# Morden theory of finance

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### Introduction

Investors would not invest if no money, profit, was to be made. All investors try to maximise returns and this involves managing the wealth effectively. But to do this there is a need to have some techniques of analysis to interpret stock market movements and decide which shares are worth investing in. However not all investors have the ability to do this and as a result most of them just decide on a limited knowledge. Others go an extra mile of using stockbrokers.

The CAPM defines systematic risk as beta. Beta measures the covariance between the returns on a particular share with the returns on the market as a whole. The sensitivity of a share to the general market movements is indicated by the Beta value of that share (Arnold, 1998:296). Alternatively Beta is the relationship of a company's returns relative to the market.

The old theory of CAPM makes the assumption that the CAPM line represents a long term model of assets fluctuations and risks versus returns. However, it is shown that the historical data does not take into consideration influential changes in the economy such as new technology. Therefore, from year to year, data can considerably change. The new CAPM theory has evolved to make different assumptions.

First, CAPM states that investors have homogenous expectations and investments horizons. Secondly, it does not take into consideration transactions and information costs (as we know however, transactions and most importantly information costs can be very expensive even though some information costs can be included in the transaction costs if done through traders).

### Discussion

The CAPM model assumes that all investors have access to the same amount of information which is not true considering that they either don't have the time or the will to go into a deep research as the optimal portfolio theory would suggest in order to maximizing profit. Although transactions and information costs along with equal access to information are important considerations, they can be eliminated for the model because they do not represent extremely changing variables for pricing an asset. Bram (2000, p1543) sates that the most important variable to include in the CAPM is the investors' expectations and investment horizons. This makes sense because as different individuals we have different needs and risks tolerance that can greatly affect the way we view an asset and the way we are going to create our portfolio.

Capital Asset Pricing Model (CAPM) rewards an investor only for systematic risk, that portion of the risk that cannot be eliminated by diversification over the market. In comparison, the expected utility theory approach evaluates the price for each risk transfer in isolation from all other transactions. Systematic risk is the risk of the movements of the market as a whole and is measured by the beta of a share. It is also referred to as market risk, non-diversifiable risk, non-specific on unavoidable risk. This type of risk represents how a share's returns are affected by factors such as business cycles, government policy and changes in interest rates (Watson and Head, 2004:p,243).

However, the effect of risk diversification in securities markets is similar except that the returns on securities tend to be correlated with one another, thereby limiting an investor's ability to reduce risk. Author provides a discussion of optimizing portfolio selection in security markets based on the objective of minimizing the investor's variance while simultaneously achieving a selected expected return.

In addition to reducing risk, diversification may also have an effect on price. Based on the principle that risk determines return, the reduction in risk that an insurer can achieve through diversification should be expected to lead to a reduction in the price it requires for a transfer of risk. For securities markets, an explicit measurement of the impact of risk diversification on price is provided by the CAPM pricing formula, which determines the expected return for a security based on its systematic risk and the expected return for the market as a whole.

The author explains in great details why this assumption is wrong in the CAPM model. First, as stated earlier, different individuals will react differently to an asset. Therefore wealthier investors will be less risk averse that the one who does not have the same amount of money and can't afford great losses. Secondly, we have different motivations to invest. Some people will want to invest in order to have liquidity fast or other will want to keep their investment longer just to make their money "work".

Therefore, the time horizons of investors will vary. Thirdly, we all have different goals, long term investors might want to save for future needs such as retirement and be less sensible to a change in the market while short term investors might want liquidity for the purpose of speculation or short term upcoming expenses therefore being very responsive to a change in the market. Fourthly, many investors are individuals and do not have the time, the knowledge or the will to go into exhaustive searches for their investments' optimal solutions. Only professionals or people with passion can go through long searches about the market therefore having a better performing portfolio.

For the preceding reasons and for other costs linked to information's researches people will not have access to perfect information (although the market is considered to give perfect information if efficient). Because of so many varying needs and horizons, investors will not view the market and it's pricing in the same way making the use of CAPM irrelevant for them.

