Bullish or Bearish. Note Quote.

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The term spread refers to the difference in premiums between the purchase and sale of options. An option spread is the simultaneous purchase of one or more options contracts and sale of the equivalent number of options contracts, in a different series of the class of options. A spread could involve the same underlying: 

  •  Buying and selling calls, or 
  •  Buying and selling puts.

Combining puts and calls into groups of two or more makes it feasible to design derivatives with interesting payoff profiles. The profit and loss outcomes depend on the options used (puts or calls); positions taken (long or short); whether their strike prices are identical or different; and the similarity or difference of their exercise dates. Among directional positions are bullish vertical call spreads, bullish vertical put spreads, bearish vertical spreads, and bearish vertical put spreads. 

If the long position has a higher premium than the short position, this is known as a debit spread, and the investor will be required to deposit the difference in premiums. If the long position has a lower premium than the short position, this is a credit spread, and the investor will be allowed to withdraw the difference in premiums. The spread will be even if the premiums on each side results are the same. 

A potential loss in an option spread is determined by two factors: 

  • Strike price 
  • Expiration date 

If the strike price of the long call is greater than the strike price of the short call, or if the strike price of the long put is less than the strike price of the short put, a margin is required because adverse market moves can cause the short option to suffer a loss before the long option can show a profit.

A margin is also required if the long option expires before the short option. The reason is that once the long option expires, the trader holds an unhedged short position. A good way of looking at margin requirements is that they foretell potential loss. Here are, in a nutshell, the main option spreadings.

A calendar, horizontal, or time spread is the simultaneous purchase and sale of options of the same class with the same exercise prices but with different expiration dates. A vertical, or price or money, spread is the simultaneous purchase and sale of options of the same class with the same expiration date but with different exercise prices. A bull, or call, spread is a type of vertical spread that involves the purchase of the call option with the lower exercise price while selling the call option with the higher exercise price. The result is a debit transaction because the lower exercise price will have the higher premium.

  • The maximum risk is the net debit: the long option premium minus the short option premium. 
  • The maximum profit potential is the difference in the strike prices minus the net debit. 
  • The breakeven is equal to the lower strike price plus the net debit. 

A trader will typically buy a vertical bull call spread when he is mildly bullish. Essentially, he gives up unlimited profit potential in return for reducing his risk. In a vertical bull call spread, the trader is expecting the spread premium to widen because the lower strike price call comes into the money first. 

Vertical spreads are the more common of the direction strategies, and they may be bullish or bearish to reflect the holder’s view of market’s anticipated direction. Bullish vertical put spreads are a combination of a long put with a low strike, and a short put with a higher strike. Because the short position is struck closer to-the-money, this generates a premium credit. 

Bearish vertical call spreads are the inverse of bullish vertical call spreads. They are created by combining a short call with a low strike and a long call with a higher strike. Bearish vertical put spreads are the inverse of bullish vertical put spreads, generated by combining a short put with a low strike and a long put with a higher strike. This is a bearish position taken when a trader or investor expects the market to fall. 

The bull or sell put spread is a type of vertical spread involving the purchase of a put option with the lower exercise price and sale of a put option with the higher exercise price. Theoretically, this is the same action that a bull call spreader would take. The difference between a call spread and a put spread is that the net result will be a credit transaction because the higher exercise price will have the higher premium. 

  • The maximum risk is the difference in the strike prices minus the net credit. 
  • The maximum profit potential equals the net credit. 
  • The breakeven equals the higher strike price minus the net credit. 

The bear or sell call spread involves selling the call option with the lower exercise price and buying the call option with the higher exercise price. The net result is a credit transaction because the lower exercise price will have the higher premium.

A bear put spread (or buy spread) involves selling some of the put option with the lower exercise price and buying the put option with the higher exercise price. This is the same action that a bear call spreader would take. The difference between a call spread and a put spread, however, is that the net result will be a debit transaction because the higher exercise price will have the higher premium. 

  • The maximum risk is equal to the net debit. 
  • The maximum profit potential is the difference in the strike
    prices minus the net debit. 
  • The breakeven equals the higher strike price minus the net debit.

An investor or trader would buy a vertical bear put spread because he or she is mildly bearish, giving up an unlimited profit potential in return for a reduction in risk. In a vertical bear put spread, the trader is expecting the spread premium to widen because the higher strike price put comes into the money first. 

