International banking and capital markets

IBCM

1 - Review of core concepts

Risk preferences

Economic behaviour can be modelled by a u lity func on re ec ng individual preferences.

For a wealth level W, individuals are described by a u lity func on, U(W), which summarises preferences

over wealth (W).

Principle of non-sa a on: Individuals prefer more wealth to less, expressed as U (W) >0.

Types of risk preferences

Risk Neutral:

Indifferent between a certain expected value of a gamble and the gamble itself.

U lity func on is linear in wealth: U (W) = 0. Curve is a straight line. U lity increases propor onally with

wealth (no diminishing returns). Only cares about expected value, not risk.

U[E(W)] = EU(W).

Risk Averse:

Prefers a certain amount to a gamble with the same expected value.

U lity func on is concave in wealth: U (W) <0. U lity increases with wealth, but each extra dollar gives less

and less sa sfac on. Prefer safety, diminishing marginal u lity.

Jensen’s Inequality: U[E(W)] >E[U(W)].

Demands a risk premium for exposure to risk.

Risk Preferring:

Prefers the riskier of two outcomes having the same expected value.

U lity func on is convex in wealth: U (W) >0. U lity increases faster as wealth increases. Likes risk,

increasing marginal u lity.

Jensen’s Inequality: U[E(W)] <E[U(W)].

Di erent types of u lity func ons Risk aversion and certainty equivalent

Certainty equivalent

The certainty equivalent (CE) of a gamble is the sure payment that makes a risk-averse individual indifferent

between that sure payment and the gamble. For a risk-averse individual, CE <E(W). The difference E(W)−CE

is the risk premium.

Diversi ca on represents a method to reduce risk by holding numerous risky assets. For diversi ca on to

be effec ve, asset returns must not be perfectly posi vely correlated.

Idiosyncra c Risk: stems from forces speci c to an asset; it is diversi able.

Systema c Risk: arises from correla on to economy-wide phenomena; it is not diversi able. 1

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Types of risks Blue -> No ma er how many numbers of stocks we

include in our por olio, the risk is the same

Green -> increasing the number of stocks the risk is

0.

Blue and green lines do not exist in the reality

The red represents the reality: increasing the

number or types of stocks, the risk decrease. It is

true, but up to a certain point: there is a part theta

we cannot diversify.

Por olio variance Impact of correla on on diversi ca on

Limits to diversi ca on

Not all risks are diversi able. Costs of administra on for holding too many securi es. Marginal bene ts of

diversi ca on decline rapidly a er a rela vely small number of securi es. Cross-sec onal reusability of

informa on can diminish the incen ve to diversify,

leading to specialisa on.

Riskless arbitrage (slides)

Arbitrage is the simultaneous purchase and sale of iden cal goods or securi es trading at different prices.

Riskless arbitrage is pro t without risk and without investment.

Exploita on of arbitrage opportuni es eliminates price

dispari es quickly. Implica on: Prices of related securi es cannot

be determined independently in equilibrium. This is crucial for 2

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pricing deriva ve securi es like op ons.

Market e ciency

An efficient capital market is one where every security’s price equals its “true” economic value. Prices

incorporate all available informa on fully and immediately. Implies that price changes in an efficient market

must be random, as prices only change with unpredictable new informa on.

Forms of market efficiency

Weak-Form Efficiency:

Prices impound all historical informa on.

E(Pt+1|Pt) = E(Pt+1|Pt,...,P0).

You cannot forecast future prices be er using historical prices than using just the current price.

Semistrong-Form Efficiency:

Prices impound all publicly available informa on.

Includes historical informa on; therefore, a semistrong-form efficient market is always weak-form efficient.

Strong-Form Efficiency:

Prices impound all informa on, including that possessed by insiders.

Few economists believe markets are strong-form efficient.

