Estudio del abandono en Ingeniería de Telecomunicaciones

In efficient markets prices change randomly. This is often misunderstood and can give rise to what Miller and Upton (2002) call the casino view of the stock market. In this view investors are gamblers whose buying and selling without apparent economic reason gives windfall profits to some and does random damage to others. The alleged casino nature of the stock market is often underlined by comparing graphs of stock price changes with graphs of random numbers, which are indistinguishable from each other. In this chapter we shall see that the opposite is true, that randomly changing prices are the hallmark of properly functioning markets. As we saw in Chapter 2, markets with properly organized price discovery processes aggregate all the information that buyers and sellers possess and that they reveal through their bidding and asking. As a result, prices in such markets will reflect all available information. By consequence, prices will only change if new information becomes available. But new information is random by nature, otherwise it would not be new. Hence, prices have to change randomly in efficient markets.

4.1 The concept of market efficiency

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Market efficiency, or the efficient market hypothesis, is a deceptively simple concept. But its consequences are profound and not at all easy to understand or accept. We shall look at the concept from different angles and review some of the empirical evidence.

4.1.1 Why prices change randomly

We can introduce market efficiency by having another look at the calculation of eco-nomic depreciation in the second chapter. The relevant data of the example project are reproduced in Table 4.1. Recall from the description that the project’s sales are highly cyclical, doubling from 125 in the first year to 250 in the second and then halving again to 125 in the third and last year. Also, a net working capital position is built up in the beginning and liquidated at the end of the project. As a result, the project’s expected cash flows fluctuate strongly but, in spite of that, the expected return is constant. We can take the argument one step further and redo the analysis in terms of expected project values.

To keep the scale of the project constant we assume that the cash flows that become avail-able from the project can be reinvested at the same rate of 25 per cent, which is also the opportunity cost of capital. The calculations are as follows.

At the end of the first year the remaining project value is 184.6 and a cash flow of 72.5 becomes available. Together, this gives a project value of:

184.6 + 72.5 = 257.1 96

97 4.1 The concept of market efficiency Table 4.1 Economic depreciation of a project

year 0 1 2 3

1 Cash inflows from project 72.5 134 121

2 PV cash inflows, year end 205.7 184.6 96.8 0

3 PV cash inflows, year begin 0 205.7 184.6 96.8 4 Economic depreciation (2 − 3) - −21.1 −87.8 −96.8

5 Profit from project (1 + 4) - 51.4 46.2 24.2

6 Return on investment (5/3) .25 .25 .25

This is the same as the future value of the project’s present value: 205.7 × 1.25 = 257.1.

At the end of the second year the remaining project value is 96.8, a cash flow of 134 becomes available and the value of last year’s reinvested cash flow is 72.5 × 1.25 = 90.6.

Together, this is:

96.8 + 134 + 72.5 × 1.25 = 321.4

the same as the future project value: 205.7 × 1.25²= 321.4. The same calculation applies to the final year where there is no remaining project value:

121 + (134 × 1.25) + (72.5 × 1.25²)= 401.7

which equals 205.7 × 1.25³= 401.7. If we call the value of the project P we can summarize this ‘present value in reverse’ calculation as:

P₀= E[Pt]

(1 + r)^t (4.1)

for each of the three t’s (t = 1, 2, 3) of the project’s life. We see that the expected future values, with cash flows reinvested and properly discounted at the opportunity cost of cap-ital, are constant and equal to the present value. The important point is that discounted future values are constant, even though the project’s sales, cash flows and net work-ing capital positions change drastically from year to year. However, all these changes are anticipated and properly accounted for, hence expected returns and future values are constants.

So what causes the project value and return to fluctuate randomly? That is the informa-tion not included in the calculainforma-tion because it was unknown and could not be anticipated when we made the calculations. Sales figures can turn out higher or lower than our best estimates at t = 0 and so can costs, inflation, taxation, etc. If these developments are truly new information, which means that they could not be anticipated, then they are random by nature. Hence, as time passes, news arrives and prices and returns adjust to the new information, which means that they change randomly. This intuition had long been rec-ognized in financial markets but it was first formulated in general terms in Samuelson’s (1965) classic proof that properly anticipated prices fluctuate randomly.

