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Simple Statistics for Investments! May 7, 2008

Posted by shaferfinancial in Uncategorized.
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Today there were several reactions to my letter to the editor in the St. Petersburg Times on teacher pay.  The first letter from a teacher made it clear she did not understand what “average” meant as in “average salary.”  So I thought I would spend a few minutes going over some basic statistics with the readers.  As many of my friends know, I taught statistics at the Univesity of South Florida for several years so please excuse this post if you already have a good understanding of basic stats or find it to didactic.

Average is one of the central tendency statistics that represents the middle of a data set.  It is the most used stat and is easily calculated by simply adding up the data set and dividing by the amount of integers in the set.  For example the average or mean of  the following numbers:  1,2,3,4,5 is three (1+2+3+4+5/5) or 15/5.  This is a good stats if you have a somewhat homogenous group like if you wanted to know what the average school teacher’s income in a school district.  It is not a great stat if you have a large number of outliers (numbers that are far away from the main group).  For example say you were looking at a group of people where 9 made $100,000 and 1 made $1,000,000.  The average would be $190,000.   That really doesn’t represent what the middle of the group makes so a better stat is the median which looks at the middle number in this case $100,000. You simply arrange the set from lowest to highest and pick the middle number.  If you have an even amount of integers you simple average the two middle numbers to get the median.  The median is really a better stat to use for income or wealth for example  because there are a few people who make so much more than the majority that it skews the average up and gives a really wrong impression.  This is why if politicians want to give a number that makes the average income look better they quote the average, while those who want a more accurate number quote the median.  Anytime you see a quote about “average income” among large groups you know they are trying to hide the real middle income which is what the median would give you.

I have posted about leverage many times before.  It is simple to calculate.  For example if you purchase a home with the traditional 20% down you have a 4 to 1 leverage situation (80%/20%).  Or if you put down 10% you have a 9 to 1 leverage situation (90%/10%).  Or if you have equity in a home worth $300,000 of $150,000 you have a 1 to 1 leverage situation (50%/50%).

A simple way to calculate capitalization rate in real estate is to add up all the yearly expenses (management fees, maintenance fees, taxes, etc.) then add up all the income (rent) and divide it by the cost of the real estate.  Say your total expenses are $15,000 and your total income is $30,000 so you have a net gain of $15,000 or a cash flow of $15,000.  You paid $150,000 for the property so the cap rate is 10% ($15,000/$150,000). Cap rates are a great way to value investment real estate, but they are usually an unleveraged valuation that doesn’t take into account debt service or leverage.

Finally rate of return is the ratio of money gain or loss on an investment.  This is calculated by looking at the total appreciation or depreciation over a given time period.  Usually, this is calcalated in years, for example the rate of return for the last 10 years for Berkshire Hathaway is 18.3%/year.  Note this is calculated by looking at the change of asset value each time period (usually a year) for example on Jan 1 the asset value is $1000 then on Dec. 31 the asset value is $1100 there is a 10% rate of return (1100/1000-1).  Also important is that you simply can’t average the annual rate of returns to get the overall rate of return because negative numbers don’t mix well with positive numbers in this statistic.  A simple way that will get you close to the annual rate of return for an investment is to divide the initial investment into the current value + any dividends paid out to get the overall rate of return and then divide that number by the amount of years the investment has been held.  For example initial investment was $1000 and the current value plus dividends is $2,000 and the investment was held for 5 year then it had a 20% annual return (2000/1000-1)/5. Note that most investments state an average rate of return which doesn’t accurately reflect the real dollars made or lost as losses count more than gains. (A $100 investment that goes up 10% one year and goes down 10% the next is worth $99 not $100).  A litle trick of the trade to fool folks!

Hope this helps some folks. 

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