# Efficiency tests sample essay

Day of the week test The day of the week efficiency test is the investigation of a particular stock market to see whether it reveals day of the week effect in volatility of returns, that is, whether stock returns in that particular stock market follow a certain pattern which is associated with what day of the week it is. Investing in the stock market is a wonderful way to make money, but it has a risk attached to it in the form of uncertainty. Stock market returns do not operate independently of the economic, political and technological environment of a country.

In fact the stock market of a country is completely driven by the aforementioned environmental stimuli. However the relationship is indirect. Changes in these environmental stimuli do not directly affect the stock market. What they do directly affect is the investor mindset. The investor mindset in turn directly affects whether the stock market returns are likely to be good or bad. A bleak economic prospect for example will make the average investor wary of investing in assets.

As a result he/she will stay away from investing in the stock market and as everyone, unsettled by the bleak economic prospect, follows suit, share prices, due to lack of demand, will drop drastically and, as returns hit the bottom, it will not make sense any more to invest in the stock market. In this manner, the stock market can behave very erratically as it is held hostage by hundreds of environmental stimuli the behavior of which few can predict to a certainly.

This is why the day of the week test is important, because by applying it, the stock market investor can predict whether stock market returns on a particular day will be high or low. He can tweak his investment pattern accordingly. The stock market is highly volatile and it has been explained above what accounts for this volatility. As mentioned before, this volatility gives rise to substantial risks which give the investor second thoughts about investing in the stock market.

However, this means that if the element of risk were to be eliminated to some extent, then that would make the stock market the original Aladin’s lamp as far as making money is concerned. Therefore every investor is always looking for ways to eliminate risk. The way the investor tries to eliminate risk to some extent, or to minimize it, is to find a way to predict what the return of a particular stock is likely to be at a certain point of time. That is why we, as the investors, use the day of the week.

If we are investing in the US equity market for example, then we apply the test to find out whether the market has a presence of the day of the week effect in it. If so, we invest only on those days on which the return of the stock we are investing in is likely to be high. In other words, we use the day of the week test to maximize the returns and minimize the risks of our portfolio. The question as to whether we benefit from this test has already been answered.

We most certainly do as otherwise we wouldn’t be able to predict how the market is going to behave on certain days and as a result our investment decisions would be very risky indeed. So we do benefit from applying the day of the week test. But how do we benefit from it? We benefit from it because the day of the week test allows us to detect whether there is an element of seasonality in stock returns of our portfolio. As soon as we have detected seasonality, that is, returns are high or low depending what time period it is, we have immediately minimized the investment risk.

An equity market for example which boasts the presence of the day of the week effect in it will tell us that returns on Mondays will be significantly lower than they are on other days of the week. Under the circumstances, the decision as when to buy stock and when to sell is not so difficult any more. In the aforementioned equity market, we should obviously stay away from making any stock purchases on any other day than Monday because the day of the week test that we have applied to the market tells us that prices will be lowest on Mondays.

Therefore, to minimize expenses, we should buy stock on Mondays. By the same reasoning, when the time comes to unload the portfolio, we should obviously do the selling on any day of the week other than Monday, because in the six days other than Monday, prices will be higher, which translate into higher returns for us investors. So clearly the benefits from applying the day of the week test are substantial. They all center around the ability of the day of the week test to introduce an element of regularity into the midst of what on first sight seems unconquerable chaos.

This test tells us there is a day of the week regularity functioning in the equity market and that if we invest accordingly, we shall have maximized our returns and minimized the associated risks. End of month test This is a test that seeks to establish the presence of a calendar anomaly in the behavior of stock market returns whereby returns are higher over a time period beginning with the last trading day of the current month and continuing over the first five days of the next month.

The importance of this test is in taking advantage of the fact that stock returns are not completely volatile, that they do have a certain pattern hidden deep under the apparently wildly fluctuating numbers. This directly contradicts the efficient market hypothesis which states that any information, whether public and private, that is available to the investors, has already been taken into account in stock pricing, therefore no single investor is in a position to take advantage of the market. According to the efficient market hypothesis, risk is the same for all investors.