In conclusion, investors and traders who are bullish on the market will either buy a bull call spread or sell a bull put spread. But those who are bearish on the market will either buy a bear put spread or sell a bear call spread. When the investor pays more for the long option than she receives in premium for the short option, then the spread is a debit transaction. In contrast, when she receives more than she pays, the spread is a credit transaction. Credit spreads typically require a margin deposit. 

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Transmission of Eventual Lending Rates: MCLRs. Note Quote.

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Given that capital market instruments are not subject to MCLR/base rate regulations, the issuances of Commercial Paper/bonds reflect the current interest rates as banks are able to buy/subscribe new deposits reflecting extant interest rates, making transmission instantaneous. 

The fundamental challenge we have here is that there is no true floating rate liability structure for banks. One can argue that banks themselves will have to develop the floating rate deposit product, but customer response, given the complexity and uncertainty for the depositor, has been at best lukewarm. In an environment where the banking system is fighting multiple battles – asset quality, weak growth, challenges on transition to Ind AS accounting practice, rapid digitization leading to new competition from non-bank players, vulnerability in the legacy IT systems –  creating a mindset for floating rate deposits hardly appears to be a priority. 

In this context, it is clear that Marginal Costs of Funds Based Lending Rates (MCLRs) have largely come down in line with policy rates. MCLR is built on four components – marginal cost of funds, negative carry on account of cash reserve ratio (CRR), operating costs and tenor premium. Marginal cost of funds is the marginal cost of borrowing and return on net worth for banks. The operating cost includes cost of providing the loan product including cost of raising funds. Tenor premium arises from loan commitments with longer tenors. Some data indicate that while MCLR has indeed tracked policy rates (especially post-demonetization), as liquidity has been abundant, average leading rates have not yet reflected the fall in MCLR rates. This is simply because MCLR reset happens over a period of time depending on the benchmark MCLR used for sanctioning the loans. 

Before jumping the gun that this is a flaw in the structure as the benefit of lower interest rates is significantly lagging, the benefit will be to the borrower when the interest cycle turns. In fact, given that MCLR benchmarks vary from one month to one year, unlike base rate, banks are in a better situation to cut MCLRs, as not the entire book resets immediately. The stakeholders must therefore want for a few more months before concluding on the effectiveness of transmission on eventual lending rates. 

Infrastructure and Asian Infrastructure and Investment Bank. Some Scattered Thoughts.

What is Infrastructure?

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Infrastructure, though definitionally an elusive term, encompasses an economic standpoint consisting of large capital intensive natural monopolies. The term attains it heterogeneity by including physical structures of various types used by many industries as inputs to the production of goods and services. By this, it has come to mean either social, or economic infrastructure, wherein, in the former, are schools, hospitals etc, while in the latter are energy, water, transport, and digital communications, often considered essential ingredients in the success of the modern economy. Conceptually, infrastructure may affect aggregate output in two main ways: (i) directly, considering the sector contribution to GDP formation and as an additional input in the production process of other sectors; and (ii) indirectly, raising total factor productivity by reducing transaction and other costs thus allowing a more efficient use of conventional productive inputs. Infrastructure can be considered as a complementary factor for economic growth. How big is the contribution of infrastructure to aggregate economic performance? The answer is critical for many policy decisions – for example, to gauge the growth effects of fiscal interventions in the form of public investment changes, or to assess if public infrastructure investments can be self-financing.