Vega's coherent market theory takes into consideration the time variable of market stating that markets are always changing so should the CAPM. A random pricing model will have a normal distribution over time which means that it can be used as an historical data.

However, because of every day's changes and innovations, markets go through multiple cycles giving it non-normal distribution for which statistics can't predict the future. Vega's theory joins Bram comments about the importance of individual decisions. Individual investors can reduce information search and find a coherent model by analyzing business cycles.

There are 4 business cycles: Easoff in which the economy has reached its point of maximum growth and slows down. Interest rates are high because the FED is trying to reduce inflation. Plunge is a slow down in which the economy is declining along with interest rate. Revival is the recovery stage from its recession or slow down.

Finally, Accelerate is the starting point again in which the economy continues its strong growth. Vega gives different strategies for the different business cycles but leaves to the individual the choice to invest in risk free assets or overseas assets when the economy booms. Vega's model is more complex than the CAPM and tries to avoid the different defects of the CAPM. Investors should look short term in the past for the model to work.

### Multifactor Models:

It is a common opinion that growth stocks are more valuable and will generate more returns than value stocks. Studies by Kenneth and French assume the opposite. Although value stocks are generally defined as low ratio to book value and market value while growth stocks have high ratio to book and market value, their studies proved the opposite. This makes sense to me because the growth of a company or an industry as seen with the dot com and many other fast growing industries forces the company to perform in a way that is sometimes not natural and will lead to a crash.

For instance, the managers in order to keep investors' expectations about their company's growth might be led to influence their stocks prices or lie in their financial reports by fear to lose inflows of capital. As we can see with such examples as Enron, the outcome is dramatic on the whole economy and many changes have to be done in terms of policies later on. Therefore what seems to be priced as a high reward stocks by the market's information may turn to be a junk stock later on.

Value stocks ask for more analytical skills and information research but is more conservative in that way that companies do not have an enormous pressure to perform therefore does not try to influence markets' decisions regarding its stocks. Some hidden gems can be in those stocks and many can be undervalued because disregarded by the public.

This represents a great opportunity for profit. The CAPM does not reflect this view of stocks. Those findings have two implications for the investors: first, it is shown that by investing in value stocks the returns are much higher in many different countries around the world, providing investors with more options. Second, investors that base their judgments on the CAPM are mistaken and do not see the importance of value stocks because the CAPM does not take into consideration 2 variables of risks.

Stock returns are commonly known today as being influenced by a one folded factor: the sensitivity of to the market return or beta. This is true but not complete. The CAPM needs to include a measure of risks between big and small stocks along with a measure of risks in value and growth stocks. This is important because once again different investors have different needs and exclude value stocks because the only available and easy data is CAPM therefore they are not interested by value stocks which may also explains their low prices while in fact the underlying company might have a growth potential. To examine stock returns, and make an informed decision you need those three measures of risks.

Risks must be tied to earning to price, cash flow to price and dividend to price in all of the three dimensions stated above: small vs. big stocks, value vs. growth stocks and market returns sensitivity. Those risks analysis are necessary for investors to make informed decisions that are hidden by the CAPM. (The problem, I believe, is that if this information becomes available to investors, profit resulting from value stocks' hidden gems will disappear to tie their prices to market's expectations therefore becoming growth stocks).

### Emperical Evidence

For over 30 years academics and practitioners have been debating the merits of the CAPM, focusing on whether beta is an appropriate measure of risk. Most of these discussions are by and large empirical; i.e. they focus on comparing the ability of beta to explain the cross-section of returns relative to that of alternative risk variables.

Most of these discussions, however, overlook where beta as a measure of risk comes from, namely, from equilibrium in which investors display mean-variance behavior (MVB). In other words, the CAPM stems from an equilibrium in which investors maximize a utility function that depends on the mean and variance of returns of their portfolio.

The variance of returns, however, is a questionable measure of risk for at least two reasons: First, it is an appropriate measure of risk only when the underlying distribution of returns is symmetric. and second, it can be applied straightforwardly as a risk measure only when the underlying distribution of returns is normal. However, both the symmetry and the normality of stock returns are seriously questioned by the empirical evidence on the subject.