Market completeness

Uncertainty is o en modelled in terms of possible states of nature (θ). For simplicity, suppose θ can take

only integer vales from 1 to some arbitrary number N. For economic efficiency is important to evaluate the

number of different nancial securi es available rela ve to the number of state of nature. Two nancial

securi es are “different” if they do not have iden cal payoffs in every state.

Primi ve state-con ngent claims (or Arrow-Debreu securi es): Securi es that pay 1 euro if a par cular

state occurs and nothing otherwise.

Example

Consider three possible states of nature and two securi es, which can be regarded as

shares issued by two different companies. The payoffs of these securi es in each state are

as follows: Consider an individual who owns 10% of security 1 and 20% of

security 2.

In state 1 we have 10% of security 1 (payo 10) and 20% of security security 2 (payo 15) -> 0.10 x 10 + 0.20

x 15 = 4

In state 2 we have 10% of security 1 (payo 20) and 20% of security security 2 (payo 0) -> 0.10 x 20 + 0.20

x 0 = 2

In state 3 we have 10% of security 1 (payo 15) and 20% of security security 2 (payo 25) -> 0.10 x 15 + 0.20

x 25 = 6,5

Complete vs. incomplete markets

Complete market:

There are as many (linearly independent) Arrow-Debreu securi es as there are states of

An individual can achieve any desired distribu on of income, subject to their budget constraint.

Allows determina on of market prices for new securi es.

Incomplete market:

Fewer Arrow-Debreu securi es than states of nature. 3

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Limits the ability of transactors to manage uncertainty (e.g., insure against con ngencies).

Informa on asymmetries

Asymmetric informa on occurs when one party in a transac on has more or be er informa on than the

counterparty. It can lead to market failures. There are two types:

Adverse selec on arises before a transac on (ex ante), when one party lacks informa on and ends up

facing riskier counterparts. In banking, for example, high interest rates may a ract mainly risky borrowers,

lowering expected returns.

Moral hazard occurs a er a transac on (ex post) when one party is incen vized to act against the other’s

interest, such as a borrower using loan funds for riskier projects than agreed.

Adverse selec on is a phenomenon where asymmetric informa on leads to the systema c withdraw of

higher-quality goods/agents from the market. In extreme cases, it can cause market breakdown. Key

assump on for market breakdown: ra onal expecta ons, uniformed buyers ra onally an cipate what

informed sellers will do.

Example

In the used-car market, differences in vehicle quality arise from how carefully owners maintain cars that

were originally iden cal. Owners have be er informa on about the quality of their cars than poten al

buyers. Assume there are three possible quality levels, q1 >q2 >q3 = 0.

A car with quality q3 is a lemon, worth nothing if its condi on is known. A car with quality q2 is worth= C5,

while one with quality q1 is worth= C10.

All agents are risk neutral: buyers will not pay more than the expected value of a car, and sellers will not

accept less than the car’s true value. Sellers know their car’s quality, but buyers cannot observe it directly.

Instead, buyers believe there is a 0.4 probability that a car is of quality q1, a 0.2 probability it is of quality

q2, and a 0.4 probability it is of quality q3. What outcome will result in the market? No cars will be bought

or sold.

Quality 10 probability 0.4

Quality 5 probability 0.2

Quality 0 probability 0.4

5 is the average, expected value. At the price of 5, q1 exits from the market because the seller will not

accept less than car’s true value (5<10). Now we have 1/3 (0.2/(0.2+0.4) probability for 5 and 2/3

probability for 0. The new price is 1.67 (average). The q2 disappears from the markets and it remains only 0,

so market breakdowns.

Signalling is a mechanisms deployed by market par cipants to prevent market failure due to asymmetric

informa on. A signal is informa on conveyed by an informed agent to an uninformed agent. For a signal to

be useful, it must be incen ve compa ble (IC). IC requires that the cost of signaling be nega vely correlated

with quality (less costly for higher quality to emit the signal).

Examples: Warran es for used cars, dividends as a signal of future cash ows.

