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Computer Exercise #3 - Statistics - 02-23-2011

# Computer Exercise #3 - Statistics - 02-23-2011 - EE 0822...

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EE 0822 INVE\$TING FOR THE FUTURE MR. LENGKEEK INVESTING TOOLS 3 STATISTICS CAN BE YOUR FRIEND Imagine you are in Philadelphia one day in the middle of the summer, say July 26 th , and it is afternoon. Here are some questions “rhetorical” about what the outside temperature might be. 1. What is the probability that it is below freezing, i.e., below 32 o F or 0 o C? 2. What is the probability that it is 60 o F? 3. What is the probability that it is 90 o F? 4. What is the probability that it is 120 o F? 5. What is the probability that it is 180 o F? One thing you can note from your answers to the above questions is that each of those temperatures do not have the same probability of occurring, i.e., 32 o F and 180 o F are very unlikely (low probability), and 90 o is very likely (high probability). If you had constructed a graph of your answers with the probability being the vertical axis and the temperature being the horizontal axis, you would have notice that it has the shape of a bell with 90 o being the middle and 32 o and 180 o being much lower and higher and on opposite ends of the plot. There is an interesting lesson here, and that is, that you have a very good working knowledge about probability, and what you have constructed is called a probability histogram. So why is statistics an important investing tool? Well, let’s say that you are interested in buying a mutual fund and you see what the price is per share. You know that the mutual fund invests in: 1.) small cap (companies that are worth \$250 million to \$1 billion. The worth of the company is calculated by multiplying the number of shares outstanding by the price per share) 2.) value companies (those companies who have a P/E (stock price divided by company earnings – ratio) below the average of the market), and 3.) U.S. stocks. The average yearly return of the fund for the past 10 years is 10%. So, the mutual fund is composed of small cap value U.S. stocks and the funds average annual return is 10%. This would seem to be all the information necessary to know if the mutual fund is a good investment – yes? Not really! One of the most important numbers is the mutual funds volatility (the variation of the mutual fund’s price over a period of time). Here is where statistics can be a real help! We know that the price doesn’t move in a 1

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EE 0822 INVE\$TING FOR THE FUTURE MR. LENGKEEK INVESTING TOOLS nice, well-defined manner, but its price pattern, as a function of time, is to some extent random. Therefore, if you know how much the price varies each day, or week, or month, then you would have an idea about how much it might vary for the next few days, or weeks or months. There could be very little variation in the price one day or it could vary by \$5 or \$10 dollars in one day. It should be evident that knowing the volatility of a mutual fund or stock can be helpful in terms of how much you can expect the stock or mutual fund to vary. To put it another way the volatility would provide you with information about the range from the “highest possible gain” to the “highest possible loss” . It should also be noted that there is a good relationship between risk
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