Malicious Machine Learnings? Privacy Preservation and Computational Correctness Across Parties. Note Quote/Didactics.

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Multi-Party Computation deals with the following problem: There are n ≥ 2 parties P1, . . ., Pn where party Pi holds input ti, 1 ≤ i ≤ n, and they wish to compute together a functions = f (t1, . . . , tn) on their inputs. The goal is that each party will learn the output of the function, s, yet with the restriction that Pi will not learn any additional information about the input of the other parties aside from what can be deduced from the pair (ti, s). Clearly it is the secrecy restriction that adds complexity to the problem, as without it each party could announce its input to all other parties, and each party would locally compute the value of the function. Thus, the goal of Multi-Party Computation is to achieve the following two properties at the same time: correctness of the computation and privacy preservation of the inputs.

The following two generalizations are often useful:

(i) Probabilistic functions. Here the value of the function depends on some random string r chosen according to some distribution: s = f (t1, . . . , tn; r). An example of this is the coin-flipping functionality, which takes no inputs, and outputs an unbiased random bit. It is crucial that the value r is not controlled by any of the parties, but is somehow jointly generated during the computation.

(ii) Multioutput functions. It is not mandatory that there be a single output of the function. More generally there could be a unique output for each party, i.e., (s1, . . . , sn) = f(t1,…, tn). In this case, only party Pi learns the output si, and no other party learns any information about the other parties’ input and outputs aside from what can be derived from its own input and output.

One of the most interesting aspects of Multi-Party Computation is to reach the objective of computing the function value, but under the assumption that some of the parties may deviate from the protocol. In cryptography, the parties are usually divided into two types: honest and faulty. An honest party follows the protocol without any deviation. Otherwise, the party is considered to be faulty. The faulty behavior can exemplify itself in a wide range of possibilities. The most benign faulty behavior is where the parties follow the protocol, yet try to learn as much as possible about the inputs of the other parties. These parties are called honest-but-curious (or semihonest). At the other end of the spectrum, the parties may deviate from the prescribed protocol in any way that they desire, with the goal of either influencing the computed output value in some way, or of learning as much as possible about the inputs of the other parties. These parties are called malicious.

We envision an adversary A, who controls all the faulty parties and can coordinate their actions. Thus, in a sense we assume that the faulty parties are working together and can exert the most knowledge and influence over the computation out of this collusion. The adversary can corrupt any number of parties out of the n participating parties. Yet, in order to be able to achieve a solution to the problem, in many cases we would need to limit the number of corrupted parties. This limit is called the threshold k, indicating that the protocol remains secure as long as the number of corrupted parties is at most k.

Assume that there exists a trusted party who privately receives the inputs of all the participating parties, calculates the output value s, and then transmits this value to each one of the parties. This process clearly computes the correct output of f, and also does not enable the participating parties to learn any additional information about the inputs of others. We call this model the ideal model. The security of Multi-Party Computation then states that a protocol is secure if its execution satisfies the following: (1) the honest parties compute the same (correct) outputs as they would in the ideal model; and (2) the protocol does not expose more information than a comparable execution with the trusted party, in the ideal model.

Intuitively, the adversary’s interaction with the parties (on a vector of inputs) in the protocol generates a transcript. This transcript is a random variable that includes the outputs of all the honest parties, which is needed to ensure correctness, and the output of the adversary A. The latter output, without loss of generality, includes all the information that the adversary learned, including its inputs, private state, all the messages sent by the honest parties to A, and, depending on the model, maybe even include more information, such as public messages that the honest parties exchanged. If we show that exactly the same transcript distribution can be generated when interacting with the trusted party in the ideal model, then we are guaranteed that no information is leaked from the computation via the execution of the protocol, as we know that the ideal process does not expose any information about the inputs. More formally,

Let f be a function on n inputs and let π be a protocol that computes the function f. Given an adversary A, which controls some set of parties, we define REALA,π(t) to be the sequence of outputs of honest parties resulting from the execution of π on input vector t under the attack of A, in addition to the output of A. Similarly, given an adversary A′ which controls a set of parties, we define IDEALA′,f(t) to be the sequence of outputs of honest parties computed by the trusted party in the ideal model on input vector t, in addition to the output of A′. We say that π securely computes f if, for every adversary A as above, ∃ an adversary A′, which controls the same parties in the ideal model, such that, on any input vector t, we have that the distribution of REALA,π(t) is “indistinguishable” from the distribution of IDEALA′,f(t).