4.1.2 Formalization and operationalization

The efficiency of markets refers to the way they incorporate information into prices, or informational efficiency, which is more general than mean-variance efficiency that we saw

in portfolio theory. The most frequently used definition of market efficiency probably is Fama’s (1970): a market in which prices always ‘fully reflect’ available information is called ‘efficient’. This is a very general statement and it has to be made more precise to give it empirically testable content. Precision is obtained by defining what ‘fully reflect’

means and by specifying what the available information set contains.

Prices that fully reflect available information can be defined using the notion of excess return, which is the difference between the realized and the expected return:

ε_i,t+1= P_i,t+1− Pi,t

where ε is the excess return, P stands for price,  is the information set and i,t are subscripts for assets and time. Written in terms of returns the excess return is

ε_i,t+1= r_i,t+1− E[ r_i,t+1

_t] (4.3)

which corresponds to the two terms in the middle part of (4.2). The expected price or return can be the result of pricing models such as the CAPM or APT or any other model in which the information set t is fully utilized. However, if the latter is true, i.e. if the information set t is fully reflected in the expected price E[ P_i,t+1

_t], then it is impossible to use the same information set t to design trading systems or investment strategies that have expected excess returns larger than zero.

In practical terms this means that if t includes information about an extra return in t + 1, then that information will be reflected in Pt and not Pt+1. Using the project in the previous subsection as example again, suppose t contains the news that next year’s project return will be 35 per cent instead of 25 per cent. Then the price now will immediately increase with the present value of the excess return, or 10/1.25 = 8 per cent, so that the expected return over the next year remains the opportunity cost of capital of 25 per cent. Hence, εt = .08 and E[ εt+1| t] = 0. Reformulated as an old phrase: if one could be sure that a price will rise, it would have already risen.

With this definition of excess return, Fama (1970) formalizes (or models) market efficiency in three different ways:

1. Fair game model.

2. Martingale model.

3. Random walk model.

The fair game model directly specifies the expectation of the excess returns ε_i,t+1 regardless of the model that is used to produce expected prices or returns:

E[ εi,t+1



_t] = 0 (4.4)

This model says that in the long run the deviations from the expected returns are zero, which means that the information set t cannot be used to systematically generate pos-itive excess returns. We have met the fair game model before in the ‘error part’ of the return generating process in APT. Note that a game can also be fair if the expected return is negative; fairness only requires the expectations to be unbiased. Gambling games such as roulette and lotteries have, in fact, negative expected returns.

The martingale model specifies the expectation of excess returns by modelling the time series properties of returns or prices. If all information regarding an asset is already

99 4.1 The concept of market efficiency

reflected in its current price, as we have just seen, then the expected future price must be the present price times the expected return:

E[ P_i,t+1

which is the same as (4.1) in expanded notation. It means that the expected future price, properly discounted, is equal to the current price, which makes it a martingale. Formally, a variable is said to follow a dynamic process called a martingale with respect to  if the conditional expected future value of that variable, given information sequence , is equal to its current value. Note that the expected price is not a martingale, but the prop-erly discounted expected price. The price itself is expected to increase with the expected return and is, thus, a submartingale.¹By specifying the expected asset price or return, the martingale model indirectly specifies the expected excess return to be zero.

The fair game and martingale model of market efficiency only consider the expectation (first moment) of the excess profits. A more strict formalization of market efficiency is the random walk model, that specifies the entire distribution of excess returns. Successive price changes are said to follow a random walk if they are independently and identically distributed (iid), which includes all moments of the distribution. Random walks have the Markov property of memorylessness (so Alzheimer property could be a better name for it).² In economic terms, this means that past returns and patterns in past returns cannot be used to predict future returns. The random walk model requires the expected return to be constant and the excess return εt+1 not only to have zero expectation but also to have identical variance and higher moments in each future period, i.e. the probability density function f (ε_t+1)must be the same for all t. The expected return is called the drift of the random walk.

Having defined what ‘fully reflected’ means, Fama (1970) then specifies the contents of the available information set in three overlapping categories. Together, they give the following, widely used taxonomy of market efficiency:

• Weak form market efficiency occurs when all past price histories are fully reflected in current prices.

• Under the semi-strong form of market efficiency current prices fully reflect all publicly available information; in addition to price histories this includes financial statements, articles in the (financial) press, product-, industry- and macroeconomic data, etc.