However it has been recently discovered that there is a end-of-month or turn-of-the-month effect when stock returns are shown to be consistently higher on the last trading day of a month and over the first five days of the following month. This probably happens because during this time period the general level of liquidity goes up as a result of settling liabilities so that the investor has more cash with which to play around in the stock market. As has been mentioned before, the performance of the stock market is a direct function of the general mindset of the investing public.

If the investing public are in a good mood, then the market will perform well. If they are in a bad mood, the market will perform badly. These mood swings on the part of the general investor are a direct function of the macroeconomic news items which they are exposed to though the different media. Therefore the timing of the release of these macroeconomic news items is an important factor in determining how the stock market will perform afterwards. Usually these news items are released during the first few days of a particular month.

Stock market returns have been shown to maintain an upbeat trend as time approaches the scheduled release of macroeconomic news. That is why end-of-month testing is important because it shows the existence of calendar anomalies in stock returns brought about by scheduled release of macroeconomic news items. That is also the reason why we use this test. By using this test, we can detect the presence of calendar anomalies in the stock in which we are investing and take advantage of it to make capital gains.

By using this test, we prove that the efficient market hypothesis is by no means the last word in the world of finance, that the risk inherent in investing in a particular stock is by no means the same and a test that gives us the ability to predict risk is a worthwhile exercise by any standards. As can be seen from above, we can benefit from the day of the month effect. The benefit to be gained from this test is inarguable inasmuch as we have the ability to minimize systematic risk inherent in any investment decision. According to the risk-return relationship, the risk in investing in a particular stock has two components.

One is the unsystematic risk and the other is the systematic risk. Investors do not worry about the unsystematic part as it can be eliminated by means of diversification. Investors put their money in a wide variety of financial instruments so that even if one company is performing not so well thus dragging down its share performance as well, there are other companies in which the same investor holds shares and which is performing well thus canceling the negative effect of the under-performing company. It is highly improbable that all the companies will be underperforming at the same time.

What is more probable is that one will outperform the other thus eliminating the unsystematic risk. However it is well nigh impossible to eliminate or to even reduce the systematic risk which affects entire market to the same extent so that no amount of diversification will cushion the effect of a high systematic risk. However that is according to the traditional finance theory. According to the new theory whereby there is a end of the month effect in every stock market, systematic risk is definitely lower in the last trading day of the month and in the first few days of the next month.

So the benefit we get from this test is that we can predict a little better how the systematic risk is likely to be at what point in time in the month. Moving average As has been mentioned before, stock prices can fluctuate significantly over a certain period of time. If these prices are charted on a graph, then the trend line will zigzag substantially, making it difficult for us to evaluate whether a particular stock is underperforming or otherwise.

Moving average is a technical analysis tool which allows us to smooth out these fluctuations, so that there is a consistent trend line which can serve as benchmark for the evaluation of stock performance. Moving average is a very important technical analysis tool. Inasmuch as it enables us to impose order upon chaos by creating a consistent trend of the performance of a particular stock, its importance can hardly be overemphasized. If the returns of a particular stock were to be presented in the form of a scatter plot, then on first sight it would appear as white noise.

It would be impossible to make head or tail of this extremely chaotic scatter plot. However if one were to apply the moving average technical analysis tool, the widely scattered points would give in to a rising or declining trend line which could then indicate whether a particular stock is performing below that trend line or above. In this respect, moving average is a very important indicator of stock market returns. Before we make any investment decisions in respect of the stock market, it is obviously important for us to find out which stocks are performing above expectations and which stocks are performing below.

Moving average allows us to make that determination and that is why we use this tool. The problem that every stock market investor faces is that the returns on the face of it seem to be impossible to predict. Charted on a scatter plot, as mentioned before, the returns are all over the place. That would not be the case however once we apply the moving average tool to these returns. Once the moving average technical analysis has been applied, it would appear that the returns conform to a predictably progressing trend line.

And that is why we use the moving average technical analysis, to introduce an element of predictability into an area which would otherwise seem impossible to predict in any way. We certainly benefit from using the moving average analysis as it allows us to determine whether a stock at a particular point of time is performing below the trend line or above. This would enable us to determine when to buy and sell. When to buy and sell is the toughest decision that a stock market investor faces.