Intuitively, the task of the ideal adversary A′ is to generate (almost) the same output as A generates in the real execution or the real model. Thus, the attacker A′ is often called the simulator of A. The transcript value generated in the ideal model, IDEALA′,f(t), also includes the outputs of the honest parties (even though we do not give these outputs to A′), which we know were correctly computed by the trusted party. Thus, the real transcript REALA,π(t) should also include correct outputs of the honest parties in the real model.

We assumed that every party Pi has an input ti, which it enters into the computation. However, if Pi is faulty, nothing stops Pi from changing ti into some ti′. Thus, the notion of a “correct” input is defined only for honest parties. However, the “effective” input of a faulty party Pi could be defined as the value ti′ that the simulator A′ gives to the trusted party in the ideal model. Indeed, since the outputs of honest parties look the same in both models, for all effective purposes Pi must have “contributed” the same input ti′ in the real model.

Another possible misbehavior of Pi, even in the ideal model, might be a refusal to give any input at all to the trusted party. This can be handled in a variety of ways, ranging from aborting the entire computation to simply assigning ti some “default value.” For concreteness, we assume that the domain of f includes a special symbol ⊥ indicating this refusal to give the input, so that it is well defined how f should be computed on such missing inputs. What this requires is that in any real protocol we detect when a party does not enter its input and deal with it exactly in the same manner as if the party would input ⊥ in the ideal model.

As regards security, it is implicitly assumed that all honest parties receive the output of the computation. This is achieved by stating that IDEALA′,f(t) includes the outputs of all honest parties. We therefore say that our currency guarantees output delivery. A more relaxed property than output delivery is fairness. If fairness is achieved, then this means that if at least one (even faulty) party learns its outputs, then all (honest) parties eventually do too. A bit more formally, we allow the ideal model adversary A′ to instruct the trusted party not to compute any of the outputs. In this case, in the ideal model either all the parties learn the output, or none do. Since A’s transcript is indistinguishable from A′’s this guarantees that the same fairness guarantee must hold in the real model as well.

A further relaxation of the definition of security is to provide only correctness and privacy. This means that faulty parties can learn their outputs, and prevent the honest parties from learning theirs. Yet, at the same time the protocol will still guarantee that (1) if an honest party receives an output, then this is the correct value, and (2) the privacy of the inputs and outputs of the honest parties is preserved.

The basic security notions are universal and model-independent. However, specific implementations crucially depend on spelling out precisely the model where the computation will be carried out. In particular, the following issues must be specified:

  1. The faulty parties could be honest-but-curious or malicious, and there is usually an upper bound k on the number of parties that the adversary can corrupt.
  2. Distinguishing between the computational setting and the information theoretic setting, in the latter, the adversary is unlimited in its computing powers. Thus, the term “indistinguishable” is formalized by requiring the two transcript distributions to be either identical (so-called perfect security) or, at least, statistically close in their variation distance (so-called statistical security). On the other hand, in the computational, the power of the adversary (as well as that of the honest parties) is restricted. A bit more precisely, Multi-Party Computation problem is parameterized by the security parameter λ, in which case (a) all the computation and communication shall be done in time polynomial in λ; and (b) the misbehavior strategies of the faulty parties are also restricted to be run in time polynomial in λ. Furthermore, the term “indistinguishability” is formalized by computational indistinguishability: two distribution ensembles {Xλ}λ and {Yλ}λ are said to be computationally indistinguishable, if for any polynomial-time distinguisher D, the quantity ε, defined as |Pr[D(Xλ) = 1] − Pr[D(Yλ) = 1]|, is a “negligible” function of λ. This means that for any j > 0 and all sufficiently large λ, ε eventually becomes smaller than λ − j. This modeling helps us to build secure Multi-Party Computational protocols depending on plausible computational assumptions, such as the hardness of factoring large integers.
  3. The two common communication assumptions are the existence of a secure channel and the existence of a broadcast channel. Secure channels assume that every pair of parties Pi and Pj are connected via an authenticated, private channel. A broadcast channel is a channel with the following properties: if a party Pi (honest or faulty) broadcasts a message m, then m is correctly received by all the parties (who are also sure the message came from Pi). In particular, if an honest party receives m, then it knows that every other honest party also received m. A different communication assumption is the existence of envelopes. An envelope guarantees the following properties: a value m can be stored inside the envelope, it will be held without exposure for a given period of time, and then the value m will be revealed without modification. A ballot box is an enhancement of the envelope setting that also provides a random shuffling mechanism of the envelopes. These are, of course, idealized assumptions that allow for a clean description of a protocol, as they separate the communication issues from the computational ones. These idealized assumptions may be realized by a physical mechanisms, but in some settings such mechanisms may not be available. Then it is important to address the question if and under what circumstances we can remove a given communication assumption. For example, we know that the assumption of a secure channel can be substituted with a protocol, but under the introduction of a computational assumption and a public key infrastructure.

