Financial Markets and Institutions

1. The Financial System

a) Definition of the Financial System

• The financial system is a structure that facilitates the circulation of capital to finance economic activities, especially business investments.
• It enables the matching of capital supply and demand, as well as their allocation and reallocation.

b) Key Functions

• Capital allocation: Directing funds from savers (suppliers) to borrowers (users).
• Liquidity provision: Allowing assets to be easily converted into cash.
• Risk management: Distributing and managing financial risks.
• Information processing: Providing information to help economic agents make decisions.

c) Components of the Financial System

d) Types of Finance

• Disintermediated Finance (Direct Finance): Capital flows directly between savers and borrowers via financial markets.
• Intermediated Finance (Indirect Finance): Capital flows through financial intermediaries like banks.

The financial system is essential for economic growth by efficiently channeling funds to their most productive uses.

e) Summary Table: Financial System Roles and Components

f) Important Notes

• The financial system supports investment and economic development by connecting those who have surplus funds with those who need funds.
• It operates through a complex network of institutions, markets, instruments, and regulations.
• Understanding its structure is crucial for grasping how economies function and grow.

1. Interest and Time Value of Money

a) Time Value of Money (TVM)

• Definition: Money available today is worth more than the same amount in the future due to its potential earning capacity.
• Key idea: A dollar today can be invested to earn interest, increasing its future value.

b) Interest

• Interest: The cost of borrowing money or the return on invested funds.
• Types of interest:
  • Simple interest: Interest earned only on the original principal.
  • Compound interest: Interest earned on the principal plus accumulated interest.

c) Simple Interest

• Formula for interest earned over $n$ periods:

  $$I = P \times r \times n$$

  where:

  • $P$ = principal (initial amount)
  • $r$ = interest rate per period
  • $n$ = number of periods

• Future value (FV) with simple interest:

  $$FV = P + I = P (1 + r \times n)$$

d) Compound Interest

• Interest earned on principal and previously earned interest.
• Future value after $n$ periods: $$FV = P (1 + r)^n$$
• Present value (PV) of a future amount $FV$: $$PV = \frac{FV}{(1 + r)^n}$$

e) Discounting

• Process of finding the present value of a future sum.
• Reflects the time value of money and risk.

f) Effective Interest Rate (EIR)

• Accounts for compounding within a year.
• Formula: $$\text{EIR} = \left(1 + \frac{r}{m}\right)^m - 1$$ where:
  • $r$ = nominal annual rate
  • $m$ = number of compounding periods per year

g) Annuities

• Series of equal payments at regular intervals.
• Present value of an annuity (payments of $C$ for $n$ periods at rate $r$): $$PV = C \times \frac{1 - (1 + r)^{-n}}{r}$$
• Future value of an annuity: $$FV = C \times \frac{(1 + r)^n - 1}{r}$$

h) Perpetuities

• Annuities with infinite payments.
• Present value of a perpetuity with payment $C$ and rate $r$: $$PV = \frac{C}{r}$$

Key takeaway: The value of money changes over time due to interest; understanding how to calculate present and future values is essential for financial decision-making.

1. Financial Assets and Markets

• Financial assets: Contracts or securities that generate future income but do not directly increase the holder's satisfaction.
• Some goods have a mixed nature (e.g., houses: both consumption and investment).
• Capital allocation occurs through the exchange of financial assets.

2. Temporality and Risk in Finance

• Agents have cash flows spread over time with different investment horizons.
• Future cash flows are uncertain and risky.
• Agents differ in their risk attitudes.
• The financial system must enable:
  • Matching of short-term and long-term capital.
  • Risk transfer between agents.

3. The Role of Interest

• Interest accounts for intertemporal preferences and risk.
• A financial flow is a capital amount received by an agent at a specific date.
• Flows are algebraic amounts: payments are negative, receipts positive.
• Flows at different dates cannot be simply summed.
• Cash flow diagram: graphical representation of flows over time.

To remember: Financial assets enable the transfer of capital and risk over time, with interest reflecting the cost of time and uncertainty.

1. Time Value of Money and Cash Flows

• Cash flows received at different dates cannot be simply added; timing matters.
• A cash flow diagram represents these flows along a timeline.
• Agents prefer to receive money sooner rather than later (preference for present consumption).
• Conversely, they prefer to pay later rather than now.

2. Preference for Present Consumption

• Given a choice between €1000 now or €1000 in one month, agents prefer €1000 now.
• To accept postponing receipt, agents require compensation (e.g., €1010 in one month instead of €1000 now).
• This compensation reflects the interest demanded for deferring consumption.

3. Interest

• Interest ($I$) is the amount demanded by an agent to postpone receiving a cash flow to a later date.
• It depends on:
  • The time horizon until payment,
  • The risk associated with receiving the payment,
  • Sometimes the amount of the cash flow.
• Interest is usually expressed as an interest rate ($R$).