Example

Consider a car market in which vehicles differ in quality, and these quality differences are associated with

varying probabili es of engine failure over a speci ed period. The economic value of each vehicle type is

represented as= C0,= C5, and= C10, respec vely.

A vehicle of quality q1is subject to a 0.1 probability of failure, a vehicle of quality q2 faces a 0.5 probability,

and a vehicle of quality q3 fails with certainty. Within this framework, what role can warran es play in

shaping market outcomes?

Q1 0.1 q2 0.5 q3 1 -> probability of failure

P1 = 10 + 0.1 warranty1 4

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P2 = 5 + 0.5 warranty2

The seller of q2 can mimic q1 so we have for q2 the price of q1, which is 10, but the probability for q2 is 0.5.

The lie payo is P1 - 0.5w1 (w1 because we are pretending to be q1). The true payo is P2 - 0.5w2.

IC: the guarantee, in order to work, must be incen ve compa ble, which is nega ve correla on.

IC -> P1 - 0.5w1 < 5. We have to subs tute P1 in the equa on. 10 + 0.10 w1 -0.5 w1= 5

w1 = 12.5 -> w1 >uguale di 12.5. Minimal guarente that prevents the mimic, q2 to pretend to be q1.

Considering w1 = 12,5 -> P1 = 11.25

Types of signals

Nondissipa ve Signals: costless in equilibrium. The cost of the signal is a transfer payment (e.g., higher

price paid for a car with a good warranty).

Dissipa ve Signals: involve a net loss due to signalling (e.g., seller absorbs a cost for which they are not fully

compensated).

Example: Seller reimburses repair costs, but the value of the repair is less than its cost to the seller.

Moral hazard describes situa ons where the incen ves of a principal (e.g., employer, property owner) and

an agent (e.g., employee, user) diverge. A ra onal agent maximizes their own expected u lity, poten ally at

the principal’s expense. The principal must design a contract to align incen ves.

Condi on for moral hazard

Moral hazard arises if:

1. the agent’s ac ons (that affect the nal outcome) cannot be costlessly observed by the principal

2. there is some noise (exogenous uncertainty) that masks the agent’s ac on in the nal outcome.

Examples:

Auto insurance (deduc bles, coinsurance). Manager’s investment choices (shareholders vs. bondholders).

Not the same as fraud; o en involves legal but self-interested behaviour.

Time consistency is an issue that arises in moral hazard and adverse selec on models. A contract or policy is

me-inconsistent if, a er an agent has taken an ac on, the principal has an incen ve to renego ate the

contract in a way that undermines the original incen ves.

Example: A principal might want to renego ate a performance-based wage to a xed wage a er effort is

expended.

The principal is risk neutral, while the agent is risk averse.

Renego a on proofness

To avoid me inconsistency, contracts need to be renego a on-proof. This means both par es to the

contract should not have an incen ve to renego ate them once they are in effect.

Example: Loan covenants that specify interest rate penal es for minor viola ons, but require full repayment

only for serious breaches. Time inconsistency can also arise in adverse selec on se ngs (for example

screening borrowing), leading to no equilibrium.

Liquidity represents the ease with which an asset can be converted into cash.

Three dimensions:

1. ∆: The difference between the asset’s maximum value (to current owner) and its value if sold.

2. t: Time it takes to sell the asset at an acceptable value.

3. c: Cost involved in selling the asset.

Liquidity is decreasing in ∆, t, and c. The most liquid asset is cash. Assets with high asymmetric informa on

and agency problems tend to have low liquidity. 5

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Systemic risk is a risk that affects the en re system, and is therefore not diversi able. Similar to systema c

risk, but typically refers to risks affec ng the whole nancial system (e.g., system-wide liquidity shortage).

Tradi onally viewed as exogenous. Seemingly idiosyncra c risks can spread and become systemic due to the

interconnectedness of nancial ins tu ons and markets (e.g., subprime mortgage crisis).

Disagreement

In mainstream economics, it’s o en assumed that agents with the same informa on will eventually agree.

