the  hype,  there  are  a  couple  more  gox   like  scandals  and  the  original  evangelists  have  moved  onto  new  things   2. Nice  but  boring  –  bitcoin  continues  its  slow  but  steady  rise,  but  there   is   no   exponential   take   off   and   usage   remains   confined   to   online   payments  by  the  relatively  tech-­‐savvy  and  libertarian   3. To   the   moon   –   bitcoin   reaches   critical   mass,   usage   becomes   easy,   widely   accepted   and   the   wider   population   starts   to   understand   it   better.   In   developed   markets   it   takes   meaningful   market   share   in   online   transactions   and   is   beginning   to   make   meaningful   inroads   in   offline   payments.   In   some   emerging   markets   it   is   trusted   more   than   the  local  currency,  and  adoption  rates  are  soaring.       Basic  considerations  on  U     I   don’t   know   the   answer   to   this,   someone   probably   does,   but   let’s   assume   that   in   2019   there   have   now   been   15   million   bitcoins   mined.   Let’s   assume   2.5   million   are   still   lost,   so   there   are   12.5   million   bitcoins,   either   being   used   as   an   investment  or  as  currency.       Scenario  1  –  Crash  and  burn     In  our  equation  T  =  0  (or  very  close  to  0)  therefore:     1  btc  =  0/V/U  =  $0     Scenario  2  –  Nice  but  boring     Let’s   say   that   bitcoin   takes   1%   of   online   spending,   and   basically   zero   offline   spending.   E-­‐commerce   in   2019   is   expected   to   be   valued   at   around   $3   trillion.   Therefore  we  assume  T  =  $30bn.  Remember  we  estimated  that  T  today  is  around   $1bn.     Since   there   is   a   material   amount   of   spending   happening   now,   let’s   assume   that   V   has  doubled  to  equal  2.       In   this   scenario   it   is   likely   that   most   people   are   still   holding   bitcoin   as   an   investment,   hopeful   of   future   price   increases,   however   it   has   been   almost   10  

years   since   bitcoin   was   founded,   bitcoin   are   a   lot   easier   to   spend   and   after   holding   for   so   long   people   are   now   more   willing   to   spend   them.   There   are   probably   a   decent   number   of   second   stage   adopters   using   bitcoin   just   as   an   online   payment   vehicle,   not   for   investment.   So   let’s   assume   that   just   70%   of   bitcoins   are   held   as   an   investment,   and   therefore   there   are   3.75m   being   used   for   transactions.  Therefore:     1btc  =  30bn/2/3.75m  =  $4,000     Scenario  3  –  To  the  moon!     In  this  scenario  bitcoin  has  really  taken  hold,  particularly  online,  where  20%  of   transactions  now  use  bitcoin.  Offline  uptake  is  slower,  but  gaining  traction.  Let’s   say   1%   of   offline   transactions   in   developed   markets   use   bitcoin.   In   emerging   markets,   where   currencies   are   volatile,   and   where   a   lot   of   people   have   been   receiving  remittances  in  bitcoin  from  relatives  abroad,  offline  uptake  is  greater,   let’s  say  2%.       Online  transactions  –  20%  x  $3  trn  =  $600bn   Developed  world  offline  –  1%  x  $45trn  =  $450bn   Developing  world  offline  –  2%  x  $30trn  =  $600bn     T  =  $1,450bn     In   this   scenario   spending   has   really   taken   off,   so   let’s   assume   velocity   (V)   has   now  reached  5.       Of  the  12.5  million  coins  in  existence  now,  a  good  chunk  are  actually  being  used   for   real   world   transactions,   so   let’s   say   only   50%   now   are   being   held   for   investment  –  i.e.,  U  =  6.25m.     1  btc  =  $1450bn  /  5  /  6.25m  =  $46,400     Probability  of  occurrence     To   estimate   our   bitcoin   value,   we   take   a   weighted   average   of   the   values   produced   by   each   scenario,   based   on   an   assumption   about   the   likelihood   of   each   coming  to  pass.     Scenario   Btc  value   Likelihood     Weighted  value   1.  Crash  and  burn   $0   50%   $0   2.  Nice  but  boring   $4,000   45%   $1,800   3.  To  the  moon   $46,400   5%   $2,320       100%   $4,120     Therefore,  if  you  accept  the  assumptions  above,  and  the  probability  attributed  to   each  scenario,  the  probability  weighted  value  of  a  single  bitcoin  in  5  years  time   will  need  to  be  $4,120.    