4. Cash Flow Patterns: Loan and Borrowing

• Borrowing can be seen as a negative investment.

5. Value Accrued and Interest Rate

• The accrued value of a cash flow is the original amount plus interest earned.
• Interest rates can be presented and calculated in various ways:
  • Annual or monthly rates,
  • Simple or compound interest.

To postpone receiving money, agents require interest that compensates for time, risk, and amount.

1. Financial Instruments: Interest and Accrued Value

Accrued value of a cash flow is the sum of the initial amount plus the interest earned over time.

2. Interest Types and Calculations

• Interest (I) on a principal amount $S$ at rate $R$ is:
  $I = R \times S$

• Accrued value (VA) after one period:
  $VA = S + I = S + R \times S = S(1 + R)$

3. Example: Simple Interest

• Loan €100, repay €106 in 1 year.
• Interest earned: €6
• Interest rate:
  $R = \frac{6}{100} = 6\% \text{ per year}$

4. Interest Over Multiple Periods

• For 2 years at 6%, simple interest:
  $VA = 100 + 6 + 6 = 112 \text{ €}$

• Compound interest:
  $VA = 100 \times (1 + 0.06)^2 = 112.36 \text{ €}$

5. Simple vs Compound Interest

6. Compound Interest Principle

• Interest earned is reinvested each period at the same rate.
• Value at time $t$ for initial flow $F_0$:
  $VA = F_0 (1 + R)^t$

7. Simple Interest Principle

• Interest is calculated only on the initial principal.
• Value at time $t$:
  $VA = F_0 (1 + t \times R)$
• $t$ can be fractional (e.g., days, months).

8. Practical Examples

1. Placing €1200 for 27 days at 2% per 27 days (simple interest):
   $VA = 1200 \times (1 + 0.02) = 1224 \text{ €}$

2. Borrowing €1200 at 1.5% per month for 3 months:

To remember: Compound interest assumes reinvestment of interest, leading to exponential growth, while simple interest grows linearly over time.

1. Interest Calculation

• Future Value (FV) with compound interest after $n$ periods at rate $r$ per period:

  $$FV = PV \times (1 + r)^n$$

• Example: Placing €1200 for 3 months at 1.5% per month:

  $$FV = 1200 \times (1 + 0.015)^3 = 1254.81\,€$$

• Simple interest formula for $n$ periods:

  $$FV = PV \times (1 + r \times n)$$

• Example: Placing €1000 for 6 months at 4% annual rate:

  • Using simple interest (6 months = 0.5 year):

    $$FV = 1000 \times (1 + 0.04 \times 0.5) = 1020\,€$$

  • Using compound interest:

    $$FV = 1000 \times (1 + 0.04)^{0.5} = 1019.80\,€$$

• Key point: Always express the duration in the same period as the interest rate.

2. Comparison of Simple vs Compound Interest

At short term or low rates, simple interest approximates compound interest well; over longer periods, compound interest yields higher returns.

3. Annualized Interest Rate

• Definition: The interest rate expressed on a yearly basis, accounting for the number of compounding periods per year.

• To convert a periodic rate $r_p$ to annualized rate $r_a$:

  $$r_a = r_p \times \text{number of periods per year}$$

• Example: Monthly rate of 0.5% corresponds to an annualized rate of:

  $$0.5\% \times 12 = 6\% \text{ per year}$$

• To use the rate for calculations, convert back to the periodic rate by dividing the annualized rate by the number of periods.

4. Multiple Payments and Cash Flow Sequences

• Financial instruments may involve multiple interest payments at different dates.

• To compare different sequences of cash flows, use discounting to bring all cash flows to a common date (usually today).

5. Present Value (PV) of Future Cash Flows

• Definition: The amount that must be invested today at rate $R$ to obtain a future cash flow.

• Present value of a single future cash flow $F_t$ received at time $t$:

  $$PV = \frac{F_t}{(1 + R)^t}$$

• For multiple cash flows $F_1, F_2, ..., F_n$ at times $1, 2, ..., n$:

  $$PV = \sum_{t=1}^n \frac{F_t}{(1 + R)^t}$$

The present value allows comparison of different cash flow sequences by expressing them in today's monetary terms.

1. Present Value (PV) and Discounting

• Present Value (PV) of a future cash flow is the amount that must be invested today to obtain that future cash flow.
• For a cash flow $F_1$ received at date 1, the present value at date 0 is: $$V = \frac{F_1}{1+R}$$ where $R$ is the discount rate.
• For a cash flow $F_t$ received at date $t$, the present value is: $$V = \frac{F_t}{(1+R)^t} = F_t \cdot (1+R)^{-t}$$
• The present value of a sequence of cash flows is the sum of the present values of each individual cash flow: $$V = \sum_{t=0}^T \frac{F_t}{(1+R)^t}$$

2. Key Concepts in Discounting

• The process of calculating present value is called discounting.
• The rate $R$ used in discounting is called the discount rate or interest rate.
• Discounting generally assumes compound interest.
• Discounting does not change the sign of cash flows.
• The internal rate of return (IRR) or yield rate of a sequence of cash flows is the discount rate $\tau$ that makes the present value zero: $$\sum_{t=0}^T \frac{F_t}{(1+\tau)^t} = 0$$

3. Interpretation of Cash Flow Sequences and IRR

• When choosing between investments, prefer the one with the highest IRR.
• When choosing between borrowings, prefer the one with the lowest IRR.

