2.4 Money
9
Since 1971 the dollar, and the currencies of the other members of the Bretton-Woods
agreement, are pure fiat-monies and the Federal Reserve does not have to limit the
amount of money they loan to commercial banks, which stimulates growth. This
increased flow of money, however, has a down-side; it reduces the value of each
dollar in circulation and thereby increases inflation.
Cryptocurrencies, such as Bitcoin, Ethereum, or Litecoin are currencies that do
not depend on central authorities to guarantee their integrity. Instead, they maintain
a distributed ledger, a database where all transactions are stored. These transactions
are digitally signed using strong cryptography and miners compete to verify the
transactions. The process is organized to make it practically impossible to reverse a
transaction and this renders the database tamper-proof and immutable. How this is
implemented in practice is the topic of Chap. 12. For cryptocurrencies the trust in a
central authority is replaced by the trust in the integrity of the ledger. As long as trading partners trust this mechanism, a cryptocurrency has a value, but this is a decision
that all trading partners collectively reach. As long as all think that bitcoins are a great
idea and that they serve a purpose, bitcoins carry a value. This communal sentiment,
however, changes over time and that causes the exchange rate of cryptocurrencies to
fluctuate more than most other currencies.
2.5 Discounting and Liquidity
When calculating the price of options and other derivatives, we compare values at
different times, for example, now and at maturity, which requires some additional
thought. Let us therefore work out how much money we can actually earn from
shorting an asset. At first sight, it is just the difference of the selling price immediately
after borrowing the stocks and the re-purchasing price at a later date. At this point we
compare money at different times, which makes little sense, because money at the
earlier time can be invested in a risk free asset, such as savings bonds or the London
Interbank Offered Rate (LIBOR). The LIBOR is the rate at which banks borrow
and loan money to each other and is considered risk-free. If invested at the LIBOR
rate, the initial money would grow at the risk-free interest rate r f by a factor e
r f t
,
where we assume continuously compounding interest. Conversely, this implies that
money at a later time is worth less compared to the earlier time, and the factor by
which it needs to be discounted is e
−r f t
, again assuming continuously compounding
interest. Essentially discounting means to back-propagate a value for the time t with
the discount factor e
−r f t
.
One of the underlying assumptions in financial theory is that there always exists
an institution, which provides liquidity. This implies that we can always borrow
unlimited amounts of money at the risk-free interest rate r f and we can always
deposit surplus funds at the same rate. In this way there is always the chance to
increase the value of ones assets by depositing at the bank with rate r f , but the hope
is, of course, to invest in some other assets that will provide a higher rate of return
ρ on the invested money, albeit at a higher risk. The gamble is getting the highest
return at the lowest tolerable risk.
9
Since 1971 the dollar, and the currencies of the other members of the Bretton-Woods
agreement, are pure fiat-monies and the Federal Reserve does not have to limit the
amount of money they loan to commercial banks, which stimulates growth. This
increased flow of money, however, has a down-side; it reduces the value of each
dollar in circulation and thereby increases inflation.
Cryptocurrencies, such as Bitcoin, Ethereum, or Litecoin are currencies that do
not depend on central authorities to guarantee their integrity. Instead, they maintain
a distributed ledger, a database where all transactions are stored. These transactions
are digitally signed using strong cryptography and miners compete to verify the
transactions. The process is organized to make it practically impossible to reverse a
transaction and this renders the database tamper-proof and immutable. How this is
implemented in practice is the topic of Chap. 12. For cryptocurrencies the trust in a
central authority is replaced by the trust in the integrity of the ledger. As long as trading partners trust this mechanism, a cryptocurrency has a value, but this is a decision
that all trading partners collectively reach. As long as all think that bitcoins are a great
idea and that they serve a purpose, bitcoins carry a value. This communal sentiment,
however, changes over time and that causes the exchange rate of cryptocurrencies to
fluctuate more than most other currencies.
2.5 Discounting and Liquidity
When calculating the price of options and other derivatives, we compare values at
different times, for example, now and at maturity, which requires some additional
thought. Let us therefore work out how much money we can actually earn from
shorting an asset. At first sight, it is just the difference of the selling price immediately
after borrowing the stocks and the re-purchasing price at a later date. At this point we
compare money at different times, which makes little sense, because money at the
earlier time can be invested in a risk free asset, such as savings bonds or the London
Interbank Offered Rate (LIBOR). The LIBOR is the rate at which banks borrow
and loan money to each other and is considered risk-free. If invested at the LIBOR
rate, the initial money would grow at the risk-free interest rate r f by a factor e
r f t
,
where we assume continuously compounding interest. Conversely, this implies that
money at a later time is worth less compared to the earlier time, and the factor by
which it needs to be discounted is e
−r f t
, again assuming continuously compounding
interest. Essentially discounting means to back-propagate a value for the time t with
the discount factor e
−r f t
.
One of the underlying assumptions in financial theory is that there always exists
an institution, which provides liquidity. This implies that we can always borrow
unlimited amounts of money at the risk-free interest rate r f and we can always
deposit surplus funds at the same rate. In this way there is always the chance to
increase the value of ones assets by depositing at the bank with rate r f , but the hope
is, of course, to invest in some other assets that will provide a higher rate of return
ρ on the invested money, albeit at a higher risk. The gamble is getting the highest
return at the lowest tolerable risk.