The semivariance of returns, on the other hand, is a more plausible measure of risk for several reasons: First, investors obviously do not dislike upside volatility; they only dislike downside volatility. Second, the semivariance is more useful than the variance when the underlying distribution of returns is asymmetric and just as useful when the underlying distribution is symmetric; in other words, the semivariance is at least as useful a measure of risk as the variance.

And third, the semivariance combines into one measure the information provided by two statistics, variance and skewness, thus making it possible to use a one-factor model to estimate required returns.

Furthermore, the semivariance of returns can be used to generate an alternative behavioral hypothesis, namely, mean-semivariance behavior (MSB). As shown in Estrada (2002b), MSB is almost perfectly correlated with expected utility (and with the utility of expected compound return) and can therefore be defended along the same lines used by Levy and Markowitz to defend MVB.

### Problems of testing and the major pricing anomalies

From a theoretical perspective, the Capital Asset Pricing Model (CAPM) of Narayanaswamy & Phillips, (1999, p86) is a one-period equilibrium model and as such, it is not designed to account for temporal dependence and nonsynchronous trading. From a practical perspective, it is well known that the distributions of asset returns exhibit volatility clustering, which manifest itself as temporal dependence in variances, and nonsynchronous trading and non-trading effects, which manifest itself as autocorrelation in mean. Turtle (1994) has shown that serial correlation will be induced into model disturbances, when conditional variances are time varying. Garrett, (2004, p113) has shown that spurious serial correlation will be induced into model disturbances.

Consequently, tests of an unconditional CAPM in the thinly traded Norwegian market may be wrongly specified.

For example, researchers estimate CAPM regressions monthly, quarterly, semiannually, and yearly using daily, weekly, or monthly returns, paying special attention to the obvious microstructure issues that affect the estimates. The literature has devoted much effort to developing tests of the conditional CAPM, but a problem common to all prior approaches is that they require the econometrician to know the 'right' state variables (e.g., Narayanaswamy & Phillips, (1999, p86). Garrett, (2004, p113) summarizes the issue this way: "Models such as the CAPM imply a conditional linear factor model with respect to investors' information sets. Thus, a conditional factor model is not testable!" (Garrett, 2004, p113).

As long as betas are relatively stable within a month or quarter, simple CAPM regressions estimated over a short window - using no conditioning variables - provide direct estimates of assets' conditional alphas and betas. Using the short-window regressions, they obtain time series of conditional alphas and betas for size, B/M, and momentum portfolios from 1964 - 2001. Researchers use the estimates in two ways.

First, they study the time-series properties of conditional betas .Second; they directly test whether average conditional alphas are zero, as implied by the conditional CAPM (Hansson, 2003, p377). It is useful to note that their tests do not require precise estimates of conditional alphas and betas from individual short-window regressions; the estimates must only be unbiased.

Estimates of conditional alphas provide a more direct test of the conditional CAPM. Average conditional alphas should be zero if the CAPM holds, but instead they find that they are large, statistically significant, and generally close to the unconditional alphas. For long-short strategies, the average conditional alpha is around 0.50% for the B/M portfolio and around 1.00% for the momentum portfolio (they say 'around' because the conditional alphas are estimated several ways; all methods reject the conditional CAPM but their point estimates differ somewhat.) The estimates are more than three standard errors from zero and close to the portfolios' unconditional alphas, 0.59% and 1.01%, respectively (Hansson, 2003, p377).

Researchers do not find a size effect in their data, with conditional and unconditional alphas both close to zero for the 'small minus big' strategy. Overall, the evidence supports analytical results. Betas vary significantly over time but not enough to explain large unconditional pricing errors. The conditional CAPM performs nearly as poorly as the unconditional CAPM.