Let us ponder on this a bit and begin with the question. Why is infrastructure even important? Extensive and efficient infrastructure is critical for ensuring the effective functioning of the economy, as it is an important factor determining the location of economic activity and the kinds of activities or sectors that can develop in a particular economy. Well-developed infrastructure reduces the effect of distance between regions, integrating the national market and connecting it at low cost to markets in other countries and regions. In addition, the quality and extensiveness of infrastructure networks significantly impact economic growth and affect income inequalities and poverty in a variety of ways. A well-developed transport and communications infrastructure network is a prerequisite for the access of less-developed communities to core economic activities and services. Effective modes of transport, including quality roads, railroads, ports, and air transport, enable entrepreneurs to get their goods and services to market in a secure and timely manner and facilitate the movement of workers to the most suitable jobs. Economies also depend on electricity supplies that are free of interruptions and shortages so that businesses and factories can work unimpeded. Finally, a solid and extensive communications network allows for a rapid and free flow of information, which increases overall economic efficiency by helping to ensure that businesses can communicate and decisions are made by economic actors taking into account all available relevant information. There is an existing correlation between infrastructure and economic activity through which the economic effects originate in the construction phase and rise during the usage phase. The construction phase is associated with the short-term effects and are a consequence of the decisions in the public sector that could affect macroeconomic variables: GDP, employment, public deficit, inflation, among others. The public investment expands the aggregate demand, yielding a boost to the employment, production and income. The macroeconomic effects at a medium and long term, associated with the utilization phase are related to the increase of productivity in the private sector and its effects over the territory. Both influence significantly in the competitiveness degree of the economy. In conclusion, investing in infrastructure constitutes one of the main mechanisms to increase income, employment, productivity and consequently, the competitiveness of an economy. Is this so? Well, thats what the economics textbook teaches us, and thus governments all over the world turn to infrastructure development as a lubricant to maintain current economic output at best and it can also be the basis for better industry which contributes to better economic output. Governments, thus necessitate realignment of countries’ infrastructure in tune with the changing nature of global political economy. Infrastructure security and stability concerns the quantity of spare capacity (or security of supply). Instead of acting on the efficiency frontier, infrastructure projects must operate with spare capacity to contribute to economic growth through ensuring reliable service provisions. Spare capacity is a necessary condition for a properly functioning system. To assure the level of spare capacity in the absence of storage and demand, the system needs to have excess supply. However, no rational profit-seeker will deliberately create conditions of excess supply, since it would produce a marginal cost lower than the average cost, and to circumnavigate this market failure, governments are invested with the responsibility of creating incentives ensuring securities of supply. This is seeding the substitutability of economics with financialization. 

So far, so good, but then, so what? This is where social analysts need to be incisive in unearthing facts from fiction and this faction is what constitutes the critique of development, a critique that is engineered against a foci on GDP-led growth model. This is to be done by asking uncomfortable questions to policy-makers, such as: What is the most efficient way to finance infrastructure spending? What are optimal infrastructure pricing, maintenance and investment policies? What have proven to be the respective strengths and weaknesses of the public and private sectors in infrastructure provision and management, and what shapes those strengths and weaknesses? What are the distributional consequences of infrastructure policies? How do political forces impact the efficiency of public sector provision? What framework deals best with monopoly providers of infrastructure? For developing countries, which have hitherto been plagued by weaker legal systems making regulation and enforcement more complicated, the fiscally weak position leads to higher borrowing costs. A most natural outcome is a systemic increase in financial speculation driven by deregulation transforming into financial assets. Contrary to common sense and what civil society assumes, financial markets are going deeper and deeper into the real economy as a response to the financial crisis, so that speculative capital is structurally being intertwined with productive capital changing the whole dynamics of infrastructure investment. The question then is, how far viable or sustainable are these financial interventions? Financialization produces effects which can create long-term trends (such as those on functional income distribution) but can also change across different periods of economic growth, slowdown and recession. Interpreting the implications of financialization for sustainability, therefore, requires a methodological diverse and empirical dual-track approach which combines different methods of investigations. Even times of prosperity, despite their fragile and vulnerable nature, can endure for several years before collapsing due to high levels of indebtedness, which in turn amplify the real effects of a financial crisis and hinder the economic growth. 

Role of Development Banks and AIIB

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Where do development banks fit into the schema as regards infrastructure investment? This question is a useful gamble in order to tackle AIIB, the new kid on the bloc. As the world struggles to find funds to meet the Sustainable Development Goals (SDGs), development banks could be instrumental in narrowing the gap. So, goes the logic promulgated by these banks. They can help to crowd-in the private sector and anchor private-public sector partnerships, particularly for infrastructure financing. However, misusing development banks can lead to fiscal risks and credit market distortions. To avoid these potential pitfalls, development banks need a well-defined mandate, operate without political influence, focus on addressing significant market failures, concentrate on areas where the private sector is not present, monitor and evaluate interventions and adjust as necessary to ensure impact, and, finally, be transparent and accountable. All of these are the ideals, which more often than not go the other way. China-led Asian Infrastructure Investment Bank (AIIB), despite having no track record still enjoys the highest ratings on par with the World Bank. This has fueled debates ranging from adding much-needed capital augmenting infrastructure to leniency in observing high standards of governance, and possibly ignoring environmental and societal impacts.

