For many years economists, statisticians, and stock market players have been interested in developing and testing models of stock price behavior. One important model that has evolved from this research is the theory of random walks. This approach assume that the underlying distribution of the stock prices is normally distributed.
In contrast, many stock market players believe that this is not the case due to many factors like sudden change of interest rate, business cycles and political climates, investors trading preferences and etc. Accordingly, the return of stock prices and market index is not random and the normal distribution does not reflect the actual distribution.
With KaotiXL, you can have the best of both world and examine the stock prices in details with
A) Value At Risk – which assume the stock prices to be normally distributed
B) Rescaled Range Analysis – which assume the stock prices is not normally distributed
A) Value At Risk
Value At Risk or VaR has been called the "new science of risk management". It is most commonly used by security firms or investment banks to measure the market risk of their asset portfolios (market value at risk). VaR is widely applied in finance for quantitative risk management for many types of risk.
Our main concern here is using KaotiXL to help us as private investors to manage our risk in stock market investment.
For investors, risk is about the odds of losing money, and VaR is based on this common-sense fact. By assuming investors care about the odds of a really big loss, VaR answers the question, "What is my worst-case scenario?" or "How much could I lose in a really bad month?"
VaR help investors to calculate the risk of a particular investment and the odds of losing money.
Consider a trading position. Its market value in US dollars today is known, but its market value tomorrow is not known. The investor holding that position might report that its position has a 1-day VaR of $1000 at the 95% confidence level.
This implies that under normal trading conditions the investor can be 95% confident that a change in the value of its stock would not result in a decrease of more than $1000 during 1 day. A 95% confidence interval does not imply a 95% chance of the event happening, the actual probability of the event cannot be determined.
The key point to note is that the target confidence level (95% in the above example) is the given parameter here; the output from the calculation ($1000 in the above example) is the maximum loss (the value at risk) at that confidence level.
From the above example, you can see how the "VaR question" has three components:
Keeping these three parts in mind, VaR will help you to answer
How VaR is calculated ?
(see details of VaR calculation here http://www.investopedia.com/articles/04/092904.asp and http://en.wikipedia.org/wiki/Value_at_risk )
KaotiXL includes all the three method of calculation and present them in a result table for easy interpretation and decision making. (see below)
With KaotiXL, you don't need to know how VaR is derived. All you need to do is to enter the historical closing price of a stock or index, and you will get the detail result in a separate worksheet. Simple...(see User Guide for details explanation)
Rescaled Range analysis is a statistical methodology used to detect the presence or absence of trend in time series by finding the Hurst exponent. For example, it is generally known that time series like stock prices, indexes of stock market, sunspot etc does exhibit the persistence of trends. R/S analysis is also highly data intensive.
Basically, this method is used to identify when a stock price is persistence i.e. the tendency of the price to continue its current direction and also antipersistence i.e. the tendency of the price to reverse itself rather than to continue its current direction. Or it is random and unpredictable.
The Hurst exponent (H) is use to determine the underlying distribution of a particular time series. As a rule of thumb...
a) 0.50 < H < 1.0 implies a persistence time series. The larger the H indicates a stronger trend. (strong position on long)
b) 0 < H < 0.5 implies antipersistence. (trade on reversal)
c) H more or less equal to 0.5 indicates random time series. (No position taken)
R/S Analysis is also use to find the primary cycle length of stock prices and market indexes. The V Statistic shown below is very efficient in doing this. Not only the primary cycle but the underlying cycle as well, as long as the subcycles is a small, finite number.
When you run KaotiXL to calculate the Hurst exponent, two charts will be generated in the Report sheet :
If you scroll down on the worksheet you will see 2 tables and 2 charts. (see Fig 1.3)
The first table on the left, display the full result of the historical calculation of the VaR.
The second table show the full result of the Monte Carlo simulation. This Monte Carlo simulation amounts to a "black box" generator of random outcomes. KaotiXL ran this simulation based on the stock/index historical trading pattern. You will get a different result each time you run this simulation.
And lastly, the two histograms (Historical and Monte Carlo) display the underlying distribution of stock returns.
NOTE: Only 10 result worksheets can be created in a workbook. Run KaotiXL on a new workbook each time it has reach “VaR Output 10”
Two charts will be generated in the Report sheet. The H is display in cell B23 : (see screenshot) - Figure 3 below
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