Introduction You have to really stretch your imagination to infer - - PowerPoint PPT Presentation

On the Value of Virtual Currencies1

Wilko Bolta and Maarten van Oordtb

aDe Nederlandsche Bank (DNB) bBank of Canada (BoC)

Mapping out the Road Ahead De Nederlandsche Bank Amsterdam, 21–22 April 2016

1Views expressed do not necessarily reflect official positions of DNB or BoC. Bolt and Van Oordt On the Value of Virtual Currencies 1 / 26

Introduction

“You have to really stretch your imagination to infer what the intrinsic value of bitcoin is. I haven’t been able to do it. Maybe somebody else can.” – Alan Greenspan, Bloomberg Interview, 4 Dec. 2013

Bolt and Van Oordt On the Value of Virtual Currencies 2 / 26

Introduction

What is the virtual currency bitcoin?

◮ Currency with a predetermined money growth path;

commodity-like properties

◮ Peer-to-peer payment system ◮ Potential benefits for users (anonymity, cost efficiency,

cross-border); benefits differ across users

◮ Prices in bitcoin usually adjusted to the current exchange rate

Bolt and Van Oordt On the Value of Virtual Currencies 3 / 26

Speculation and the USD/bitcoin exchange rate

2011 2012 2013 2014 2015 200 400 600 800 1000

Source: www.blockchain.info.

Bolt and Van Oordt On the Value of Virtual Currencies 4 / 26

Speculation and the USD/bitcoin exchange rate

2011 2012 2013 2014 2015 200 400 600 800 1000

Source: www.blockchain.info and authors’ calculations.

Bolt and Van Oordt On the Value of Virtual Currencies 5 / 26

Introduction

How affect transactions and speculation the exchange rate?

◮ Based on the transaction version of the quantity equation

◮ Fisher (1911) ◮ Friedman (1970)

Role of virtual currency for transactions

◮ Based on two-sided market theory with network effects

◮ Armstrong (2006) ◮ Rochet and Tirole (2006)

Role of virtual currency as “stored-value”

◮ Based on exchange rate models with speculation

◮ Hirshleifer (1988) ◮ Viaene and De Vries (1992) Bolt and Van Oordt On the Value of Virtual Currencies 6 / 26

Preliminaries: Fisher’s quantity equation

◮ Transaction version of quantity equation

PB

t T B t = MB t V B t . ◮ Deviation from version popularized by Fisher (1911):

◮ V B

t

is the average number of times a unit of the virtual currency is used to purchase real goods and services within period t;

◮ T B

t is the quantity of real goods and services purchased with

virtual currency B.

Bolt and Van Oordt On the Value of Virtual Currencies 7 / 26

Preliminaries: Fisher’s quantity equation

◮ Electronic stores adjust prices in virtual currencies instantly to

the latest available exchange rate: PB

t = P$ t /S$/B t

.

◮ Some manipulation:

PB

t

P$

t

• 1/S$/B

t

(P$

t T B t ) T B∗

t

= MB

t V B t . ◮ Note: star in T B∗ t

signifies that value of transactions is now measured in terms of the “established” currency.

◮ This gives the exchange rate as

S$/B

t

= T B∗

t

MB

t V B t

.

Bolt and Van Oordt On the Value of Virtual Currencies 8 / 26

Preliminaries: Fisher’s quantity equation

◮ Suppose Z B t of the MB t units are not used for purchasing

goods or services.

◮ Velocity, V B t , is the weighted average of the velocity of units

used to settle payments for goods and services, V B∗

t

, and those that are not V B

t = MB t − Z B t

MB

t

V B∗

t

+ Z B

t

MB

t

0.

◮ This gives the exchange rate as

S$/B

t

= T B∗

t

/V B∗

t

(MB

t − Z B t ).

◮ Essentially, Z B

t units are “stored-value”. In the context of

virtual currencies, we suggestively refer to those units as the speculative position.

Bolt and Van Oordt On the Value of Virtual Currencies 9 / 26

Virtual currency value as a function of speculation

4 8 12 4 8 12 Mt

B

Zt

B

St Speculative position Transactions

S$/B

t

= T B∗

t

/V B∗

t

(MB

t −Z B t ) Bolt and Van Oordt On the Value of Virtual Currencies 10 / 26

Virtual currency value as a function of speculation

2011 2012 2013 2014 2015 200 400 600 800 1000

S$/B

t

= T B∗

t

/V B∗

t

(MB

t −Z B t )

Source: www.blockchain.info and authors’ calculations.

Bolt and Van Oordt On the Value of Virtual Currencies 11 / 26

Model

Setup:

◮ One-shot model: period t refers to the initial state; period

“t + 1” refers to the moment at which use of the virtual currency network reaches its steady state.

◮ Two extremes:

◮ With probability q, the virtual currency network reaches its full

potential in the steady state;

◮ With probability 1 − q, virtual currency is abandoned.

◮ The number of virtual currency units at t + 1 that follows a

predetermined growth rule MB

t+1 = MB t

• 1 + mB

t+1

• .

Bolt and Van Oordt On the Value of Virtual Currencies 12 / 26

Model building block: Two-sided markets

What determines future usage of the virtual currency?

• ✒

❅ ❅ ❅ ■ ✓ ✒ ✏ ✑ ✓ ✒ ✏ ✑ ✓ ✒ ✏ ✑ ✛ ✲ Merchant Virtual Currency Consumer transaction cost profit prices benefit benefit

◮ Both sides need to be “on board”. ◮ Indirect network effects are important for total usage. ◮ But not all consumers/merchants are the same.