Obviously an investor would like to buy a stock when the price is at its lowest and would like to sell when the price at its highest. But how does an investor know when the price has bottomed out so that he should buy and when it has topped out so that she should sell? These points the investor must determine and the benefit of using the moving average technical analysis lies in the fact that it allows the investor to determine those points. An additional benefit of the moving average analysis is that it can be calculated both short-term and long-term.

A short term moving average can be defined as a 15-day moving average while a long-term moving average can be defined as a 50-day moving average. Thus there are two trend lines and when the short-term trend line moves below the long-term, the stock is on a downward momentum and it is time to sell. Conversely, when the short-term trend line is passing above the long-term, the stock is on an upward momentum and it is time to buy. In this way the moving average technical analysis allows the investor to decide when to buy and when to sell a particular stock.

Correlation Correlation allows us to test whether there is any relationship between two variables and if there is a relationship, whether the relationship is positive or it is negative. For example, a correlation of +1 indicates a positive relationship exists between two variables. A correlation of -1 indicates that the relationship between two variables is negative. When the relationship is positive, it indicates that the two variables move in the same direction and when the relationship is negative, it indicates that the two variables move in opposite directions.

Correlation is an important indicator of the future behavior of a particular variable in relation to another variable. It allows us to determine what other variables affect the performance of the variable of interest and to what extent. Once we have correlation figures quantifying the relationship between the variable of interest and other variables, we can predict how the variable of interest will change when the other related variables change. Inasmuch as correlation allows us to reduce uncertainty by enabling us to enhance predictability, it is an important indicator.

We use it for example when we are trying to decide whether or not to invest in a particular stock market. As has been mentioned before, the performance of a stock market is affected by a wide variety of factors. The most prominent environmental stimuli are the economic, sociological, political and technological changes taking place both nationally and internationally. It is important to know therefore to what extent these stimuli affect the performance of a particular stock market. Correlation allows us to determine that extent.

By applying correlation, we can find out how a certain change in the economy is likely to affect the stock market performance of that country. We come to know about these changes in the form of microeconomic news items which can be categorized based on their content. If we already have the correlation figures for these categories of news items, then as soon as they are announced, we can reasonably expect to be able to apply the correlation statistics to assess how the news items are likely to affect the performance of the stock market we are interested in.

This reduces risk to a substantial extent. Risk reduction is the most important consideration in the mind of an investor. For this reason, we use the correlation statistic. We do benefit from the use of correlation inasmuch as it gives us a window into the future regarding the performance of particular stock market. An example of a benefit would be an US investor considering investing in one of the Arab stock markets. In assessing whether it would be a good idea or not to go ahead with the investment, the investor would find use of correlation of immense value.

The investor would have to collect a great deal of knowledge connected to the economic, sociological, political and technological scenarios of the Arab country and determine by means of correlation how the different environmental factors are correlated to the portfolio performance in that stock market. Once that is done, he or she would be in a position to foresee how the different changes in the Arab country would affect the performance of the stock market in that country. This would enable the investor to buy and sell at the right time.

As has been mentioned before, there are also international forces at work which will affect stock market performance in the Arab country. In this respect, what the investor can do is to run correlation tests between the Arab stock market and the US stock market to see how the two markets are related. In this respect, the two markets would be two variables which the correlation test will examine to find out whether any relationship exists between the two variables and if so, if the relationship is positive or whether it is negative.

If the relationship is a positive one, then whenever the US market is performing well, the Arab market can also be expected to perform well and vice versa. Clearly this is of immense value to the investor as it allows him to pick the time as to when he should invest in the Arab stock market. That is the benefit. Descriptive Statistics So far the discussion has focused on predicting the future performance of the stock market. Now it’s time to focus on assessing the current performance of the stock market. That is what the descriptive statistics are for.

Descriptive statistics such as the mean and the standard deviation and the normal distribution help us evaluate the existing performance of a particular stock market. Descriptive statistics are very important because they quantify the performance of the stock market. The most widely used descriptive statistic is the mean. We can calculate the mean stock return by calculating the average of several stock returns from past time periods. This tells us the return we are likely to get if we invest in that stock. However the mean does not take into account the risk that comes associated with investing in stock.