The AIIB was officially launched in Beijing on January 16th, 2016, with 57 founding members, including 37 in Asia and 20 non-regional countries. Being the largest shareholder of the AIIB, China has an initial subscription of $29.78 billion in authorized capital stock in the AIIB out of a total of $100 billion, and made a grant contribution of another $50 million to the AIIB Project Preparation Special Fund on January 16th, 2017. India is the second-largest shareholder, contributing $8.4 billion. Russia is the third-largest shareholder, contributing $6.5 billion, and Germany is the largest non-regional shareholder (also the fourth largest shareholder), contributing $4.5 billion. While being open to the participation of non-regional members, the AIIB is committed to and prioritizes the ownership of Asian members. This is reflected in the capital structure requirement and the requirements for the composition of Board of Governors in the AIIB’s Article of Agreement (AOA), which requires no less than 75 percent of the total subscribed capital stock to be held by regional members unless otherwise agreed by the Board of Governors by a Super Majority vote. The AOA also requires that 9 out of the AIIB’s 12 members be elected by the Governors representing regional members, and 3 representing non-regional members. The prioritization of Asian-members’ ownership of the AIIB does not necessarily mean that the AIIB’s investment is restricted only to Asia. According to its AOA, the AIIB aims to “improve infrastructure connectivity in Asia,” and it will invest in Asia and beyond as long as the investment is “concerned with economic development of the region.” The bank currently has 64 member states while another 20 are prospective members for a total of 84 approved members. 

The AIIB’s EU/OECD members potentially could have some positive influence over the institutional building and standard setting of the young institution. The European Commission has recognized that an EU presence in China-driven institutions would contribute to the adoption of best practices and fair, global standards. Adherence to such standards will be promoted by the AIIB entering into partnership with existing Multilateral Development Banks. It has also been argued that joining the AIIB would give the European countries access to the decision-making process within the AIIB, and may even allow the European countries to play a role in shaping the AIIB’s organizational structure. As an example of EU/OECD members’ activism in monitoring the AIIB’s funds allocation, both Denmark and the UK, who are AIIB’s OECD members, proposed that contributions to the AIIB would qualify as official development aid (ODA). After a thorough review of AIIB’s AOA, mandate, work plan and other available materials, the OECD’s Secretariat of the Development Assistance Committee (DAC) recommended including AIIB on the List under the category of “Regional development banks,” which means the OECD would recognize the AIIB as one of the ODA-eligible international organizations. Once approved, the Secretariat of DAC will be able to “monitor the future recipient breakdown of the AIIB’s borrowers through AIIB’s future Creditor Reporting System and thereby confirm that the actual share of funds going to countries on the DAC List of ODA Recipients is over 90%.” That is to say, if approved, there would be additional external monitor to make sure that the funds channeled through the AIIB to recipient countries are used properly. 

The AIIB’s initial total capital is $100 billion, equivalent to about 61 percent of the ADB’s initial total capital, 43 percent of the World Bank’s, 30 percent of the European Investment Bank’s (EIB), and more than twice of the European Bank for Reconstruction and Development’s (EBRD). Of this $100 billion initial capital, 20 percent is to be largely paid-in by 2019 and fully paid-in by 2024, and the remaining 80 percent is in callable capital. It needs to be noted that according to the AOA, payments for paid-in capital are due in five installments, with the exception of members designated as less developed countries, who may pay in ten installments. As of any moment, the snapshot of AIIB’s financial sheet includes total assets, members’ equities and liabilities, the last of which has negligible debt at the current stage since the AIIB has not issued any debenture or borrowed money from outside. However, to reduce the funding costs and to gain access to wider source of capital, the AIIB cannot rely solely on equity and has to issue debenture and take some leverage, particularly given that the AIIB intends to be a for-profit institution. In February 2017, the AIIB signed an International Swaps and Derivatives Association (ISDA) Master Agreement with the International Finance Corporation (IFC), which would facilitate local currency bond issuance in client countries. Moreover, AIIB intends to actively originate and lead transactions that mobilize private capital and make it a trusted partner for all parties involved in the transactions that the Bank leads. In the long term, the AIIB aims to be the repository of know-how and best practices in infrastructure finance. 

It is widely perceived that the AIIB is a tool of Chinese foreign policy, and that it is a vehicle for the implementation of the Belt and Road (One Belt, One Road) Initiative. During a meeting with global executives in June 2016, the AIIB President Jin Liqun clarified China’s position, saying the AIIB “was not created exclusively for this initiative,” and that the AIIB would “finance infrastructure projects in all emerging market economies even though they don’t belong to the Belt and Road Initiative.” It is worth pointing out that despite the efforts on trying to put some distance between the AIIB and the Belt and Road Initiative, there is still a broad perception that these two are closely related. Moreover, China has differentiated AIIB projects from its other foreign assistance projects by co-financing its initial projects with the preexisting MDBs. Co-financing, combined with European membership, will make it more likely this institution largely conforms to the international standards” and potentially will steer the AIIB away from becoming solely a tool of Chinese foreign policy. This supports China’s stated intention to complement existing MDBs rather than compete with them. It also means that the AIIB can depend on its partners, if they would allow so, for expertise on a wide range of policy and procedural issues as it develops its lending portfolio.

