Análisis de sensibilidad

Financial markets facilitate, simplify and increase the possibilities to choose. We will first illustrate their role in a simple theoretical setting, using Fisher’s (1930) model. We will then have a brief look at how the complex system of financial markets and institutions works in practice.

2.5.1 Fisher’s model

The effect of financial markets on decision making is very elegantly illustrated in Fisher’s (1930) intertemporal analysis of optimal investment and consumption choices. It pro-vides, in very simple terms, two major results. It shows why the decision by individuals to consume or save can be separated from the decision by firms to invest. It also demonstrates why net present value is the correct criterion for investment decisions. The following gives an informal presentation of the model; a formal treatment can be found in MacMinn (2005).

Financial markets

The setting of Fisher’s analysis is very simple. It involves decisions regarding two periods without uncertainty, so that the problem can be graphically represented in two dimen-sions. The purpose of the analysis is to investigate how individuals allocate their budgets to consumption, saving and investments in the two periods. The analysis is built up grad-ually, first without, then with a financial market and finally with productive investment opportunities.

Assuming a world without financial markets looks absurdly restricted, but it is a real life situation for many employees in bureaucracies. At the time of writing, scientists at the institute where the author is employed receive a yearly budget of 10K, not enough to buy a good computer.¹² The budget cannot be saved (deposited at a bank), hoarded (put as cash in a drawer) or borrowed against. Without possibility to ‘move’ consumption of the budget over time, the scientists have no other option than to spend the whole budget every year. This situation is shown for two periods in the picture on the left hand side of Figure 2.5, where the entire budget space consists of the single point with coordinates (10, 10). Also depicted are the indifference curves of two persons with different time prefer-ences. Both curves are tangent to the budget point, reflecting the choice that maximizes utility. Individual 2 can be thought of as a scientist in need of a computer and, hence, with a preference for spending in period 0: her indifference curve is tilted towards the x-axis.

Individual 1 has less need of spending in period 0: his indifference curve is tilted towards the y-axis. However, without a financial market both spend 10K, not less.

The effect of a financial market is illustrated in the picture on the right hand side of Figure 2.5. A financial market gives the opportunity to borrow and lend and, hence, to move consumption back and forth in time. For simplicity we assume a perfect finan-cial market. In perfect markets there are no transaction costs and all assets are infinitely and costlessly divisible. All investors have simultaneous access to the same information and they can unrestrictedly borrow and lend at the same rate. In short: all deals can be

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12 I do not dare say in which currency.

done free of charge. Assuming an interest rate of 10 per cent, the single budget point is extended into the budget line between 21K and 19K. The slope of the budget line is -(1+r), where r is the interest rate. Borrowing against the entire next period budget, the maximum spending this period is the t₀budget of 10 plus the present value of the t₁ bud-get: 10 + 10/1.1 = 19. Of course, this means no spending next period. Depositing all of this period’s budget at the bank, maximum spending next period is 10 × 1.1 + 10 = 21.

The introduction of a financial market makes nobody worse off and most people better off. The two individuals in Figure 2.5 are better off: they can now attain an indifference curve that is farther from the origin and, thus, represents a higher utility. This is a classic example of economic decision making: people maximize their utility given the budget restriction. Individual 2 can now buy her computer by borrowing ±2.5K against next period’s budget and spend 12.5K this period. Individual 1 can deposit the unused part of the period 1 budget at the bank. Only an individual who happens to prefer spending 10K in each period is not better off with a financial market.

Budget t = 0 Budget

t = 1

10 10

Ind.1

Ind.2

Budget t = 0 Budget

t = 1

10 19

10 21

Ind.1

Ind.2

Figure 2.5 Consumption choices in a budget space

Productive investment opportunities

We now introduce the possibility to invest a part of this period’s budget in productive projects, first without a financial market. Figure 2.6 depicts the available investment opportunities.

