Loans and money issues

Having gone through the basic building blocks of technical analysis and the technical indicators that are used, we will now look at the major technical schools of thought that have dominated the way technical analysts and traders look at price patterns. The first one to focus on is the Fibonacci school of thought, named after Leonardo Fibonacci, an Italian mathematician born in 1170. Fibonacci discovered a series of numbers such that each number is the sum of the two previous numbers:
1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233 and so on . . . To some, these numbers may seem more or less random. In fact, they are actually far from random, containing important interrelationships, and they are found in a surprising number of real-life examples. Indeed, it is not too much of an exaggeration to suggest that these numbers represent the mathematical building blocks of life. For a start, note that any given number is roughly 1.618 times the previous one. Equally, any number is 0.618 times the following number. As it stands, this does not answer the question of how Fibonacci happened to found, albeit inadvertently, a type of technical analysis. For this, we have to look first at Fibonacci’s so-called “rabbit problem”, which relates to his attempt to demonstrate the application of Hindu–Arabic numerals through the example of rabbits. The mathematical problem that Fibonacci posed is that if two rabbits were put in an isolated place, how many pairs of rabbits could be produced from that pair in a year if every month each pair produces a new pair, which itself from the second month also becomes reproductive? At the start of the first month, there would only be the first pair. By the start of the second month, there would be the original pair plus one new pair, resulting in two pairs of rabbits. However, during that second month, the original pair will again produce another pair while the second pair is maturing. Thus, at the start of the third month, there should be three pairs, which brings us back to the Fibonacci number series. In terms of a mathematical formula, this can be expressed as: X n +1 = X n + X n−1 where X n is the number of pairs of rabbits after n months.
This became known as the Fibonacci sequence, as coined by the French mathematician Edouard Lucas (1842–1891). As the Fibonacci sequence progresses, a clear relationship between the numbers becomes apparent, as reflected by the 0.618 and 1.618 ratios mentioned above. The very fact that there can be a consistent ratio between numbers is itself “statistically significant”, confirming that there is more in this than just a random series of numbers. Note also that if you take any number and divide it by the number two higher in the sequence the ratio comes to 0.382. Not coincidentally, 38.2% and 61.8% are major Fibonacci retracement levels within the Fibonacci school of technical analysis.
While we look to Fibonacci and Lucas as the founders of modern-day Fibonacci analysis, it appears that long before them the importance of this sequence of numbers and ratios was well known and appreciated. Indeed, these ratios appear to have been used in the construction of both the Great Pyramid of Giza in Egypt and the Parthenon in Greece. The 0.618 or 1.618 ratio, also known as the Golden ratio, is commonly viewed in mathematics as one of the building blocks of natural growth patterns — in geometry as in life. Even the human body can be shown to contain elements of the Golden ratio, measuring the distance from the feet to the navel and in turn from the navel to the top of the head as a ratio. The basic building blocks of human beings, the DNA double helix, also contains the Golden ratio.

A layman might not be able to tell much apart from the fact that Euro–dollar has been in a downtrend. Sometimes, such basic observations, made either by a layman or by a practising technical analyst, are the most important ones. However, a “technician” should be armed with a skill set that at least allows for the possibility of a more complex and sophisticated analysis. Looking at the charts again, we can identify the following points accordingly:
Euro–dollar has traded within a long-term downward sloping trend-channel.
It has only broken that channel on a sustained basis to the downside up until July of 2001
when it broke through and held above channel resistance.
Before that, in December 2000, Euro–dollar briefly managed to exceed that trend-channel resistance and made a major high of 0.9595. Major highs and lows usually reflect theultimate extension of a trend reversal. Thus, 0.9595 needs to be exceeded for the medium- term downward trend to be negated.
The fact that a shorter-term moving average has broken up through the longer-term counterpart would appear to validate the view that Euro–dollar trades higher in the short term, whether or not it actually manages to breach that level of 0.9595.
More specifically, however, the fact that the 55-day moving average has broken up through the 200-day moving average is potentially very significant. Why? As we noted above, certain moving averages are seen as more equal than others. Notably, the break of a 200-day by a 55-day MA usually can potentially lead to impulsive moves and signal a short-term trend reversal. Here, the 55-day MA has broken up through the 200-day MA, which we call a “golden cross”, arguing for potentially dramatic gains. Conversely, if the 55-day MA were to break down through the 200-day MA, that would be termed a “death cross” and be correspondingly bearish as the name might suggest.
One could go on, but I hope from this that the reader gets a picture of charts being able to reflect substantial amounts of potentially important information, information that in the absence of major changes in fundamentals may be the primary reason for subsequent, future price action. Along with support, resistance and moving averages, there is another technical tool that is useful in determining short-term moves in exchange rates — the relative strength index (RSI). The aim of this indicator is to discover overbought or oversold levels, against which the index is measured. The time period for RSI is usually 14 days and overbought and oversold levels are usually taken as 70 and 30 for the index.
The two dotted lines indicate the 30 and 70 oversold and overbought levels for 14-day RSI. Hence, we can note from this that according to the charts the RSI reading is currently roughly in the middle of its range. Combining this with the underlying charts, we note that at the same time as the RSI reading is in the middle of its bands, Euro–dollar has broken to the upside of a trend channel and the 55-day moving average has broken up through the 200-day moving average. We can potentially conclude from this that the benign RSI indicator may suggest there is more upside to come. Note that the RSI reading usually exceeds its 70 or 30 overbought or oversold levels before the peak or trough in the spot exchange rate. RSI analysis can be particularly useful when comparing divergences between it and the spot price action. For instance, if a spot exchange rate is making new highs while the RSI reading has already peaked, it may suggest that the spot exchange rate is itself about to peak and subsequently head lower.
RSI is one type of technical indicator. More generally, technical indicators reflect a mathematical calculation that can be applied to either an exchange rate’s price or its volume. The result is of course a value, which is then used to try and predict future prices. By this definition, both RSI and moving averages are technical indicators. Another widely used technical indicator is the moving average convergence divergence (MACD) indicator. The MACD is usually calculated by subtracting a 26-day moving average of an exchange rate from its 12-day moving average. The result is an oscillator that reflects the convergence or divergence between these moving averages.
Here, we get a somewhat different picture than shown by the RSI comparison. While that appeared to suggest the Euro–dollar exchange rate may have been about to make further gains given the benign RSI reading relative to the move higher in price, this MACD comparison appears to be suggesting the opposite. For just at the time the Euro–dollar exchange rate ismaking gains, the MACD reading has clearly failed well ahead of its previous high and is heading lower. This suggests bearish divergence on MACD and a potentially bearish signal as well for the Euro–dollar exchange rate. MACD oscillates above and below a zero level. When it is above zero, it means the 12-day moving average is higher than the 26-day moving average, which is potentially bullish as it suggests that “current” expectations (as reflected by the 12-day moving average) are more bullish than those expectations made prior to the 12-day moving average. Equally, when the MACD falls below zero, it suggests a bearish divergence between the moving averages. In our example, the MACD reading is still above zero, but it is heading lower towards that level. Moving averages and MACD are examples of lagging technical indicators as they reflect previous price action and are particularly useful when an exchange rate trends over a long period of time. On the other hand, leading technical indicators give some indication of a price being overbought or oversold, thus RSI is an example of a leading indicator. Divergence occurs when the exchange rate trend does not agree with the trend of the technical indicator of that exchange rate.