Fragmentation – Lit and Dark Electronic Exchanges. Thought of the Day 116.0

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Exchanges also control the amount and degree of granularity of the information you receive (e.g., you can use the consolidated/public feed at a low cost or pay a relatively much larger cost for direct/proprietary feeds from the exchanges). They also monetise the need for speed by renting out computer/server space next to their matching engines, a process called colocation. Through coloca­tion, exchanges can provide uniform service to trading clients at competitive rates. Having the traders’ trading engines at a common location owned by the exchange simplifies the exchange’s ability to provide uniform service as it can control the hardware connecting each client to the trading engine, the cable (so all have the same cable of the same length), and the network. This ensures that all traders in colocation have the same fast access, and are not disadvantaged (at least in terms of exchange-provided hardware). Naturally, this imposes a clear distinction between traders who are colocated and those who are not. Those not colocated will always have a speed disadvantage. It then becomes an issue for reg­ulators who have to ensure that exchanges keep access to colocation sufficiently competitive.

The issue of distance from the trading engine brings us to another key dimen­sion of trading nowadays, especially in US equity markets, namely fragmentation. A trader in US equities markets has to be aware that there are up to 13 lit electronic exchanges and more than 40 dark ones. Together with this wide range of trading options, there is also specific regulation (the so-called ‘trade-through’ rules) which affects what happens to market orders sent to one exchange if there are better execution prices at other exchanges. The interaction of multiple trading venues, latency when moving be­tween these venues, and regulation introduces additional dimensions to keep in mind when designing success l trading strategies.

The role of time is fundamental in the usual price-time priority electronic ex­change, and in a fragmented market, the issue becomes even more important. Traders need to be able to adjust their trading positions fast in response to or in anticipation of changes in market circumstances, not just at the local exchange but at other markets as well. The race to be the first in or out of a certain position is one of the focal points of the debate on the benefits and costs of ‘high-frequency trading’.

The importance of speed permeates the whole process of designing trading algorithms, from the actual code, to the choice of programming language, to the hardware it is implemented on, to the characteristics of the connection to the matching engine, and the way orders are routed within an exchange and between exchanges. Exchanges, being aware of the importance of speed, have adapted and, amongst other things, moved well beyond the basic two types of orders (Market Orders and Limit Orders). Any trader should be very well-informed regarding all the different order types available at the exchanges, what they are and how they may be used.

When coding an algorithm one should be very aware of all the possible types of orders allowed, not just in one exchange, but in all competing exchanges where one’s asset of interest is traded. Being uninformed about the variety of order types can lead to significant losses. Since some of these order types allow changes and adjustments at the trading engine level, they cannot be beaten in terms of latency by the trader’s engine, regardless of how efficiently your algorithms are coded and hardwired.

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Another important issue to be aware of is that trading in an exchange is not free, but the cost is not the same for all traders. For example, many exchanges run what is referred to as a maker-taker system of fees whereby a trader sending an MO (and hence taking liquidity away from the market) pays a trading fee, while a trader whose posted LO is filled by the MO (that is, the LO with which the MO is matched) will a pay much lower trading fee, or even receive a payment (a rebate) from the exchange for providing liquidity (making the market). On the other hand, there are markets with an inverted fee schedule, a taker-maker system where the fee structure is the reverse: those providing liquidity pay a higher fee than those taking liquidity (who may even get a rebate). The issue of exchange fees is quite important as fees distort observed market prices (when you make a transaction the relevant price for you is the net price you pay/receive, which is the published price net of fees).

Convertible Arbitrage. Thought of the Day 108.0

A convertible bond can be thought of as a fixed income security that has an embedded equity call option. The convertible investor has the right, but not the obligation, to convert (exchange) the bond into a predetermined number of common shares. The investor will presumably convert sometime at or before the maturity of the bond if the value of the common shares exceeds the cash redemption value of the bond. The convertible therefore has both debt and equity characteristics and, as a result, provides an asymmetrical risk and return profile. Until the investor converts the bond into common shares of the issuer, the issuer is obligated to pay a fixed coupon to the investor and repay the bond at maturity if conversion never occurs. A convertible’s price is sensitive to, among other things, changes in market interest rates, credit risk of the issuer, and the issuer’s common share price and share price volatility.