The picture on the left-hand side shows the opportunities as discrete projects, ordered left to right from bad to good. For each project, the horizontal distance along the x-axis shows how much budget must be invested in t = 0 and the vertical distance along the y-axis shows the payoff in t = 1. The bad projects on the left require a large investment and give a low payoff. The project on the extreme left, for example, may require an investment of 1 in t = 0 and pay off only 0.2 in t = 1, a loss of 80 per cent. The good projects on the right require a small investment and give a large payoff. The project on the extreme right may require an investment of 1 in t = 0 and pay off 2.5 in t = 1, a profit of 150 per cent.

They are accumulated (stacked on top of each other) from right to left in the picture on

37 2.5 The role of financial markets

Budget t = 0 Budget

t = 1

Budget t = 0 Budget

t = 1

Figure 2.6 Investment opportunities and their continuous approximation

Budget t = 0 Budget

t = 1

bad projects

good projects

Budget t = 0 Budget

t = 1

Ind.1

Ind.2

Figure 2.7 Investment opportunities and choices

the right-hand side. The picture also shows the cumulative, continuous approximation that corresponds to a large number of projects, each of which is small relative to the total.

Figure 2.7 summarizes the investment opportunities in the picture on the left-hand side.

The continuous line connecting all investment opportunities is called the investment fron-tier along which choices are made. The picture on the right-hand side of Figure 2.7 shows how much our two individuals choose to invest in the absence of a financial market. Indi-vidual 2, who has a greater preference for consumption now (she needs money), wants to invest little. Individual 1, who has money to spare, wants to invest more. So different investors have different ideas about which projects should be taken into production. This looks trivial but it has important consequences. It means that the attractiveness of a project depends on who wants to carry it out, i.e. it matters ‘where the money comes from’.

This, in turn, means that there is no general rule saying which projects are worthwhile.

If a professional manager is hired to make the investment decisions on behalf of our indi-viduals, the manager has to know the individual’s time preferences to make an optimal decision. The introduction of a financial market remedies all this.

In the presence of a financial market, choices are made in two steps. First, the opti-mal investment plan is chosen. For greedy investors, this is the plan that maximizes the present value of the total (t₀+ t₁) budget. In graphical terms, it is the plan that gives the highest attainable budget line. That plan is the point where the new budget line is tangential to the investment frontier, i.e. the point where the marginal rate of return on investments equals the interest rate. The alternative to productive investments is deposit-ing money at a bank, so the interest rate is the opportunity cost of capital, the return that is given up to make the investments. This is depicted in the graph on the left-hand side of Figure 2.8. In investment terms, the production optimum is reached by selecting all projects with a positive NPV (discounted at the opportunity cost of capital, i.e. the interest rate). Those are the projects to the right of the optimum, that earn more than the interest rate. Investments to the left of the optimal point earn less than the interest rate, so that they are unprofitable. In the second step, the optimal budget is spent by allocating it optimally to consumption over time. The preferred consumption patterns are reached by borrowing and lending in the financial market. This allows our individuals 1 and 2 to jump to higher indifference curves, as the graph on the left-hand side of Figure 2.8 shows.

Budget t = 0 19 21

Budget t = 1

Ind.1

Ind.2 productive optimum

b₀₂b₀₁

Budget t = 0 Budget

t = 1

b₁₂ b₁₁

Ind.1

Ind.2

Figure 2.8 Production and consumption choices with a financial market

The introduction of a financial market has some far-reaching consequences. As before, nobody is made worse off by the introduction and most are better off. Further, everybody agrees on the optimal investment plan, because everybody prefers more budget to less and nobody needs productive investments to allocate consumption over time. This means that it does not matter ‘where the money comes from’, only ‘where it goes to’. Consequently, the investment and consumption decisions can be separated; this is called Fisher separa-tion. Under Fisher separation, professionals hired to manage investments do not have to

39 2.5 The role of financial markets

know the individual preferences of their clients to make optimal decisions. Instead, they can use objective market data such as the returns on investment projects and the interest rate. Moreover, they can use a simple rule to manage investments: maximize net present value, which is equivalent to selecting all projects with a positive NPV. Note that the NPV rule is not imposed or assumed, it is a consequence of the assumption of greedy investors.