Although AIIB has attracted a great number of developing and developed countries to join as members and it has co-financed several projects with other MDBs, there is no guarantee for any easy success in the future. There are several formidable challenges for the young multilateral institution down the road. Not all the infrastructure investment needs in Asia is immediately bankable and ready for investors’ money. Capital, regardless it’s sovereign or private, will not flow in to any project without any proper preparation. Although Asia faces a huge infrastructure financing gap, there is a shortage of ‘shovel-ready’ bankable projects owing to the capacity limitations. The young AIIB lacks the talent and expertise to create investor-ready bankable projects, despite that it has created a Project Preparation Special Fund thanks to $50 million by China. The AIIB aims to raise money in global capital markets to invest in the improvement of trans-regional connectivity. However, infrastructure projects are not naturally attractive investment due to huge uncertainties throughout the entire life cycle as well as unjustified risk-profit balance. Getting a top-notch credit rating is just a start. The AIIB has to find innovative ways to improve the risk-adjusted profitability of its projects. This issue itself has been a big challenge for many MDBs who engage in infrastructure financing for a long time. It is uncertain if the AIIB could outperform the other much more matured MDBs to find a solution to tackle the profitability problem in infrastructure financing. The highest rating it has received from ratings agencies could pose a challenge in itself. The high rating not only endorses the bank’s high capital adequacy and robust liquidity position, but also validates the strong political will of AIIB’s members and the bank’s governance frameworks. A good rating will help the AIIB issue bonds at favorable rate and utilize capital markets to reduce its funding costs. This certainly will contribute to AIIB’s efforts to define itself as a for-profit infrastructure investment bank. However, there is no guarantee that the rating will hold forever. Many factors may impact the rating in the future, including but not limited to AIIB’s self-capital ratio, liquidity, management, yieldability, risk management ability, and its autonomy and independency from China’s influence. 

Game Theory and Finite Strategies: Nash Equilibrium Takes Quantum Computations to Optimality.

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Finite games of strategy, within the framework of noncooperative quantum game theory, can be approached from finite chain categories, where, by finite chain category, it is understood a category C(n;N) that is generated by n objects and N morphic chains, called primitive chains, linking the objects in a specific order, such that there is a single labelling. C(n;N) is, thus, generated by N primitive chains of the form:

x0 →f1 x1 →f2 x1 → … xn-1 →fn xn —– (1)

A finite chain category is interpreted as a finite game category as follows: to each morphism in a chain xi-1 →fi xi, there corresponds a strategy played by a player that occupies the position i, in this way, a chain corresponds to a sequence of strategic choices available to the players. A quantum formal theory, for a finite game category C(n;N), is defined as a formal structure such that each morphic fundament fi of the morphic relation xi-1 →fi xis a tuple of the form:

fi := (Hi, Pi, Pˆfi) —– (2)

where Hi is the i-th player’s Hilbert space, Pi is a complete set of projectors onto a basis that spans the Hilbert space, and Pˆfi ∈ Pi. This structure is interpreted as follows: from the strategic Hilbert space Hi, given the pure strategies’ projectors Pi, the player chooses to play Pˆfi .

From the morphic fundament (2), an assumption has to be made on composition in the finite category, we assume the following tensor product composition operation:

fj ◦ fi = fji —– (3)

fji = (Hji = Hj ⊗ Hi, Pji = Pj ⊗ Pi, Pˆfji = Pˆfj ⊗ Pˆfi) —– (4)

From here, a morphism for a game choice path could be introduced as:

x0 →fn…21 xn —– (5)

fn…21 = (HG = ⊗i=n1 Hi, PG = ⊗i=n1 Pi, Pˆ fn…21 = ⊗i=n1fi) —– (6)

in this way, the choices along the chain of players are completely encoded in the tensor product projectors Pˆfn…21. There are N = ∏i=1n dim(Hi) such morphisms, a number that coincides with the number of primitive chains in the category C(n;N).

Each projector can be addressed as a strategic marker of a game path, and leads to the matrix form of an Arrow-Debreu security, therefore, we call it game Arrow-Debreu projector. While, in traditional financial economics, the Arrow-Debreu securities pay one unit of numeraire per state of nature, in the present game setting, they pay one unit of payoff per game path at the beginning of the game, however this analogy may be taken it must be addressed with some care, since these are not securities, rather, they represent, projectively, strategic choice chains in the game, so that the price of a projector Pˆfn…21 (the Arrow-Debreu price) is the price of a strategic choice and, therefore, the result of the strategic evaluation of the game by the different players.

