Financial issues: loans, mortgage, investment

Medians and Means

admin — Wed, 09 Dec 2009 18:35:00 +0000

Although the inflation-adjusted long-term distributions show that prices spend much more time at lower levels, there is a tendency to consider the average price of a market as the midpoint between the highest and lowest prices. Using the gold example, the midpoint for 1979 to 1993 was $451. The average of all monthly prices will give a reasonable approximation of a normal price; however, the best measure is the median, or middle, value when all monthly prices are sorted from high to low. The median value for gold over the same period was $381. If we look back at earlier posts we find that skewness is measured as the difference between the mean and the median, as a percentage of the standard deviation. In this case, the difference of $70 is a very large value, indicating a distribution with a peak far to the left of center. For price distributions, the median is a much more useful value than the average, although not as convenient to calculate. The median naturally adjusts for the skewness in the price patterns.

USE OF PRICE DISTRIBUTIONS AND PATTERNS TO ANTICIPATE MOVES

admin — Sat, 05 Dec 2009 18:33:36 +0000

Prices often form patterns that can be evaluated using probability methods, or simply viewed in much the same way as a frequency distribution, or histogram. Because the concepts are sound, but the statistical analysis is often difficult because of limited amounts of data or changing conditions, analysts have taken a much more empirical approach toward studying price distributions. The following section will look at some innovative ways to look at price distributions and how they are interpreted into trading opportunities.

Risk Premium

admin — Wed, 02 Dec 2009 18:32:40 +0000

A risk-free investment was defined as one for which the investor is certain of the amount and timing of the expected returns. The returns from most investments do not fit this pattern. An investor typically is not completely certain of the income to be received or when it will be received. Investments can range in uncertainty from basically risk-free securities, such as T-bills, to highly speculative investments, such as the common stock of small companies engaged in high-risk enterprises.
Most investors require higher rates of return on investments if they perceive that there is any uncertainty about the expected rate of return. This increase in the required rate of return over the NRFR is the risk premium (RP). Although the required risk premium represents a composite of all uncertainty, it is possible to consider several fundamental sources of uncertainty. In this section, we identify and discuss briefly the major sources of uncertainty, including: (1) business risk, (2) financial risk (leverage), (3) liquidity risk, (4) exchange rate risk, and (5) country (political) risk.

Problems in Using Moving Standard Deviations

admin — Sat, 28 Nov 2009 18:31:05 +0000

Applying any technique to a rolling time interval of the most recent N bars is a common method of keeping in tune with current market conditions. in the case of a simple moving average, we should be very familiar with the lag that is introduced. For trends, when prices are moving steadily higher, the lag causes the trendline to be much lower.There is a similar lag when using the most recent N bars to calculate a standard deviation, even when the data has been detrended. If we are measuring the volatility of the market, and prices rally quickly, the volatility rises. This will be seen in the larger value of 1 standard deviation measured over a fixed number of days, or bars. If we are looking for a confirmation of a buy signal based on an increase in volatility, we should get it.
However, the volatility represented by the standard deviation will not decline as fast as we expect because of the same lag. Once higher volatility has occurred on a single day. it will remain part of the standard deviation value until it passes completely out of the calculation window. That will prevent a new volatility event from being recognized soon after a short decline in volatility. It will also make it difficult, if not impossible, to get a timely exit signal on reduced volatility, because the lag keeps the volatility appearing high until at least part of this new, more active price movement begins to pass out of the end of the calculation window.

Standard Deviation Bands

admin — Thu, 26 Nov 2009 18:30:01 +0000

Bollinger bands are a very popular application of price distributions. They do not detrend price, but calculate the standard desiation of prices over a period of 20 days and form a band of 2 standard deviations around the trendline. It is common for traders to vary both the period and the number of standard deviations used to construct the band. Once calculated, Bollinger bands can be displayed on any price chart and used to generate buy and sell signals, much the same as any other channel breakout system. Using a smaller Bollinger band, for example, 1 standard deviation, will give many more signals than using one of 3 standard deviations. At the same time, a band of 3 standard deviations translates into risk that is 3 times greater than 1 standard deviation. Signals produced with a larger band tend to be more reliable, but have greater risk.

USING THE STANDARD DEVIATION

admin — Mon, 23 Nov 2009 18:28:20 +0000

The data used to determine the standard deviation is very important. Because it is a statistical measure, it is most accurate when a large amount of data is applied. For example. you might find that 1 standard deviation of the crude oil daily price move is only SO.25 per barrel when measured over the past 10 years, but during the 6 months of the Gulf War the same measurement yielded $.50, twice as large.
Most trading applications using the standard deviation tend to apply short data intervals to its calculation, such as 20 days. This short period is not likely to represent the same price distribution as a 10-year calculation; therefore, the probabilities given by the resulting standard deviation value must be interpreted differently. While it is less likely that the price will make a move of 3 standard deviations compared with 1 standard deviation, the probabilities can be misleading. Statistics tell us that there is only a 1% chance that prices will move a distance of 3 standard deviations higher or lower; however. that value is reliable only when measured over a long data period. If you selected 20 days of unusually low volatility, the chance of a 3standard deviation move Would be very high.
The frequency distribution is another very practical approach to measuring price distributions. It has the advantage of having a much clearer visual interpretation. While the standard deviation gives us what appears to be a highly mathematical probability, the large error factor that is caused by small amounts of data may make its usefulness about the same as the frequency distribution.