Ex ante theory with ex post testing: the Capital asset pricing model follows ex ante (before the event) line of reasoning; it describes expected returns and future beta. Meanwhile on test point of view theory we observe what has already occurred - these are ex post observation. There are usually a large difference between investor's expectations and the outcome. The CAPM do not support the most basic prediction of the SLB model, that average stock return are positive related to marker beta, bottom line results are doesn't seem to help explain the cross-section of average stock return and combination of size and book-to-market equity or we can saying that beta has not explain returns whereas two other factors have. (Arnold, 2005; p, 352, 357)

Early Empirical Tests. There are problems in these tests quickly became apparent. First, estimates of beta for individual assets are imprecise, creating a measurement error problem when they are used to explain average returns. Second, the regression residuals have common sources of variation, such as industry effects in average returns. Positive correlation in the residuals produces downward bias in the usual ordinary least squares estimates of the standard errors of the cross-section regression slopes.

While CAPM pricing anomalies has been the subject of study for years, it was Gomez, (2003, p343) who first examined the anomaly effects independently and jointly using the approach on a unified US database. They found that the relation between beta and average stock returns is flat, that the combination of size and BE/ME seems to have absorbed the pricing effects of leverage and E/P, and that the size and BE/ME variables suffice to explain the cross-sectional variation in average returns.

The firm size anomaly: Perhaps the most puzzling asset pricing anomaly reported in the previous literature is the so-called firm size effect or small firm effect. Researchers, e.g., Banz (1981) and Reinganum (1981), discovered that stock returns tended to be substantially higher for small firms than for large firms even after controlling for the effect of beta risk. The firm size effect is thus widely regarded as inconsistent with the Sharpe-Lintner CAPM. Reinganum, for example, argued (1981, p. 45):

CAPM might hold, period-by-period, and that time-varying betas can explain the failures of the simple, unconditional CAPM. We argue, however, that significant departures from the unconditional CAPM would require implausibly large time-variation in betas and expected returns. Thus, the conditional CAPM is unlikely to explain asset-pricing anomalies like book-to-market and momentum. We test this conjecture empirically by directly estimating conditional alphas and betas from short-window regressions (avoiding the need to specify conditioning information). The tests show, consistent with our analytical results, that the conditional CAPM performs nearly as poorly as the unconditional CAP.

Recognizing that a part of the unobservable market portfolio is certainly observable, we first reformulate the CAPM so that asset returns can be related to the 'benchmark' beta computed against a set of observable assets as well as the `latent' beta computed against the remaining unobservable assets, and then show that when the pricing effect of the latent beta is ignored, assets would appear to be systematically mispriced even if the CAPM holds. We further show that various pricing anomalies, such as the firm size effect and the Friend/Blume anomaly, can be, in fact, predictable consequences of the CAPM.

### Conclusion

Tests of the CAPM, and other factor models, nearly always use monthly returns. Researchers use daily or weekly returns because the regressions are estimated over very short windows - quarterly and semiannually in most cases. In principle, betas will be estimated more precisely by using high-frequency data, just as researchers observed for variances.

In practice, using daily and weekly returns creates at least two problems. First, ignoring microstructure issues, betas estimated for different return horizons will differ slightly because of compounding. Second, and more importantly, nonsynchronous prices can have a big impact on short-horizon betas. In particular, some researchers show that small stocks react with a significant (week or more) delay to common news, so a daily or weekly beta will miss much of the small stock covariance with market returns.

Our analysis in this paper shows that when the CAPM is tested or applied using a component beta, it is important to consider the multi-dimensional nature of the beta risk. We should not treat the benchmark beta as if it is the true market beta. Rather, we should treat it as the beta computed against an observable component of the true but unobservable market portfolio. Once this point is recognized, then we can see that such well known asset pricing phenomena as the firm size effect, the Friend/Blume anomaly and various anomalous test results of the CAPM are, in fact, predictable consequences of the CAPM. The failure to consider the pricing effect of the latent beta risk can give rise to various seemingly anomalous asset pricing phenomena reported in the literature. Lastly, the CAPM-OB also allows us to derive various implications of the CAPM that are amenable to tests without the knowledge of the true market portfolio.

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