Now, let |Ψ⟩ be a ket vector in the game’s Hilbert space HG, such that:

|Ψ⟩ = ∑fn…21 ψ(fn…21)|(fn…21⟩ —– (7)

where ψ(fn…21) is the Arrow-Debreu price amplitude, with the condition:

fn…21 |ψ(fn…21)|2 = D —– (8)

for D > 0, then, the |ψ(fn…21)|corresponds to the Arrow-Debreu prices for the game path fn…21 and D is the discount factor in riskless borrowing, defining an economic scale for temporal connections between one unit of payoff now and one unit of payoff at the end of the game, such that one unit of payoff now can be capitalized to the end of the game (when the decision takes place) through a multiplication by 1/D, while one unit of payoff at the end of the game can be discounted to the beginning of the game through multiplication by D.

In this case, the unit operator, 1ˆ = ∑fn…21 Pˆfn…21 has a similar profile as that of a bond in standard financial economics, with ⟨Ψ|1ˆ|Ψ⟩ = D, on the other hand, the general payoff system, for each player, can be addressed from an operator expansion:

πiˆ = ∑fn…21 πi (fn…21) Pˆfn…21 —– (9)

where each weight πi(fn…21) corresponds to quantities associated with each Arrow-Debreu projector that can be interpreted as similar to the quantities of each Arrow-Debreu security for a general asset. Multiplying each weight by the corresponding Arrow-Debreu price, one obtains the payoff value for each alternative such that the total payoff for the player at the end of the game is given by:

⟨Ψ|1ˆ|Ψ⟩ = ∑fn…21 πi(fn…21) |ψ(fn…21)|2/D —– (10)

We can discount the total payoff to the beginning of the game using the discount factor D, leading to the present value payoff for the player:

PVi = D ⟨Ψ|πiˆ|Ψ⟩ = D ∑fn…21 π (fn…21) |ψ(fn…21)|2/D —– (11)

, where π (fn…21) represents quantities, while the ratio |ψ(fn…21)|2/D represents the future value at the decision moment of the quantum Arrow- Debreu prices (capitalized quantum Arrow-Debreu prices). Introducing the ket

|Q⟩ ∈ HG, such that:

|Q⟩ = 1/√D |Ψ⟩ —– (12)

then, |Q⟩ is a normalized ket for which the price amplitudes are expressed in terms of their future value. Replacing in (11), we have:

PVi = D ⟨Q|πˆi|Q⟩ —– (13)

In the quantum game setting, the capitalized Arrow-Debreu price amplitudes ⟨fn…21|Q⟩ become quantum strategic configurations, resulting from the strategic cognition of the players with respect to the game. Given |Q⟩, each player’s strategic valuation of each pure strategy can be obtained by introducing the projector chains:

Cˆfi = ∑fn…i+1fi-1…1 Pˆfn…i+1 ⊗ Pˆfi ⊗ Pˆfi-1…1 —– (14)

with ∑fi Cˆfi = 1ˆ. For each alternative choice of the player i, the chain sums over all of the other choice paths for the rest of the players, such chains are called coarse-grained chains in the decoherent histories approach to quantum mechanics. Following this approach, one may introduce the pricing functional from the expression for the decoherence functional:

D (fi, gi : |Q⟩) = ⟨Q| Cˆfi Cgi|Q⟩  —– (15)

we, then have, for each player

D (fi, gi : |Q⟩) = 0, ∀ fi ≠ gi —– (16)

this is the usual quantum mechanics’ condition for an aditivity of measure (also known as decoherence condition), which means that the capitalized prices for two different alternative choices of player i are additive. Then, we can work with the pricing functional D(fi, fi :|Q⟩) as giving, for each player an Arrow-Debreu capitalized price associated with the pure strategy, expressed by fi. Given that (16) is satisfied, each player’s quantum Arrow-Debreu pricing matrix, defined analogously to the decoherence matrix from the decoherent histories approach, is a diagonal matrix and can be expanded as a linear combination of the projectors for each player’s pure strategies as follows:

Di (|Q⟩) = ∑fi D(fi, f: |Q⟩) Pˆfi —– (17)

which has the mathematical expression of a mixed strategy. Thus, each player chooses from all of the possible quantum computations, the one that maximizes the present value payoff function with all the other strategies held fixed, which is in agreement with Nash.