However, formal theories suggest that agents may con nue to disagree even when receiving the same

informa on signals. This can occur if the probability distribu on of the underlying economic variable is

nonsta onary (changes over me). This concept helps understand phenomena like nancial innova on

triggering crises.

Mark-to-market accoun ng

Prac ce of revising the value of an asset or liability to re ect its es mated (or actual) market value, rather

than its historical cost (book value). Controversial: Some blame mark-to-market accoun ng for exacerba ng

nancial crises by leading to “ re sales” and downward price spirals.

2 - Financial intermedia on and bank ac vi es

Flow of funds through the nancial system Direct channel for nancial intermediaries and

indirect channel for nancial markets. They are

connected because we can access nancial markets

through nancial intermediaries.

The nancial system

The main role of nancial intermediaries and nancial markets is to provide a mechanism for transferring

and alloca ng funds to their most produc ve opportuni es.

A bank is a nancial intermediary that provides loans and deposits, as well as payment services. Banks act

as intermediaries between savers (surplus units) and borrowers (de cit units): banks collect surplus funds

from savers and allocate them to those (both people and companies) with a de cit of funds (borrowers).

They channel funds and increase economic efficiency by promo ng a be er alloca on of resources. This

process is known as indirect nance, in contrast to direct nance where borrowers do not need banks to

intermediate their funds: borrowers obtain funds directly from lenders in nancial markets. A nancial

claim is a claim to the payment of a future sum of money and/or a periodic payment of money. More

generally, a nancial claim carries an obliga on on the issuer to pay interest periodically and to redeem the

claim at a stated value in one of three ways: on demand; a er giving a stated period of no ce; on a de nite

date or within a range of dates.

Link between nancial system and economic growth

Suppose we have an economy in which there are four people who own produc ve resources:

Mary has some money saved at her house; Peter owns a piece of land and some apple seeds, which he can

use to plant and grow trees that will yield apples; Paul has a farm where he naturally produces fer lizer;

Sally owns some farm equipment that is useful for farming the land. Without a nancial system, Peter

would be limited to plan ng whatever apple trees he can using his own seeds and labour, but without any 6

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fer lizer or farm equipment. Now suppose that the economy has a nancial system in place which includes

a bank and nancial market where nancial securi es are traded.

The nature of nancial intermedia on

Lenders’ requirements: minimising risk, including default risk (the borrower not mee ng repayment

obliga ons); minimising cost; liquidity (valuing assets that are easily converted to cash without loss)

Borrowers’ requirements: funds at a speci c date; funds for a speci c, preferably long, period of me; funds

at the lowest possible cost.

The majority of lenders want to lend their assets for short periods of me and for the highest possible

return. In contrast the majority of borrowers demand liabili es that are cheap and for long periods.

These incompa ble needs create barriers to direct nancing, which banks help to bridge.

What is a bank and what does it do?

De ni on of the legislator -> A bank is an ins tu on whose principal opera ons consist of gran ng loans

and accep ng deposits from the public. Contemporary banking theory classi es banking func ons into four

main categories:

1. offering access to payment system: historically, banks have played a dual role in the management of cash

payments: currency exchange and deposit management. Originally, deposited funds were not lent out, but

kept securely. In managing the payment system, banks provided a more reliable and efficient mechanism for

se ling debtor and creditor posi ons than the physical transporta on of coins and banknotes

2. transforming assets: banks bridge the gap between the needs of lenders and borrowers by performing

three types of assets transforma on:

- size transforma on: banks pool small deposits from savers and convert them into larger loans, leveraging

economies of scale;

- maturity transforma on: banks transform short-term deposits into longer-term loans, a prac ce called

borrowing short and lending long (banks mismatch their assets and liabili es -> liquidity risk problems);

- risk transforma on: banks reduce loan risk by diversifying investments, pooling risks, and screening

borrowers;

3. managing risk: the main types of risks associated with banking ac vi es are: 7

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