As has been mentioned before, the stock market is a wonderful way to make money but every rose has it thorn and that thorn in this case is the risk. Stock returns are affected by so many variables both internal and external to the company that it is impossible to take into account all of them. This is where risk springs from. Because there are so many forces at work playing sixes and sevens with stock market returns, wild fluctuations are a necessary evil for the stock market investor. However even here, descriptive statistics can help by introducing order into chaos.

The descriptive statistic in question is the standard deviation. Because stock returns fluctuate extensively, they are scarcely at the mean. Sometimes they are above the mean and sometimes they are below. Standard deviation tells us the percentage of returns which will deviate from the mean to a certain extent. Most stock returns conform to the normal distribution, that is, most of the returns are clustered around the mean return. 66% of the observations fall within one standard deviation away from the mean. 95% of the observations fall within two standard deviations away from the mean.

And 99% of the observations fall within three standard deviations away from the mean. Inasmuch as stock market returns, given a sufficiently large sample size, follow the normal distribution, descriptive statistics are very important as they enable the formation of the normal distribution. This facilitates investment decisions. Descriptive statistics also come into play when determining the risk-return relationship. Risk is a prime consideration in any investor’s mindset. Investment in the stock market is meaningless unless a way can be found to minimize the influence of risk.

To complicate matters further, there are two categories of risk: systematic risk and unsystematic risk. There is hardly anything the investor can do about the systematic risk. It affects all the stocks present to an equal extent. An example of a systematic risk is when there is a sudden political eruption. The political turmoil will have a negative effect in all areas of the business sector. Therefore even if the investor is holding a portfolio of stocks, it will be of little avail. The other element of risk however, the unsystematic risk, is more manageable.

It means not putting all eggs in one basket. Managing a portfolio of stocks is key to eliminating or reducing unsystematic risk. An investor who has invested in a portfolio of stocks will reap more than an investor who has invested in only one stock. This is for the simple reason that external environmental stimuli do not hit all industries of the business sector to the same extent. If there is a technological change for example, some industries will benefit more and some less. Therefore the wise investor will invest in those industries which benefit more as a result of the technological change.

Alongside the technological change, there will be other changes, economic or political or sociological, which will have a negative impact on some of the industries. As a result the stock returns in those industries will take a nosedive. However an investor who is maintaining a portfolio of a wide variety of stocks will not be hit adversely as he will have stocks in that portfolio of his which were immune to the economic or political or sociological change in question. In this manner the unsystematic part of the risk has been eliminated. The stocks present in a portfolio will be negatively correlated.

That is, if one stock goes down in terms of returns, then another will go up. Thus the investor is well protected. However he is by no means protected from the systematic risk which no amount of diversification can eliminate. However all is not lost because descriptive statistics are there to help the investor. He already knows from the central limit theorem that most stock returns conform to the normal distribution. Once that is known, the investor can make an accurate prediction as to where the stock returns are likely to fall. This substantially reduces systematic risk.

As mentioned before, there are some exceptions in terms of stock market returns which do not strictly follow the normal distribution pattern. These returns follow a different probability distribution. The use of kurtosis and skewness can help to identify that particular category of probability distribution. Determining which probability distribution a particular stock market conforms to, in which the use of descriptive statistics is key, is vital for picking the optimum portfolio. An investor would obviously want to invest in only those stocks the returns of which stick most closely to the mean.

What the investor can do is to collect the percentage returns of a stock for a number of time periods and calculate the mean and standard deviation of these percentages to find out whether that stock shows a high volatility or a low volatility. The intelligent investor will obviously want to pick those stocks which have low volatility because their returns will be more predictable. So what descriptive statistics are very good at making sense of historical information to the immense benefit to the investor.

As has been discussed so far, the historical returns examined without the benefit of descriptive statistics will not generate a lot of information. To the naked eye, stock returns on a historical basis reveal no pattern. There is no discernible trend. Viewed through the lens of descriptive statistics however, stock market returns suddenly become very orderly and systematic. Now the investor knows which stocks to embrace and which stocks to keep away from. Now the investor knows what the optimum portfolio will be which will take into account both systematic risk and unsystematic risk and generate the highest returns.

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