Expected Rate of Inflation

admin — Fri, 20 Nov 2009 18:27:13 +0000

If investors expected the price level to increase during the investment period, they would require the rate of return to include compensation for the expected rate of inflation. Assume that you require a 4 percent real rate of return on a risk-free investment but you expect prices to increase by 3 percent during the investment period. In this case, you should increase your required rate of return by this expected rate of inflation to about 7 percent [(1.04 × 1.03) – 1]. If you do not increase your required return, the $104 you receive at the end of the year will represent a real return of about 1 percent, not 4 percent. Because prices have increased by 3 percent during the year, what previously cost $100 now costs $103, so you can consume only about 1 percent more at the end of the year [($104/103) – 1]. If you had required a 7.12 percent nominal return, your real consumption could have increased by 4 percent [($107.12/103) – 1].

Price Distribution Systems

admin — Mon, 16 Nov 2009 18:26:04 +0000

Price movement is usually viewed as a chart on which each new time period is seen as a new bar or point recorded to the right of the previous prices. There are many applications that need to look at the way prices cluster, or distribute, rather than sequences of patterns. In options, it is important to evaluate the current market volatility to decide the chances of prices remaining in a specific range for a specific amount of time. The standard deviation gives the most basic measure of price distribution. From the value of 1 standard deviation we can estimate the chances of a price remaining within a range over time. The key values to remember are that 1 standard deviation defines 68% of the price movement (both up and down), 2 standard deviations contain 95%. and 3 standard deviations contain 99% of all price movement based on the sample of data used to calculate the standard deviation value.

Support and Resistance

admin — Wed, 11 Nov 2009 18:25:12 +0000

Support and resistance levels are important to the short-term trader. if prices start to move higher, slow down, and finally reverse, it is natural to consider the top price as a resistance point. Prices are thought to have been stretched to their extreme at that level. Any subsequent attempt to approach the previous high price will be met with professional selling in anticipation of prices stopping again at the same point. In addition, it is common for the same traders and others to place orders above the previous high prices to take new long positions or close out shorts in the event of a breakout.
This method, very popular among floor traders and active speculators, tends to create and emphasize the support and resistance price levels until they define a clear trading range. Within a Ito 3-day period, these ranges can be narrow and yet effectively contain price movement. During the life of the trading range, it will continue to narrow as the levels become clear to more traders and the anticipation of a reversal at those levels becomes imminent.
To take advantage of the smaller ranges caused in this manner, it is necessary to enter positions during the middle of a trading session, frequently holding that trade until the middle of the next session. An example using the Chicago Board of Trade December 75 Silver contract, during August 1975, will help to illustrate this. The opening and closing prices for the first 3 days do not indicate any opportunity for trading. Prices were generally in the middle of the daily range. By using the high and low of the previous day, this situation can be traded either of two ways.
Thursday, August 2 1, forms a range of 505 to 493, closing near the center of the range. After the next open, buy just above 493 and sell just below 505 to be certain of entering and exiting the position. For protection, a stop can be entered at about 506 and 492 to reverse the position on a breakout. Had this procedure been followed, entering 29 (200 points) before the bounds of the range.
In each case, the entry was 200 points before the level at which prices had reversed on the prior day. The Stop-Loss order was placed to limit losses to a 100-point penetration. Although this is an ideal situation, professional traders frequently use this method. It can be seen that the support levels did actually rise from 493.00 to 494.50, and then to 496.00. When support was penetrated, prices rapidly broke to new lows of 483.80, down to the permissible limit. Similarly, the resistance level remained intact going from 505.00 to 504.00, 504.50, and finally, 504.00. It is generally accepted that the resistance level represents a more volatile area that must be watched closely for false breakouts.
Support and resistance levels gain importance the more time they remain intact. The high and low of the prior day are not as significant as the weekly or the monthly range. Each can be traded using the same technique. The major support and resistance levels are contract highs and lows, which rarely allow breakouts with less than one attempt. Longerterm price objectives can be identified using a continuation chart. This chart plots only the nearest (spot) futures contract of a specific market to allow the location of support and resistance levels when the current contracts are in a new high or low area.
Before 1990 there were very few published day trading systems. The more recent ones have had the benefit of sophisticated computer programs and large historical databases. The following method precedes this era and remains unique and a valuable part of our literature.

MARKET PATTERNS

admin — Mon, 09 Nov 2009 18:24:51 +0000

A trade that lasts from 1 to 3 days can be improved if short-term patterns or cycles can be found. For example, in a trending market there are outstanding weekly and weekend patterns. It is most common to find that the price movements from Thursday to Friday (closeto-close) are in the direction of the major trend and that the movement on Monday is a continuation of that trend. By Tuesday (or sometimes Wednesday), the strength of new buyers or sellers has faded, and the market reverses due to lack of activity and some profit taking. It often stays in this state through Wednesday or early Thursday when it a~ resumes the trend. In a sideways market, the Friday and Monday directions differ from the direction during the prior week and often differ from each other.