# Statistical Yardstick Strategy

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Hello all,

I have escaped from the mystical land of finals and class for a few weeks and I finally have time to ask this question. A couple of weeks ago while taking a class on inferential statistics I thought of applying some of the stuff I learned about to stock analysis. Comparing simple data to the averages of ratios seems a little too inaccurate for me. For example: "Company X has a P/E of 10 and the industry average is 15, it must be cheap!" Instead of eye balling numbers like that I started building Z distributions to better represent the data. I used the Z because with the help of a screener I can round up all of the companies I want (the entire population). I used the mean (central point) and standard deviation (how far the data are from the mean) to get a better picture of what I am dealing with. I am attaching an excel worksheet with a very basic model I set up. The population of companies I am looking at is P & C insurance firms on the NYSE and NASDAQ. I computed the sdev and mean for the last 5 years. This is to see how the distribution of P/BV has moved around over the last 5 years. I also created a frequency histogram to see if the data appear to be normally distributed and to better visualize things. Below the table and above the histogram data I calculated the cumulative area up to Alleghany Corporation's 2013 P/BV just to test this out against a ticker (Y). If the area is below 50 then the value is below the mean (cheap) and if the area is above 50 the value is above the mean (expensive). In this case, the data shows that Alleghany is trading cheaply compared to the last fiscal year's distribution of P/BV. Companies have also become more expensive over the last few years but Alleghany will still be below the mean if prices go down to previous levels. This method is not meant to be a mechanical way to invest but rather just a better way to look at the data. This combined with a few other ratio distribution comparisons will give a better view of a company's metrics. Once a company looks good across several distribution comparisons I will start reading the annual and quarterly reports. In this case I would figure out how the company would boost their BV which should make the price go up. Again, this method is just a way to throw down some yardsticks to see which companies are worth while to look at and better see how they compare to others across different metrics.

Does this make sense to anyone out there? Did I mess anything up? Anyone do anything similar?

Also, the screener I used is Edgar's IMetrix.

P.S. Math question: These distributions seem to be skewed to the right, I can still normalize them right? I think so because most of the data are bunched up near the mean and they can't be spread more leftwards because most ratios cannot be lower than 0.

PC-Insturance-Stat-PBV-Distributions_-_Copy.xlsx

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P/B - ROE charts are often used to visualize the relative values of insurers and banks. You can also look at those trendlines over time.

http://av.r.ftdata.co.uk/files/2011/08/US-banks-historical-PB-and-ROEs-Nomura.jpg

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P/B - ROE charts are often used to visualize the relative values of insurers and banks. You can also look at those trendlines over time.

http://av.r.ftdata.co.uk/files/2011/08/US-banks-historical-PB-and-ROEs-Nomura.jpg

Those graphs are a nice way to visualize trends. Personally, I tread very lightly when looking at trend lines or anything like that. There are a million things from diminishing returns to a change in management that can drastically change trend lines. I really like to stay away from forward looking ratios. How is your forward ROE estimated? Also, it looks like you can construct a normal distribution around the Onshore P & C Insurers graph. Looking at measures of dispersion around a mean rather than just a trend line looks like a better picture to me. How else do you look at past data? Any normalized statistical distributions?

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Those graphs are a nice way to visualize trends. Personally, I tread very lightly when looking at trend lines or anything like that. There are a million things from diminishing returns to a change in management that can drastically change trend lines. I really like to stay away from forward looking ratios. How is your forward ROE estimated? Also, it looks like you can construct a normal distribution around the Onshore P & C Insurers graph. Looking at measures of dispersion around a mean rather than just a trend line looks like a better picture to me. How else do you look at past data? Any normalized statistical distributions?

I just grabbed those from Google. I would tweak the format of the first graph a bit. I'd use 3 year average ROE and tangible book value. All the points would be current values, but I'd also add a couple of trendlines showing past historical periods. And then maybe group similar companies within a sector by color.

To me the histogram / statistical distribution doesn't seem that useful. I'm more interested in identifying and comparing the outliers than analyzing the group as a whole.

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Those graphs are a nice way to visualize trends. Personally, I tread very lightly when looking at trend lines or anything like that. There are a million things from diminishing returns to a change in management that can drastically change trend lines. I really like to stay away from forward looking ratios. How is your forward ROE estimated? Also, it looks like you can construct a normal distribution around the Onshore P & C Insurers graph. Looking at measures of dispersion around a mean rather than just a trend line looks like a better picture to me. How else do you look at past data? Any normalized statistical distributions?

I just grabbed those from Google. I would tweak the format of the first graph a bit. I'd use 3 year average ROE and tangible book value. All the points would be current values, but I'd also add a couple of trendlines showing past historical periods. And then maybe group similar companies within a sector by color.

To me the histogram / statistical distribution doesn't seem that useful. I'm more interested in identifying and comparing the outliers than analyzing the group as a whole.

Yeah that makes more sense to me. I also think I messed up the distributions. The mean, median, and mode all need to be on the same place for me to normalize. Adjusting the data to make them more normal could take hours. When you linearize like that, can you tell that distance between the outliers and the regression line? Also the correlation between Forward ROE and P/BV is moderate (around 0.67). Is it a safe bet to make that historical ROEs and P/BV have a stronger correlation? Then I would focus on finding the outliers and trying to figure out how they could increase ROE.

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