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Analysis of convertible bond prices factors in three different sources of value: investment value, conversion value, and option value. The investment value is the theoretical value at which the bond would trade if it were not convertible. This represents the security’s floor value, or minimum price at which it should trade as a nonconvertible bond. The conversion value represents the value of the common stock into which the bond can be converted. If, for example, these shares are trading at $30 and the bond can convert into 100 shares, the conversion value is $3,000. The investment value and conversion value can be considered, at maturity, the low and high price boundaries for the convertible bond. The option value represents the theoretical value of having the right, but not the obligation, to convert the bond into common shares. Until maturity, a convertible trades at a price between the investment value and the option value.

A Black-Scholes option pricing model, in combination with a bond valuation model, can be used to price a convertible security. However, a binomial option model, with some adjustments, is the best method for determining the value of a convertible security. Convertible arbitrage is a market-neutral investment strategy that involves the simultaneous purchase of convertible securities and the short sale of common shares (selling borrowed stock) that underlie the convertible. An investor attempts to exploit inefficiencies in the pricing of the convertible in relation to the security’s embedded call option on the convertible issuer’s common stock. In addition, there are cash flows associated with the arbitrage position that combine with the security’s inefficient pricing to create favorable returns to an investor who is able to properly manage a hedge position through a dynamic hedging process. The hedge involves selling short a percentage of the shares that the convertible can convert into based on the change in the convertible’s price with respect to the change in the underlying common stock price (delta) and the change in delta with respect to the change in the underlying common stock (gamma). The short position must be adjusted frequently in an attempt to neutralize the impact of changing common share prices during the life of the convertible security. This process of managing the short position in the issuer’s stock is called “delta hedging.”

If hedging is done properly, whenever the convertible issuer’s common share price decreases, the gain from the short stock position should exceed the loss from the convertible holding. Equally, whenever the issuer’s common share price increases, the gain from the convertible holding should exceed the loss from the short stock position. In addition to the returns produced by delta hedging, the investor will receive returns from the convertible’s coupon payment and interest income associated with the short stock sale. However, this cash flow is reduced by paying a cash amount to stock lenders equal to the dividend the lenders would have received if the stock were not loaned to the convertible investor, and further reduced by stock borrow costs paid to a prime broker. In addition, if the investor leverages the investment by borrowing cash from a prime broker, there will be interest expense on the loan. Finally, if an investor chooses to hedge credit risk of the issuer, or interest rate risk, there will be additional costs associated with credit default swaps and a short Treasury position. This strategy attempts to create returns that exceed the returns that would be available from purchasing a nonconverting bond with the same maturity issued by the same issuer, without being exposed to common share price risk. Most convertible arbitrageurs attempt to achieve double-digit annual returns from convertible arbitrage.

Greed

In greedy exchange, when two individuals meet, the richer person takes one unit of capital from the poorer person, as represented by the reaction scheme (j, k) → (j + 1, k − 1) for j ≥ k. In the rate equation approximation, the densities ck(t) now evolve according to

dck/dt = ck-1j=1k-1cj + ck+1j=k+1cj – ckN – c2k —– (1)

The first two terms account for the gain in ck(t) due to the interaction between pairs of individuals of capitals (j, k−1), with j k, respectively. The last two terms correspondingly account for the loss of ck(t). One can check that the wealth density M1 ≡ ∑k=1 k ck(t) is conserved, and that the population density obeys

dN/dt = -c1N —– (2)

Equation (1) are conceptually similar to the Smoluchowski equations for aggregation with a constant reaction rate. Mathematically, however, they appear to be more complex and we have been unable to solve them analytically. Fortunately, equation (1) is amenable to a scaling solution. For this purpose, we first re-write equation (1) as

dck/dt = -ck(ck + ck+1) + N(ck-1 – ck) + (ck+1 – ck-1)∑j=kcj —– (3)

Taking the continuum limit and substituting the scaling ansatz,

ck(t) ≅ N2C(x), with x = kN —– (4)

transforms equations (2) and (3) to

dN/dt = -C(0)N3 —– (5)

and

C(0)[2C + xC’] = 2C2 + C'[1 – 2∫xdyC(y)] —– (6)

where C ′ = dC/dx. Note also that the scaling function must obey the integral relations

xdxC(x) = 1 and ∫xdxxC(x) = 1 —– (7)

The former follows from the definition of density, N = ∑ck(t) ≅ N∫dx C(x), while the latter follows if we set, without loss of generality, the conserved wealth density equal to unity, ∑kkck(t) = 1.