4. Examples of Present Value and IRR

• Given a discount rate of 3% per period, the present value of the cash flow sequence: $$-100 + \frac{5}{1.03} + \frac{105}{(1.03)^2} = 3.83 \text{ €}$$
• For another sequence: $$-102 + \frac{10}{1.03} + \frac{100}{(1.03)^2} = 1.97 \text{ €}$$
• The IRR $\tau$ satisfies: $$-100 + \frac{5}{1+\tau} + \frac{105}{(1+\tau)^2} = 0 \implies \tau = 5\%$$ $$-102 + \frac{10}{1+\tau} + \frac{100}{(1+\tau)^2} = 0 \implies \tau = 4.04\%$$

The internal rate of return (IRR) is the discount rate that makes the net present value of a sequence of cash flows equal to zero.

1. Finance Direct vs Finance Intermédiée

• Finance directe (désintermédiée) : Les agents à capacité de financement et ceux à besoins de financement échangent directement entre eux, sans intermédiaire. C’est la finance de marché (ex : émission de titres, crédit non bancaire).
• Finance indirecte (intermédiée) : L’échange de capitaux se fait via un intermédiaire financier (ex : banque, institutions d’épargne contractuelles, entreprises d’investissement).

2. Trois modes d’obtention de capitaux

3. Structure des systèmes financiers

• Opposition classique entre orientation banque et orientation marché.
• Le développement financier repose sur la complémentarité des banques et des marchés financiers (titres et contrats).
• Les banques jouent un rôle central dans la finance intermédiée, facilitant le transfert des fonds entre agents à capacité et à besoin de financement.

À retenir : La finance directe implique un contact direct entre prêteurs et emprunteurs, tandis que la finance intermédiée utilise des institutions financières comme intermédiaires essentiels.

1. Financial Systems: Banks and Markets Interconnection

• Since the 1980s, capital markets have developed significantly, but this has not reduced the importance of banks.
• The key change lies in the structure of financial systems and the activities of intermediaries, who now rely more on markets.
• Financial systems combine both bank-based and market-based financing, which are increasingly intertwined.

2. Bank-Based vs Market-Based Financial Systems

3. Intermediation Rates and Measures

• Intermediation rate measures the share of external financing that is intermediated (via banks or financial intermediaries).
• Definitions:
  • Strict intermediation = Bank credit only.
  • Broad intermediation = Bank credit + securities purchased by financial intermediaries.
• Formula:

$$\text{Intermediation Rate} = \frac{\text{Intermediated Financing}}{\text{External Financing}} \times 100\%$$

• Across countries (France, Germany, UK), intermediation rates vary but remain significant, with differences between strict and broad definitions.

4. Sectoral Differences in Financing

• Public administrations have increased their use of market financing, especially via debt securities.
• Enterprises show heterogeneous reliance on bank credit vs market financing depending on the country.

Key point: Despite the rise of capital markets since the 1980s, bank intermediation remains crucial, with financial systems combining both bank and market financing in varying proportions across countries and sectors.

1. Green Finance

a) Importance of Credit for Enterprises

• Credit remains a key external financing mode for companies.
• External financing by credit varies by country:
  • Less than 50% in France, Belgium, Finland.
  • More than 66% in Austria, Germany, Italy, Denmark.
• High share of intermediated financing in Germany and the UK.

b) Regulation of Financial Markets

Financial markets must be regulated to:

c) Key Regulatory Actors

• States: Enact laws (e.g., Financial Security Laws in France).
• Supervisory Authorities:
  • AMF (Autorité des marchés financiers): Oversees financial markets.
  • ACPR (Autorité de contrôle prudentiel et de résolution): Supervises banks and insurance companies.

d) Six Core Functions of the Financial System

1. Transfer resources across time and space: Facilitate moving funds between savers and borrowers.
2. Risk management: Provide instruments like insurance contracts and derivatives.
3. Settlement and clearing mechanisms: Enable smooth transaction processing.
4. Pooling and subdividing ownership: Allow shared ownership and risk (e.g., co-ownership of assets).
5. Information provision: Deliver data on asset values and prices.
6. Incentive alignment: Solve principal-agent problems by aligning interests (e.g., investment fund shares to managers).

The financial system’s regulation ensures stability, investor protection, and market efficiency by harmonizing rules and preventing abuses like insider trading.