• A market is strong form efficient if all information is reflected in current prices, including private and inside information.

Obviously, strong form efficiency implies also semi-strong form efficiency which, in turn, implies weak form efficiency.

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1 Martingales are usually defined with respect to their observation history. A variable follows a martingale if the conditional expected future value of that variable, given all past values, is equal to its current value. Formally: X is a martingale if E(X_t+1| X₀, ...X_t)= Xt.Similarly, X is a submartingale if E(X_t+1| X₀, ...X_t) > X_tand X is a supermartingale if E(X_t+1| X₀, ...X_t) < X_t.

2 A dynamic process has the Markov property if the conditional probability distribution of future states of the process only depends upon the current state, i.e. it is independent of the past states (the path of the process to the present state).

4.1.3 Empirical implications

With these specifications, market efficiency yields a number of testable predictions. The common denominator of these predictions is that in efficient markets returns cannot be systematically increased without also systematically increasing risk. This means that it is impossible to systematically earn excess returns or, popularly summarized, efficient mar-kets offer no ‘free lunch’. The predictions can be grouped in the following four categories, which are based on Haugen (1990):

1. There should be no autocorrelation in excess returns.

2. Investment strategies that are based on historical information should not consistently give positive excess returns.

3. Differences in excess returns between investment funds and (groups of) investors should be caused by chance and, hence, not be persistent.

4. Security prices should adjust to new information in an efficient way, i.e. quickly and without bias.

Autocorrelation (or serial correlation) is the correlation of return with itself one or more periods back: corr(rt,r_t−x) where x = 1, 2,.. etc. It is a formal expression of the idea that the excess return in this period says nothing about the return next period. As we have seen with the example project in the beginning of the chapter, all predictable cyclical movements in costs and revenues, etc. are already included in properly anticipated prices.

What remains are the responses to new (random) information, which are uncorrelated by nature. Technically, the absence of autocorrelation in excess returns follows directly from the definition of a random walk: independently distributed means no autocorrelation. The fair game and martingale model imply the absence of autocorrelation in the deviations from expected returns (i.e. in excess returns) but the expected returns themselves can be autocorrelated.

Many investment strategies are based on the idea that future returns can be predicted using information from the past. These strategies assume some regularity or recognizable patterns in prices and returns. Some strategies predict that price movements will persist (have ‘momentum’), others that they will reverse (contrarian) while still others base their predictions on patterns in prices plotted in graphs (chartists). The latter are printed on a daily basis in financial newspapers all around the world and are spread on an enormous scale. Yet if markets are efficient, all these strategies fail to consistently produce positive excess returns.

Selecting and managing a well-diversified portfolio requires some time and skills, and many investors prefer to outsource these activities to professionals. These services are provided by a large variety of mutual funds. Different types of funds operate under differ-ent restrictions and have differdiffer-ent purposes, resulting in differdiffer-ent investmdiffer-ent strategies.

Actively managed funds aim to outperform the market as a whole by using the exper-tise of the fund’s management, while passively managed funds seek to follow a market as closely as possible without the purpose of performing better. Similarly, some mutual funds may focus on long-term value increase and choose a risky portfolio, while pen-sion funds that have to pay penpen-sions every month probably prefer a more conservative strategy. If markets are efficient, differences in risk-adjusted performance between such

101 4.2 Empirical evidence

funds should be random, i.e. no fund should be able to systematically earn positive excess returns.

Finally, if new information becomes available, the response in prices should be quick and unbiased. There should be no predictable pattern after the news event that could be exploited by investors. Some possible patterns are schematically drawn in Figure 4.1.

The solid line depicts an efficient response to bad news: the price drops instantaneously to its new level. The upper dashed line shows underreaction: a slow reaction that takes several periods to materialize. The lower dashed line depicts an overreaction that is fol-lowed by a correction. If prices would systematically under- or overreact, one of the dashed patterns would occur and the market would be inefficient. In efficient markets, however, investors would exploit such patterns and their trading would eliminate them.

For instance, if investors would recognize a systematic slow reaction to bad news, they would short sell the security involved. This would drive the price down until it reaches the correct level. Similarly, if systematic overreaction could be recognized, investors would buy the security involved. This would drive the price up until the investment opportunity (free lunch) disappears.

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