Bolt and Van Oordt On the Value of Virtual Currencies 13 / 26

Model building block: Two-sided markets

◮ Standard two-sided market theory with network effects

provides solutions for the number of agents using the network

• nce it reaches its full potential, i.e., N∗

c and N∗ m.

The number of users increases in the

◮ Cost efficiency of the network; ◮ Magnitude of the benefits to (some) users of the network; ◮ Strength of the network effects.

◮ The value of virtual currency units necessary to make

payments increases in the number of users of the network, i.e., T B∗

t

V B∗

t

= f (Nc,t, Nm,t) = φNc,t.

Bolt and Van Oordt On the Value of Virtual Currencies 14 / 26

Model building block: Speculative motive

Simple standard model for speculators

◮ Each speculator maximizes

U = E(Wt+1) − γ 2σ2(Wt+1)

◮ Wealth is given by Wt+1 = ˜

S$/B

t+1 zB t + R(Wt − S$/B t

zB

t ),

where

◮ zB

t is number of units held by each speculator;

◮ ˜

S$/B

t+1 is the uncertain future exchange rate.

◮ Optimal aggregate speculative demand of Ns,t speculators:

Z B

t = Ns,tzB t = E(˜

S$/B

t+1 ) − RS$/B t γ Ns,t σ2(˜

S$/B

t+1 )

.

Bolt and Van Oordt On the Value of Virtual Currencies 15 / 26

Speculative motive results in a demand schedule

Demand depends on expectations regarding the exchange rate.

4 8 12 4 8 12 Mt

B

E(St+1) R−1 St|T=0

Bolt and Van Oordt On the Value of Virtual Currencies 16 / 26

Two building blocks act as a demand and supply schedule

Equilibrium price has an analytical solution.

4 8 12 4 8 12 Mt

B

Zt

B

E(St+1) R−1 St Speculative position Transactions

Bolt and Van Oordt On the Value of Virtual Currencies 17 / 26

What moves the exchange rate of a virtual currency?

Increase in usage and value of real payments (T B∗

t

↑)

4 8 12 4 8 12 Mt

B

Zold

B

Sold Znew

B

Snew

Bolt and Van Oordt On the Value of Virtual Currencies 18 / 26

What moves the exchange rate of a virtual currency?

More optimistic expectations of speculators (E(˜ S$/B

t+1 ) ↑)

4 8 12 4 8 12 Mt

B

Zold

B

Sold Znew

B

Snew

Bolt and Van Oordt On the Value of Virtual Currencies 19 / 26

What moves the exchange rate of a virtual currency?

An influx of new speculators (Ns,t ↑)

4 8 12 4 8 12 Mt

B

Zold

B

Sold Znew

B

Snew

Bolt and Van Oordt On the Value of Virtual Currencies 20 / 26

Impact of speculative environment

Virtual currencies have suffered from highly volatile exchange rates compared to the exchange rates of established currencies; see, e.g., Yermack (2015). Theoretical prediction: As the use of a virtual currency increases, its exchange rate becomes less sensitive to

◮ Shocks to speculators’ expectations; ◮ Influx and outflow of speculators.

Bolt and Van Oordt On the Value of Virtual Currencies 21 / 26

Rational expectations equilibrium

Speculators with rational expectations gives E(˜ S$/B

t+1 ) = q

• φN∗

c

MB

t+1

• ,

σ2(˜ S$/B

t+1 ) = q(1 − q)

• φN∗

c

MB

t+1

2 .

Bolt and Van Oordt On the Value of Virtual Currencies 22 / 26

Rational expectations equilibrium

This gives the current exchange rate as S$/B

t

= q

• φN∗

c

MB

t+1

• ×
• 1

2

• δ2

t + 1

2

• δ2

t + 4γφNc,t

Ns,t 1 − q q R−1

• ,

where δt represents the hypothetical “discount factor” in case of no real transactions using the virtual currency, i.e., if Nc,t = 0. This hypothetical discount factor is calculated as δt =

• 1 − (1 − q)

1 + mB

t+1

γφ N∗

c

Ns,t

• R−1.

Current adoption Nc,t, results in a higher actual discount factor, and, therefore, in a higher current exchange rate S$/B

t

.

Bolt and Van Oordt On the Value of Virtual Currencies 23 / 26

Conclusions

Take-aways:

◮ A steep increase in the exchange rate due to speculative

motives is exactly what you can expect at the introduction of a potentially successful virtual currency. “Some of them were withdrawn from circulation to be held for the rise. (...) Thus speculation acted as a regulator of the quantity of money.” – Fisher, The Purchasing Power of Money, 1911.

◮ Current high level of volatility is a childhood disease:

Theoretically, volatility should drop if the adoption by consumers and merchants increases.

◮ Conditional upon survival, deflationary virtual currency prices

should also be expected during the early adopters stage.

Bolt and Van Oordt On the Value of Virtual Currencies 24 / 26

Conclusions

Future work:

◮ “Full-fledged” dynamics in adoption and speculation. ◮ Data on actual virtual currency payments and adoption. ◮ Empirical determinants of switching behaviour.

Bolt and Van Oordt On the Value of Virtual Currencies 25 / 26

Thank you!

2011 2012 2013 2014 2015 200 400 600 800 1000

◮ Don’t hesitate to contact me at w.bolt@dnb.nl,

• r Maarten van Oordt at mvanoordt@bankofcanada.ca.

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