Introducing B(x) = ∫0x dyC(y) recasts equation (6) into C(0)[2B′ + xB′′] = 2B′2 + B′′[2B − 1]. Integrating twice gives [C(0)x − B][B − 1] = 0, with solution B(x) = C(0)x for x < xf and B(x) = 1 for x ≥ xf, from which we conclude that the scaled wealth distribution C(x) = B′(x) coincides with the zero-temperature Fermi distribution;

C(x) = C(0), for x < xf

= 0, for x ≥ xf —– (8)

Hence the scaled profile has a sharp front at x = xf, with xf = 1/C(0) found by matching the two branches of the solution for B(x). Making use of the second integral relation, equation (7), gives C(0) = 1/2 and thereby closes the solution. Thus, the unscaled wealth distribution ck(t) reads,

ck(t) = 1/(2t), for k < 2√t

= 0, for k ≥ 2√t —– (9)

and the total density is N(t) = t-1/2

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Figure: Simulation results for the wealth distribution in greedy additive exchange based on 2500 configurations for 106 traders. Shown are the scaled distributions C(x) versus x = kN for t = 1.5n, with n = 18, 24, 30, and 36; these steepen with increasing time. Each data set has been av- eraged over a range of ≈ 3% of the data points to reduce fluctuations.

These predictions by numerical simulations are shown in the figure. In the simulation, two individuals are randomly chosen to undergo greedy exchange and this process is repeated. When an individual reaches zero capital he is eliminated from the system, and the number of active traders is reduced by one. After each reaction, the time is incremented by the inverse of the number of active traders. While the mean-field predictions are substantially corroborated, the scaled wealth distribution for finite time actually resembles a finite-temperature Fermi distribution. As time increases, the wealth distribution becomes sharper and approaches equation (9). In analogy with the Fermi distribution, the relative width of the front may be viewed as an effective temperature. Thus the wealth distribution is characterized by two scales; one of order √t characterizes the typical wealth of active traders and a second, smaller scale which characterizes the width of the front.

To quantify the spreading of the front, let us include the next corrections in the continuum limit of the rate equations, equation (3). This gives,

∂c/∂t = 2∂/∂k [c∫kdjc(j)] – c∂c/∂k – N∂c/∂k + N/2 ∂2c/∂k2 —– (10)

Here, the second and fourth terms on the RHS denote the second corrections. since, the convective third term determines the location of the front to be at kf = 2√t, it is natural to expect that the diffusive fourth term describes the spreading of the front. the term c∂c/∂k  turns out to be negligible in comparison to the diffusive spreading term and is henceforth neglected. The dominant convective term can be removed by transforming to a frame of reference which moves with the front namely, k → K = k − 2√t. among the remaining terms in the transformed rate equation, the width of the front region W can now be determined by demanding that the diffusion term has the same order of magnitude as the reactive terms, i.e. N ∂2c/∂k∼ c2. This implies W ∼ √(N/c). Combining this with N = t−1/2 and c ∼ t−1 gives W ∼ t1/4, or a relative width w = W/kf ∼ t−1/4. This suggests the appropriate scaling ansatz for the front region is

ck(t) = 1/t X(ξ), ξ = (k – 2√t)/ t1/4 —– (11)

Substituting this ansatz into equation (10) gives a non-linear single variable integro-differential equation for the scaling function X(ξ). Together with the appropriate boundary conditions, this represents, in principle, a more complete solution to the wealth distribution. However, the essential scaling behavior of the finite-time spreading of the front is already described by equation (11), so that solving for X(ξ) itself does not provide additional scaling information. Analysis gives w ∼ t−α with α ≅ 1/5. We attribute this discrepancy to the fact that w is obtained by differentiating C(x), an operation which generally leads to an increase in numerical errors.

Arbitrage, or Tensors thereof…

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What is an arbitrage? Basically it means ”to get something from nothing” and a free lunch after all. More strict definition states the arbitrage as an operational opportunity to make a risk-free profit with a rate of return higher than the risk-free interest rate accured on deposit.