Time  value  of  money     To  reach  a  valuation  for  a  bitcoin  today,  we  need  to  discount  backwards  from  the   value   in   5   years   time.   This   is   very   simple,   since   we   do   not   need   to   discount   heavily  as  we  have  already  considered  the  ‘risk’  within  our  scenario  analysis.  The   only   discounting   we   need   to   do   is   therefore   at   the   risk   free   rate,   which   is   usually   taken   to   be   the   yield   you   would   get   if   you   held   a   US   Treasury   bond   of   similar   duration.   Let’s   say   this   is   3%.   Discounting   $4,120   back   to   today   we   therefore   arrive  at  our  final  ‘finger  in  the  air’  value  for  one  bitcoin  today:     1  bitcoin  =  $3,554     4.  Implications  of  the  current  btc  value     As   of   April   12   2014,   the   value   of   one   bitcoin   is   around   $420.   We   can   take   this   value   and,   holding   other   assumptions   as   they   are,   solve   for   a   single   variable   to   see  what  might  be  happening.       For  instance,  perhaps  I  am  being  unfair  in  treating  some  bitcoins  as  out  of  use.     If  we  solve  for  U,  taking  $422  as  the  value  of  one  bitcoin,  the  implied  number  of   bitcoins  in  use  is  43  million  –  an  impossible  number.  Let’s  assume  that  in  2019   all   15   million   bitcoins   ever   mined   are   ‘in   use’,   and   that   the   velocity   of   transactions  stays  the  same.  If  so,  the  value  of  1  bitcoin  today  ought  to  be  $1,222.       If  we  solve  for  the  probability  of  scenario  1  happening  (keeping  the  ratio  of  the   likelihood  of  scenario  2  and  3  the  same),  we  discover  that  today’s  $422  valuation   implies  a  likelihood  of  bitcoin  ‘crashing  and  burning’  of  94.06%.     5.  Theoretical  upper  bound     Lots  of  people  have  thrown  out  ideas  for  how  much  a  bitcoin  could  be  worth  in   the   future.   Someone   recently   predicted   it   could   be   $500,000.   Using   the   framework   above   we   can   make   some   assumptions   about   what   is   theoretically   possible  (beyond  ‘to  the  moon’!).  Note  that  including  this  sort  of  analysis  in  the   basic  valuation  above  would  be  overly  bullish  and  distorting  –  this  is  ‘how  long  is   a  piece  of  string’  sort  of  territory.       Let’s     say   in   20   years   Bitcoin   has   become   an   established   global   currency   or   payment   system.   There   is,   in   my   view,   no   way   it   could   ever   be   the   sole   global   currency   –   the   forces   of   competition   and   risk   aversion,   not   to   mention   governments,   would   probably   ensure   that.   I   think   if   bitcoin   were   to   facilitate   20%   of   global   GDP,   that   would   already   be   an   extremely   bullish   upper   bound   proposal.   Assuming   3%   annual   growth   in   global   GDP   for   20   years,   we   can   calculate  the  transaction  value  [T]  as:     T  =  $63trn  x  1.03^20  x  20%  =  $22.8trn     At   that   level,   the   velocity   [V]   of   bitcoin   would   be   high   –   let’s   just   say   for   argument’s  sake  it  is  10.    

  By  the  time  we  reach  this  level  the  value  of  bitcoin  will  have  topped-­‐out.  It  might   even   be   depreciating,   so   let’s   assume   that   people   only   hold   bitcoin   in   order   to   spend  it.  In  this  case  bitcoins  in  use  [U]  will  equal  to  the  total  volume  ever  mined,   minus   those   lost.   Let’s   assume   the   total   volume   mined   in   20   years   time   is   18   million,  and  that  2.5  million  remain  lost,  we  have  a  value  for  U  of  15.5m.     Using   the   above   input   we   can   calculate   the   theoretical   upper   bound   value   (in   today’s  money)  of  a  single  bitcoin  as:     1  btc  =  ($22.8trn  /  10  /  15.5mn)  =  $147,097     x  (discount  factor  of  1/1.03^20)  =  $81,444     Once   you   reach   this   theoretical   upper   bound   sort   of   level   it   is  easier   to   trust   that   the  assumptions  are  relatively  accurate,  because  there  is  simply  not  much  room   to  be  more  aggressive  on  the  assumptions.