But the NPV rule does ensure an optimal allocation of investments: it includes all projects that earn more than the opportunity cost of capital.

How does individual 2 reach her optimal consumption pattern of b₀₁in t₀and b₁₁in t₁, as depicted in the graph on the right-hand side of Figure 2.8? This is done with the following steps:

• At t₀, borrow the maximum against the t₁ budget; this gives a total t₀ budget of 19 (where the investment frontier reaches the x-axis).

• Of this 19, invest 19 − b₀₂in productive assets, leaving b₀₂− 0 for spending in t₀.

• The productive investments pay off b₁₂− 0 in t₁; borrow against a part of this return, b₁₂− b₁₁. That part has a present value of b₀₁− b₀₂.

• This gives the optimal spending pattern:

• in t₀: (b₀₂− 0) + (b₀₁− b₀₂)= b₀₁

• in t₁: (b₁₂− 0) − (b₁₂− b₁₁)= b₁₁ 2.5.2 The financial system in practice

Real world financial markets have many more functions than just allowing people to bor-row and lend, as in the simple Fisher model. The modern financial system of markets and institutions facilitates trade in a wide range of financial assets, such as stocks, bonds, currencies, insurance, and derivatives like options and futures. That system is vast and complex and it has an immense infrastructure to carry out the enormous number of finan-cial transactions that take place every day. In this section we will have a brief look at what the system does and how it does it; a more detailed description can be found in the spe-cialized literature, e.g. Kohn (2004), Mishkin and Eakins (2009), Kidwell et al. (2008), and Saunders and Cornett (2011).

Functions of financial markets and institutions

Financial markets perform their functions in cooperation with a variety of financial insti-tutions, intermediaries, service companies and regulators. For example, stock brokers and investment banks channel buyers and sellers to financial markets, clearing houses and regulators see to it that transactions are properly effectuated, and financial intermediaries such as commercial banks partly perform the same functions as financial markets. We will meet these institutions and companies later on; we begin by looking at the multitude of interrelated functions that the system of financial markets and institutions performs in modern economies. We summarize them in four main categories.

1. The system facilitates the flow of funds from units with a money surplus to units with a money deficit, and the flow of claims (securities) in the opposite direction.

2. It determines prices (facilitates price discovery).

3. It provides marketability and liquidity.

4. It maintains a system for settling payments and clearing.

A major function of the financial system is to facilitate the flow of funds from units with more money than investment opportunities (money surplus units) to units that have more investment opportunities than money (money deficit units). The surplus and deficit units can be people, companies and governments, both at home and abroad. In return for their money, the surplus units receive financial assets such as stocks, bonds, other securi-ties or simply a bank account. An efficient flow of funds through the system has important benefits. It enables the allocation of capital to the most productive uses, e.g. by allowing companies to buy machines before they have sold the products made with them. Since most business investments are risky, this also involves an efficient allocation of risk (or risk transfer), particularly by spreading it among a large number of investors. An effi-cient flow of funds also gives people the opportunity to buy houses when they are young and to save money for retirement. More generally, it enables people, companies and gov-ernments to make their time patterns of consumption and investment independent of the time patterns of their incomes. The flow of funds can take many different routes; the most important distinction is between direct and indirect finance. Direct finance occurs when a money surplus unit buys securities straight from the issuer on a private or public mar-ket. A typical example is a so-called private placement, in which a company sells a large number of its shares to e.g. a pension fund. Direct financial markets are mostly whole-sale markets where each transaction involves many securities and large sums of money.

However, the main flow of funds follows the indirect route and does not pass through a financial market. Instead, it flows from surplus to deficit units through financial interme-diaries. A common example is savings that people and companies deposit at commercial banks and that the banks use to make loans to other people and companies. The flows of funds through the financial system are schematically illustrated in Figure 2.9.