Probability Space Intertwines Random Walks – Thought of the Day 144.0

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agByQMany deliberations of stochasticity start with “let (Ω, F, P) be a probability space”. One can actually follow such discussions without having the slightest idea what Ω is and who lives inside. So, what is “Ω, F, P” and why do we need it? Indeed, for many users of probability and statistics, a random variable X is synonymous with its probability distribution μX and all computations such as sums, expectations, etc., done on random variables amount to analytical operations such as integrations, Fourier transforms, convolutions, etc., done on their distributions. For defining such operations, you do not need a probability space. Isn’t this all there is to it?

One can in fact compute quite a lot of things without using probability spaces in an essential way. However the notions of probability space and random variable are central in modern probability theory so it is important to understand why and when these concepts are relevant.

From a modelling perspective, the starting point is a set of observations taking values in some set E (think for instance of numerical measurement, E = R) for which we would like to build a stochastic model. We would like to represent such observations x1, . . . , xn as samples drawn from a random variable X defined on some probability space (Ω, F, P). It is important to see that the only natural ingredient here is the set E where the random variables will take their values: the set of events Ω is not given a priori and there are many different ways to construct a probability space (Ω, F, P) for modelling the same set of observations.

Sometimes it is natural to identify Ω with E, i.e., to identify the randomness ω with its observed effect. For example if we consider the outcome of a dice rolling experiment as an integer-valued random variable X, we can define the set of events to be precisely the set of possible outcomes: Ω = {1, 2, 3, 4, 5, 6}. In this case, X(ω) = ω: the outcome of the randomness is identified with the randomness itself. This choice of Ω is called the canonical space for the random variable X. In this case the random variable X is simply the identity map X(ω) = ω and the probability measure P is formally the same as the distribution of X. Note that here X is a one-to-one map: given the outcome of X one knows which scenario has happened so any other random variable Y is completely determined by the observation of X. Therefore using the canonical construction for the random variable X, we cannot define, on the same probability space, another random variable which is independent of X: X will be the sole source of randomness for all other variables in the model. This also show that, although the canonical construction is the simplest way to construct a probability space for representing a given random variable, it forces us to identify this particular random variable with the “source of randomness” in the model. Therefore when we want to deal with models with a sufficiently rich structure, we need to distinguish Ω – the set of scenarios of randomness – from E, the set of values of our random variables.

Let us give an example where it is natural to distinguish the source of randomness from the random variable itself. For instance, if one is modelling the market value of a stock at some date T in the future as a random variable S1, one may consider that the stock value is affected by many factors such as external news, market supply and demand, economic indicators, etc., summed up in some abstract variable ω, which may not even have a numerical representation: it corresponds to a scenario for the future evolution of the market. S1(ω) is then the stock value if the market scenario which occurs is given by ω. If the only interesting quantity in the model is the stock price then one can always label the scenario ω by the value of the stock price S1(ω), which amounts to identifying all scenarios where the stock S1 takes the same value and using the canonical construction. However if one considers a richer model where there are now other stocks S2, S3, . . . involved, it is more natural to distinguish the scenario ω from the random variables S1(ω), S2(ω),… whose values are observed in these scenarios but may not completely pin them down: knowing S1(ω), S2(ω),… one does not necessarily know which scenario has happened. In this way one reserves the possibility of adding more random variables later on without changing the probability space.

These have the following important consequence: the probabilistic description of a random variable X can be reduced to the knowledge of its distribution μX only in the case where the random variable X is the only source of randomness. In this case, a stochastic model can be built using a canonical construction for X. In all other cases – as soon as we are concerned with a second random variable which is not a deterministic function of X – the underlying probability measure P contains more information on X than just its distribution. In particular, it contains all the information about the dependence of the random variable X with respect to all other random variables in the model: specifying P means specifying the joint distributions of all random variables constructed on Ω. For instance, knowing the distributions μX, μY of two variables X, Y does not allow to compute their covariance or joint moments. Only in the case where all random variables involved are mutually independent can one reduce all computations to operations on their distributions. This is the case covered in most introductory texts on probability, which explains why one can go quite far, for example in the study of random walks, without formalizing the notion of probability space.

Global Significance of Chinese Investments. My Deliberations in Mumbai (04/03/2018)

Legends:

What are fitted values in statistics?

The values for an output variable that have been predicted by a model fitted to a set of data. a statistical is generally an equation, the graph of which includes or approximates a majority of data points in a given data set. Fitted values are generated by extending the model of past known data points in order to predict unknown values. These are also called predicted values.

