I. Physics, Mathematics and finance: Bachelier and the Brown-movements » More!
II. Game: How much does the” FAIN IT!” token worth? » More!
III. Options » More!
IV. Options positions » More!
V. Price fluctuation on the financial markets » More!
VI. Buying volatility, sending volatility » More!
VII. Covering the options undertaking » More!
VIII. The pricing of options » More!
IX. Some edification » More!
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V. Price fluctuation on the financial markets
Let's compare the daily percentage change of the Euro with the average daily fluctuations on the stock market.
Without titles it would be quiet impossible to decide which illustration is for the stock market, which for the exchange rate and which for the fluctuations of the interest rate. The stock market is like Brazilian football: for a bit it seems like it's sleeping then two flashes and the goal is there.
As the illustrations show, there is a great obscurity on the stock market. Nevertheless, it doesn't necessarily have a negative influence on investors. In spite of guessing the future, it is better to select an appropriate mode of risk management. The majority simply do not buy shares in order to protect themselves from risks. It's like staying at home when we see clouds in the sky in spite of just taking an umbrella and getting on our way.
We have seen that with the call option we can secure our investment not to fall under a level and with the put option we can protect our exchange rate from going above the given level.
Beyond the options there is another risk management method on the stock market. In spite of following our broker's councils about what share to buy in this week and for what to change it in the next month we should listen to Andrew Kosztolány, the famous Hungarian expert of exchange. For those who wanted to invest in shares he advised to go first to the drugstore and buy some sleeping-pills and sleep years on the investments.
9th illustration
In the last 14 years there were 3500 dealing days on the BUX (Budapest Stock Exchange Index) until the beginning of this year. In 14 years the index has shown a 15fold growth, which is more than yearly a 21% yield. The exchange rate grew on 53% of the days and declined on 47%. So it's a bit like the “heads or tails” game but the chances of winning are a little better. Furthermore, on those days when the index rose the average profit margin was 0.6% and on the falling period it showed an average of 0.5% decline, which makes the winning chances better. In addition, these zigzags rack up the 15fold growth in 14 years. On the other hand, if somebody 14years ago had invested his money in bank deposits the value of his money would have only grown 8fold in the same period of time. (9th illustration)
10th illustration
If we have invested our money for more years in a portfolio that consists of more shares, in spite of trying our luck in a one-day long-period, then we could have reached the following yields on the BSE (Budapest Stock Exchange) in the last 14 years (10th illustration).
As we can see on the illustration, the more time our money stays in a portfolio grouping at least 20 shares the more the yields fall in a narrower interval.
The conclusion is evident: we should invest in more shares at the same time and we should sleep on it the more time we can. If, by any chance, we see rocks ahead then we would feel more comfortable with portfolio insurance- the same form as for the put options.
The nutrient for the finance market options is price fluctuation. Now we are not interested in the probable rate development of shares or foreign bills - i.e. the rate increases or decreases – the important for us now are the amplitudes in the fluctuation- how big are the margins. We can easily prepare ourselves for a warm or also for cold weather. The worst is when the weather changes quickly. For an investor the variability of the economic weather is not beside the point, either.
The first outstanding phenomenon is that we can highlight deliberately ascending or descending periods within the rate chart but if we examine it the whole day round we cannot find only positive or only negative daily price changes. The rate never falls like a stone but it follows a scalloped line.
It can be also noticed that the width of the zone within the yields spread shows a grate change from time to time. It is worth comparing the summer of 1995 with the autumn of 1998.
If the yields are plotted against the last day's yields, instead of the time, then we realise that we can nothing do with the information i.e. the previous day the rate was ascendant: today it can rise or decrease.
Rates change because of new information that is unexpected. Because of this fact each day's changes are independent of each other. It would be quite easy to flutter if the changes were strongly dependant on each other i.e. the points would fall in the right top and the left bottom. In that case we should just check if yesterday the yields were rising or not: so today they will be probably rise, as well. We buy shares in the morning we sell them in the evening and we become rich.
As for a share price, the direction of the previous day's changes does not have influence on the direction of today's changes but we can discover a little dependence: the changes of the other shares (the whole stock market) on the current day have influence on the given share's price.
How does a stock price react to the mass of information that affects it? In the 11th illustration the same hazardous effects touch three simulated stock price but they react with different sensitivity to them. They have different volatility. If it was a human we would say that the most volatile stock is like a moody person: he reacts with great feelings to everything. A stock's price is like a dog that is taken for a walk by its owner: sometimes it runs ahead, sometimes it lags behind but in reality it's always attached to the owner. What are the fundamental factors that give a loose dependence to the meandering path of the stock prices? Generally speakking the given company's future perspectives and the stock market.
In the illustration the difference of the three curves depends on their volatility: the length of the leading-strings. In the equation shown on the illustration the sigma parameter has three different values that stand for the volatility. The percental change of the stock price is on the left-hand side: dt is the duration of one step, dw is a randomly given small figure fluctuating around zero. We have used the same random realisation for the three curves in the on the illustration. So the 3 curves were influenced by the same random effects but they reacted with different intensity.
The volatility shows meaning difference in each period of time and it is different for each shares. The Russian crisis of the autumn of 1998 had a great influence on almost every stock's volatility. Rising volatility, it was also seen on the BUX index's, which presents the movements of the whole market.
In the stock market and, in general, in the finance markets the rate of the obscurity is also obscure. It is not accidental, that the stock market, by and large, has to provide bigger yield in long terms because in short terms the excursions are bigger. Somebody who, unluckily, bought shares in the end of the July of 1998, when the BUX index was at ca. 8300 points, lost half of his investments buy the middle of September. In that time the BUX index was stagnating at around 3800 points. If somebody in this way, heedlessly, had invested his savings coming from. 40years of work then he saw himself losing the fruits of 20 years's work. The BUX index regained the 8300 points for December the folowing year. Those who could wait until this point, instead of loosing their head and selling all their shares in the critical period, didn't even really notice the stagnation the market suffered.