= Funds = Securities

Financial Intermediaries Clearing House

Market Financial Buyers

= Surplus

Units

Sellers

= Deficit

Units

Figure 2.9 Flows of funds through the financial system

The second main function of the financial system is to determine prices of financial assets such as stocks, government and commercial bonds, derivatives, etc. In more gen-eral terms, financial markets determine the time value of money and the market price of risk. Market prices are found where demand meets supply and in financial markets this

‘matchmaking’ is organized as a continuous process in which buyers and sellers interact

41 2.5 The role of financial markets

to determine the price of the specific quantity of financial assets at hand. The process by which buyers and sellers arrive at market prices is called price discovery. Financial markets facilitate this process by bringing many buyers and sellers together, setting rules to regulate the process and making it transparent. If the process is properly organized, the resulting market prices will reflect all the relevant information that buyers and sellers possess. Market participants reveal their private information through their bidding and asking in the market and by adjusting their bid and ask prices in reaction to other par-ticipants’ actions. The price discovery process picks up all these private bits and pieces of information and expresses them in market prices. This phenomenon is called informa-tion aggregainforma-tionand it is an important function of financial markets. It generates public information about the value of investments and resources such as oil or gold. Markets in which prices reflect all available information are called efficient markets and they have important consequences for financial decision making. We will look at market efficiency in a later chapter.

Financial assets such as shares can have ownership and voting rights attached to them, so financial markets are also markets for ownership and control. Trading in ownership allows investors to diversify, i.e. to spread their ownership over many different compa-nies. It also creates the possibility of capital market intervention. By buying a majority of a company’s shares, outsiders can take control and restructure companies e.g. through takeovers and mergers or, conversely, through spin-offs and split-offs. The threat of cap-ital market intervention, which will cost them their jobs, gives corporate managers an important incentive to keep their companies profitable and efficient.

The third main function of the financial system is to provide marketability and liquidity.

Marketability measures how easy it is to buy and sell a financial asset; liquidity measures how much value is lost in the transaction. Good marketability and liquidity make financial markets attractive because they give investors the flexibility to convert financial assets back to cash if and when they want to. It also gives them the possibility to make the length of their investment period independent of the maturity of financial assets. For example, they can buy a ten-year bond and sell it after two years, and they can buy a one-year bond and when it is paid back re-invest the money in another one-year bond, etc. Financial markets can increase their liquidity primarily by attracting large numbers of buyers and sellers, but also by keeping their transaction and information costs low.

The last but not the least main function of financial markets and institutions is to provide a system for settling payments and clearing. The origins of interbank payment systems go back more than two centuries, to the days when bank clerks in London started meeting in coffee houses to exchange cheques. Instead of one clerk walking from bank A to bank B to collect a £100 cheque and another clerk walking from bank B to bank A to collect an £80 cheque, they would meet half way, exchange cheques and settle only the

£20 difference. Today, that job is done by the huge electronic infrastructure that banks and other financial institutions have created to deal with the enormous number of payments that take place every day.

When financial assets are traded, the transaction not only involves payment, but also the transfer of securities from the seller to the buyer. The tasks of settling payment and trans-ferring securities can be outsourced to specialized financial service companies known as clearing houses (or clearing companies). When a securities deal is agreed upon, the

clearing house takes over the clearing (or execution) of the deal by positioning itself between the buyer and the seller, as Figure 2.9 depicts. Buyers pay to the clearing house and sellers receive payment from it. The clearing house takes over the counterparty risk, i.e. the risk that the other party defaults its obligations. Buyers receive their securities and sellers get paid, even if their trading partner fails to deliver or pay. All exchanges have engaged clearing houses; they stimulate trade by making it safe.

Taxonomy of financial markets

There are many different financial markets; they can be classified according to the charac-teristics of the traded securities and the organization of the market and the price discovery process. Describing the various segments of financial markets gives a good impression of

There are many different financial markets; they can be classified according to the charac-teristics of the traded securities and the organization of the market and the price discovery process. Describing the various segments of financial markets gives a good impression of