The arbitrage appears in the theory when we consider a curvature of the connection. A rate of excess return for an elementary arbitrage operation (a difference between rate of return for the operation and the risk-free interest rate) is an element of curvature tensor calculated from the connection. It can be understood keeping in mind that a curvature tensor elements are related to a difference between two results of infinitesimal parallel transports performed in different order. In financial terms it means that the curvature tensor elements measure a difference in gains accured from two financial operations with the same initial and final points or, in other words, a gain from an arbitrage operation.

In a certain sense, the rate of excess return for an elementary arbitrage operation is an analogue of the electromagnetic field. In an absence of any uncertanty (or, in other words, in an absense of walks of prices, exchange and interest rates) the only state is realised is the state of zero arbitrage. However, if we place the uncertenty in the game, prices and the rates move and some virtual arbitrage possibilities to get more than less appear. Therefore we can say that the uncertanty play the same role in the developing theory as the quantization did for the quantum gauge theory.

What of “matter” fields then, which interact through the connection. The “matter” fields are money flows fields, which have to be gauged by the connection. Dilatations of money units (which do not change a real wealth) play a role of gauge transformation which eliminates the effect of the dilatation by a proper tune of the connection (interest rate, exchange rates, prices and so on) exactly as the Fisher formula does for the real interest rate in the case of an inflation. The symmetry of the real wealth to a local dilatation of money units (security splits and the like) is the gauge symmetry of the theory.

A theory may contain several types of the “matter” fields which may differ, for example, by a sign of the connection term as it is for positive and negative charges in the electrodynamics. In the financial stage it means different preferances of investors. Investor’s strategy is not always optimal. It is due to partially incomplete information in hands, choice procedure, partially, because of investors’ (or manager’s) internal objectives. Physics of Finance

 

 

Fractional Reserve Banking. An Attempt at Demystifying.

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FRB is a technique where a bank can lend more money than it has itself available (‘deposited’ by clients). Normally, a ratio is 9:1 is used, money lent vs. the base product of banking.

This base product used to be gold. So, a bank could issue 9 times more ‘bank notes’ (‘rights to gold’) than it had gold in its vault. Imagine, a person comes with a sack of 1 kilo of gold. This person gets a note from the bank saying “you have deposited 1 kilo of gold in my bank. This note can be exchanged for that 1 kilo of gold any time you want”. But it can legally give this same note to 8 more people! 9 notes that promise 1 kilo of gold for every kilo of gold deposited. Banks are masters of promising things they in no way whatsoever can ever fulfill. And, everybody knows it. And, still we trust the banks. It is an amazing mass denial effect. We trust it, because it gives us wealth. This confidence in the system is what is, actually, essential in the economy. Our civilization depends on the low-morality of the system and our unwavering confidence in it. You are allowed to lie even if the lie is totally and utterly obvious and undeniably without a shred of doubt a lie.

In modern times, the gold standard has been abandoned, because it limits the game. Countries with the most advanced financial structures are the richest. Abandoning the gold standard creates enormous wealth. Rich, advanced nations, therefore, have abandoned the gold standard. In modern banks, no longer gold, but money itself is the base. That is, the promissory notes promise promissory notes. It is completely air. Yet, it works, because everybody trusts it’ll work.

Moreover, banks no longer issue bank notes themselves, except the central bank. The ‘real’ money of the central bank is called ‘base money’ (M0 or ‘Tier 1’) and serves as ‘gold’ in modern banks. The ‘bank notes’ from the bank promise bank notes from the central bank.

Banks use this base money no longer to directly print money (bank notes), but something that is equivalent, namely to lend money to their clients by just adding a number on their account. This, once again, works because everybody trusts it works. But is has become even thinner than air. It is equal to vacuum. There is no physical difference whatsoever anymore between having money and not having it. If I have 0 on my account, or 10000000000000000 rupees, I have the same size information on the computer of my bank. The same number of bytes (however many they may be). I just hope that one day a tiny random fluctuation occurs in their computer and sets me the first bit to a ‘1’ (unless it is the ‘sign’ bit, of course!). Nobody would notice, since there is nowhere money disappearing in the world. Simply more vacuum has been created.

But, it gets even worse. This newly created ‘money’ (the number on an account of bank A) can be deposited in other banks (write a cheque, deposit it, or make a bank transfer to bank B). In this other bank B, it can again be used as a base for creating money by adding a number to peoples’ bank account. As long as a certain amount of base money (M0, or ‘Tier 1’) is maintained. As a side mark, note that bankers do not understand the commotion of the people in calling their rewards astronomical, since they know – in contrast to the people that think that money represents earning based on hard work – that money is vacuum. Giving a bonus to the manager in the form of adding a couple of zeros to her account in her own bank is nothing but air. The most flagrant case of self-referential emptiness is the bank that was bought with its own money.

