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On the Value of Virtual Currencies 1 Wilko Bolt a and Maarten van Oordt b a De Nederlandsche Bank (DNB) b Bank of Canada (BoC) Mapping out the Road Ahead De Nederlandsche Bank Amsterdam, 2122 April 2016 1 Views expressed do not necessarily

  1. On the Value of Virtual Currencies 1 Wilko Bolt a and Maarten van Oordt b a De Nederlandsche Bank (DNB) b Bank of Canada (BoC) Mapping out the Road Ahead De Nederlandsche Bank Amsterdam, 21–22 April 2016 1 Views expressed do not necessarily reflect official positions of DNB or BoC. Bolt and Van Oordt On the Value of Virtual Currencies 1 / 26

  2. 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

  3. 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

  4. Speculation and the USD/bitcoin exchange rate 1000 800 600 400 200 0 2011 2012 2013 2014 2015 Source: www.blockchain.info. Bolt and Van Oordt On the Value of Virtual Currencies 4 / 26

  5. Speculation and the USD/bitcoin exchange rate 1000 800 600 400 200 0 2011 2012 2013 2014 2015 Source: www.blockchain.info and authors’ calculations. Bolt and Van Oordt On the Value of Virtual Currencies 5 / 26

  6. 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

  7. Preliminaries: Fisher’s quantity equation ◮ Transaction version of quantity equation P B t T B t = M B t V B t . ◮ Deviation from version popularized by Fisher (1911): ◮ V B is the average number of times a unit of the virtual t 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

  8. Preliminaries: Fisher’s quantity equation ◮ Electronic stores adjust prices in virtual currencies instantly to t / S $ / B the latest available exchange rate: P B t = P $ . t ◮ Some manipulation: P B t ( P $ t T B = M B t V B t ) t . P $ � �� � t T B ∗ ���� t 1 / S $ / B t ◮ Note: star in T B ∗ signifies that value of transactions is now t measured in terms of the “established” currency. ◮ This gives the exchange rate as T B ∗ S $ / B t = . t M B t V B t Bolt and Van Oordt On the Value of Virtual Currencies 8 / 26

  9. Preliminaries: Fisher’s quantity equation ◮ Suppose Z B t of the M B 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 ∗ , and t those that are not t = M B t − Z B + Z B t t V B V B ∗ 0 . t M B M B t t ◮ This gives the exchange rate as = T B ∗ / V B ∗ S $ / B t t t ) . t ( M B t − Z B ◮ 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

  10. Virtual currency value as a function of speculation 12 8 = T B ∗ / V B ∗ S $ / B t t t ( M B t − Z B t ) 4 S t 0 B B Z t M t 0 4 8 12 Speculative position Transactions Bolt and Van Oordt On the Value of Virtual Currencies 10 / 26

  11. Virtual currency value as a function of speculation 1000 800 = T B ∗ / V B ∗ S $ / B t t t ( M B t − Z B t ) 600 400 200 0 2011 2012 2013 2014 2015 Source: www.blockchain.info and authors’ calculations. Bolt and Van Oordt On the Value of Virtual Currencies 11 / 26

  12. 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 M B t +1 = M B 1 + m B . t t +1 Bolt and Van Oordt On the Value of Virtual Currencies 12 / 26

  13. Model building block: Two-sided markets What determines future usage of the virtual currency? ✓ ✏ cost Virtual Currency profit ✒ ✑ ✒ � ❅ ■ prices � ❅ � ❅ ✓ ✏ ✓ ✏ ✛ ✲ Consumer Merchant ✒ ✑ transaction ✒ ✑ 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

  14. Model building block: Two-sided markets ◮ Standard two-sided market theory with network effects provides solutions for the number of agents using the network once 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 = f ( N c , t , N m , t ) = φ N c , t . V B ∗ t Bolt and Van Oordt On the Value of Virtual Currencies 14 / 26

  15. Model building block: Speculative motive Simple standard model for speculators ◮ Each speculator maximizes U = E ( W t +1 ) − γ 2 σ 2 ( W t +1 ) ◮ Wealth is given by W t +1 = ˜ S $ / B t + R ( W t − S $ / B t +1 z B z B t ) , t where ◮ z B t is number of units held by each speculator; ◮ ˜ S $ / B t +1 is the uncertain future exchange rate. ◮ Optimal aggregate speculative demand of N s , t speculators: t = E (˜ S $ / B t +1 ) − RS $ / B t Z B t = N s , t z B . N s , t σ 2 (˜ γ S $ / B t +1 ) Bolt and Van Oordt On the Value of Virtual Currencies 15 / 26

  16. Speculative motive results in a demand schedule Demand depends on expectations regarding the exchange rate. 12 E ( S t + 1 ) R − 1 8 S t|T=0 4 0 B M t 0 4 8 12 Bolt and Van Oordt On the Value of Virtual Currencies 16 / 26

  17. Two building blocks act as a demand and supply schedule Equilibrium price has an analytical solution. 12 E ( S t + 1 ) R − 1 8 S t 4 0 B B Z t M t 0 4 8 12 Speculative position Transactions Bolt and Van Oordt On the Value of Virtual Currencies 17 / 26

  18. What moves the exchange rate of a virtual currency? Increase in usage and value of real payments ( T B ∗ ↑ ) t 12 S new 8 S old 4 0 B B B Z new Z old M t 0 4 8 12 Bolt and Van Oordt On the Value of Virtual Currencies 18 / 26

  19. What moves the exchange rate of a virtual currency? S $ / B More optimistic expectations of speculators ( E (˜ t +1 ) ↑ ) 12 8 S new S old 4 0 B B B Z old Z new M t 0 4 8 12 Bolt and Van Oordt On the Value of Virtual Currencies 19 / 26

  20. What moves the exchange rate of a virtual currency? An influx of new speculators ( N s , t ↑ ) 12 8 S new S old 4 0 B B B Z old Z new M t 0 4 8 12 Bolt and Van Oordt On the Value of Virtual Currencies 20 / 26

  21. 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

  22. Rational expectations equilibrium Speculators with rational expectations gives � � φ N ∗ E (˜ S $ / B c t +1 ) = q , M B t +1 � � 2 φ N ∗ S $ / B σ 2 (˜ c t +1 ) = q (1 − q ) . M B t +1 Bolt and Van Oordt On the Value of Virtual Currencies 22 / 26

  23. Rational expectations equilibrium This gives the current exchange rate as � � � � � � φ N ∗ 1 t + 1 t + 4 γφ N c , t 1 − q S $ / B c δ 2 δ 2 R − 1 = q , × t M B 2 2 N s , t q t +1 where δ t represents the hypothetical “discount factor” in case of no real transactions using the virtual currency, i.e., if N c , t = 0. This hypothetical discount factor is calculated as � � 1 − (1 − q ) γφ N ∗ c R − 1 . δ t = 1 + m B N s , t t +1 Current adoption N c , 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

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