What are outliers in statistics?

These are observation points that are distant from other observations and may arise due to variability in the measurement  or it may indicate experimental errors. These may also arise due to heavy tailed distribution.

What is LBS (Locational Banking statistics)?

The locational banking statistics gather quarterly data on international financial claims and liabilities of bank offices in the reporting countries. Total positions are broken down by currency, by sector (bank and non-bank), by country of residence of the counterparty, and by nationality of reporting banks. Both domestically-owned and foreign-owned banking offices in the reporting countries record their positions on a gross (unconsolidated) basis, including those vis-à-vis own affiliates in other countries. This is consistent with the residency principle of national accounts, balance of payments and external debt statistics.

What is CEIC?

Census and Economic Information Centre

What are spillover effects?

These refer to the impact that seemingly unrelated events in one nation can have on the economies of other nations. since 2009, China has emerged a major source of spillover effects. This is because Chinese manufacturers have driven much of the global commodity demand growth since 2000. With China now being the second largest economy in the world, the number of countries that experience spillover effects from a Chinese slowdown is significant. China slowing down has a palpable impact on worldwide trade in metals, energy, grains and other commodities.

How does China deal with its Non-Performing Assets?

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China adopted a four-point strategy to address the problems. The first was to reduce risks by strengthening banks and spearheading reforms of the state-owned enterprises (SOEs) by reducing their level of debt. The Chinese ensured that the nationalized banks were strengthened by raising disclosure standards across the board.

The second important measure was enacting laws that allowed the creation of asset management companies, equity participation and most importantly, asset-based securitization. The “securitization” approach is being taken by the Chinese to handle even their current NPA issue and is reportedly being piloted by a handful of large banks with specific emphasis on domestic investors. According to the International Monetary Fund (IMF), this is a prudent and preferred strategy since it gets assets off the balance sheets quickly and allows banks to receive cash which could be used for lending.

The third key measure that the Chinese took was to ensure that the government had the financial loss of debt “discounted” and debt equity swaps were allowed in case a growth opportunity existed. The term “debt-equity swap” (or “debt-equity conversion”) means the conversion of a heavily indebted or financially distressed company’s debt into equity or the acquisition by a company’s creditors of shares in that company paid for by the value of their loans to the company. Or, to put it more simply, debt-equity swaps transfer bank loans from the liabilities section of company balance sheets to common stock or additional paid-in capital in the shareholders’ equity section.

Let us imagine a company, as on the left-hand side of the below figure, with assets of 500, bank loans of 300, miscellaneous debt of 200, common stock of 50 and a carry-forward loss of 50. By converting 100 of its debt into equity (transferring 50 to common stock and 50 to additional paid-in capital), thereby improving the balance sheet position and depleting additional paid-in capital (or using the net income from the following year), as on the right-hand side of the figure, the company escapes insolvency. The former creditors become shareholders, suddenly acquiring 50% of the voting shares and control of the company.

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The first benefit that results from this is the improvement in the company’s finances produced by the reduction in debt. The second benefit (from the change in control) is that the creditors become committed to reorganizing the company, and the scope for moral hazard by the management is limited. Another benefit is one peculiar to equity: a return (i.e., repayment) in the form of an increase in enterprise value in the future. In other words, the fact that the creditors stand to make a return on their original investment if the reorganization is successful and the value of the business rises means that, like the debtor company, they have more to gain from this than from simply writing off their loans. If the reorganization is not successful, the equity may, of course, prove worthless.

The fourth measure they took was producing incentives like tax breaks, exemption from administrative fees and transparent evaluations norms. These strategic measures ensured the Chinese were on top of the NPA issue in the early 2000s, when it was far larger than it is today. The noteworthy thing is that they were indeed successful in reducing NPAs. How is this relevant to India and how can we address the NPA issue more effectively?

For now, capital controls and the paying down of foreign currency loans imply that there are few channels through which a foreign-induced debt sell-off could trigger a collapse in asset prices. Despite concerns in 2016 over capital outflow, China’s foreign exchange reserves have stabilised.

But there is a long-term cost. China is now more vulnerable to capital outflow. Errors and omissions on its national accounts remain large, suggesting persistent unrecorded capital outflows. This loss of capital should act as a salutary reminder to those who believe that China can take the lead on globalisation or provide the investment or currency business to fuel things like a post-Brexit economy.

The Chinese government’s focus on debt management will mean tighter controls on speculative international investments. It will also provide a stern test of China’s centrally planned financial system for the foreseeable future.

Global Significance of Chinese investments