In this way, the money circulating in the economy can be much larger than the base money (of the central bank). And, all this money is completely air. The amount of money in the world is utterly baseless. Since it is air, moreover an air-system that is invented to facilitate the creation of wealth, we can intervene in the system in any way we want, if we see that this intervention is needed to optimize the creation of wealth. Think of it like this: the money and the money system was invented to enable our trade to take place. If we see that money no longer serves us (but we, instead, seem to serve the money) and decide to organize this trade in another way, we can do so without remorse. If we want to confiscate money and redistribute it, this is morally justified if that is what it takes to enable the creation of wealth.

Especially since, as will be shown, there is no justice in the distribution. It is not as if we were going to take away hard-earned money from someone. The money is just accumulated on a big pile. Intervention is adequate, required and justified. Not intervening makes things much worse for everybody.

Important to make this observation: All money thus circulating in the world is borrowed money. Money is nothing less and nothing more than debt. Without lending and borrowing, there is no debt and there is no money. Without money, there is no trade and no economy. Without debt, the economy collapses. The more debt, the bigger the economy. If everybody were to pay back his/her debt, the system would crash.

Anyway, it is technically not possible to pay back the money borrowed. Why? Because of the interest rates.

Interest is the phenomenon that somebody who lends money – or actually whatever other thing – to somebody that borrows it, wants more money back than it gave. This is impossible.

To give you an example. Imagine we have a library, and this library is the only entity in the world that can print books. Imagine it lends books to its customers and after one week, for every book that it lent out, it wants two back. For some customers it may still be possible. I may have somehow got the book from my neighbor (traded it for a DVD movie?), and I can give the two books the library demands for my one book borrowed. But that would just be passing the buck around; now my neighbor has to give back to the library two books, where he has none. This is how our economy works. And, to explain you what the current solution is of our society is that the library says “You don’t have two books? Don’t worry. We make it a new loan. Two books now. Next week you can give us four”. This is the system we have. Printing money (‘books’) is limited to banks (‘libraries’). The rest borrow the money and in no way whatsoever – absolutely out of the question, fat chance, don’t even think about it – is it possible to give back the money borrowed plus the interest, because this extra money simply does not exist, nor can it be created by the borrowers, because that is reserved to the lenders only. Bankrupt, unless these lenders refinance our loans by new loans.

When explaining this to people, they nearly always fervently oppose this idea, because they think that with money new wealth can be created, and thus the loan can be paid back including the interest, namely with the newly created wealth. This, however, is wrong thinking, because wealth and the commodity used in the loan are different things.
Imagine it like this: Imagine I lend society 100 rupees from my bank with 3% interest. The only rupees in circulation, since I am the only bank. Society invests it in tools for mining with which they find a mother lode with 200 million tons of gold. Yet, after one year, I want 103 rupees back. I don’t want gold. I want money! If they cannot give me my rightful money, I will confiscate everything they own. I will offer 2 rupees for all their possessions (do they have a better offer somewhere?!). I’ll just print 2 extra rupees and that’s it. Actually it is not even needed to print new money. I get everything. At the end of the year, I get my 100 rupees back, I get the gold and mining equipment, and they still keep a debt of 1 rupee.

A loan can only be paid back if the borrower can somehow produce the same (!) commodity that is used in the loan, so that it can give back the loan plus the interest. If gold is lent, and the borrower cannot produce gold, he cannot give back the gold plus interest. The borrower will go bankrupt. If, on the other hand, chickens or sacks of grain are borrowed, these chickens or grain can be given back with interest.

Banks are the only ones that can produce money, therefore the borrowers will go bankrupt. Full stop.

To say it in another way. If we have a system where interest is charged on debt, no way whatsoever can all borrowers pay back the money. Somebody has to go bankrupt, unless the game of refinancing goes on forever. This game of state financing can go on forever as long as the economy is growing exponentially. That is, it is growing with constant percentage. The national debt, in terms of a percentage of the gross domestic product (GDP) remains constant, if we continuously refinance and increase the debt, as long as the economy GDP grows steadily too. The moment the economy stagnates, it is game over! Debt will rise quickly. Countries will go bankrupt. (Note that increasing debt is thus the result of a stagnating economy and not the other way around!).

The way the system decides who is going bankrupt, is decided by a feed-back system. The first one that seems to be in trouble has more difficulty refinancing its loans (”You have low credit rating. I fear you will not give me back my books. I want a better risk reward. It is now three books for every book borrowed. Take it or leave it! If you don’t like it, you can always decide to give me my books now and we’ll call it even”).

Thus, some countries will go bankrupt, unless they are allowed to let the debt grow infinitely. If not, sooner or later one of them will go bankrupt. In other words, the average interest rate is always zero. One way or another. If x% interest is charged, about x% go bankrupt. To be more precise, y% of the borrowed money is never returned, compensating for the (100 − y%) that do return it with x% profit. In a mathematical formula: (1 − y/100) × (1 + x/100) = 1, or y = 100x/(100 + x). This percentage goes bankrupt. For example, if 100% interest is charged, 50% goes bankrupt.

To take it to the extreme. If the market is cautious – full of responsible investors – and decides to lend money only to ‘stable’ countries, like Germany, which lately (times are changing indeed) has a very good credit rating from the financial speculators, even these ‘stable’ countries go bankrupt. That is, the weakest of these stable countries. If only money is borrowed to Germany, Germany goes bankrupt. Apart from the technical mathematical certainty that a country can only have a positive trade balance – essential in getting a good credit rating – if another country has a negative trade balance (the sum, being a balance, is always zero). Germany needs countries like Greece as much as it despises them.

Well, in fact, this is not true. A country does not – nay, it cannot – go bankrupt for money borrowing. Not if it is an isolated country with its own currency, being also the currency in which the money is borrowed. It can simply print money. That is because the money is their own currency based on their own economy!!!

Kōjin Karatani versus Moishe Postone. Architectonics of Capitalism.

Kōjin Karatani’s theory of different modes of intercourse criticizes architectonic metaphor thinking that the logic of mods of production in terms of base and superstructure without ceding grounds on the centrality of the critique of political economy. the obvious question is what remains of theory when there is a departure not from the objective towards the subjective, but rather the simultaneous constitution of the subjective and the objective dimensions of the social under capitalism. One way of addressing the dilemma is to take recourse to the lesson of commodity form, where capitalism begets a uniform mode of mediation rather than disparate. The language of modes of production according to Moishe Postone happens to be a transhistorical language allowing for a transhistorical epistemology to sneak in through the backdoor thus outlining the necessity of critical theory’s existence only in so far as the object of critique stays in existence. Karatani’s first critique concerns a crude base-superstructure concept, in which nation and nationalism are viewed merely as phenomena of the ideological superstructure, which could be overcome by reason (enlightenment) or would disappear together with the state. But the nation functions autonomously, independent of the state, and as the imaginative return of community or reciprocal mode of exchange A, it is egalitarian in nature. As is the case with universal religions, the nation thus holds a moment of protest, of opposition, of emancipatory imagination. The second critique concerns the conception of the proletariat, which Marxism reduced to the process of production, in which its labor force is turned into a commodity. Production (i.e., consumption of labor power) as a fundamental basis to gain and to increase surplus value remains unchanged. Nonetheless, according to Karatani surplus value is only achieved by selling commodities, in the process of circulation, which does not generate surplus value itself, but without which there cannot be any surplus value. Understanding the proletariat as producer-consumer opens up new possibilities for resistance against the system. In late capitalism, in which capital and company are often separated, workers (in the broadest sense of wage and salary earners) are usually not able to resist their dependency and inferiority in the production process. By contrast, however, in the site of consumption, capital is dependent on the worker as consumer. Whereas capital can thus control the proletariat in the production process and force them to work, it loses its power over them in the process of circulation. If, says Karatani, we would view consumers as workers in the site of circulation, consumer movements could be seen as proletariat movements. They can, for example, resort to the legal means of boycott, which capital is unable to resist directly. Karatani bases his critique of capitalism not on the perspectives of globalization, but rather on what he terms neo-imperialism meaning state-based attempt of capital to subject the entire world to its logic of exploitation, and thus any logic to overcoming the modern world system of capital-nation-state by means of a world revolution and its sublation in a system is to be possible by justice based on exchange. For Postone Capital generates a system characteristically by the opposition of abstract universality, the value form, and particularistic specificity, the use value dimension. It seems to me that rather than viewing a socialist or an emancipatory movement as the heirs to the Enlightenment, as the classic working class movement did, critical movements today should be striving for a new form of universalism that encompasses the particular, rather than existing in opposition to the particular. This will not be easy, because a good part of the Left today has swung to particularity rather than trying to and a new form of universalism. I think this is a fatal mistake.