Finding the Distance From the Mean
1. Finding the Distance From the Mean
Once we know that data is normally distributed, we can approach the scenario from the previous lesson from a different perspective. Imagine for a moment that you own the equity that has a daily standard deviation of 2.35%. You want to know how much you could lose on a really bad trading day, in other words, you want to know how far from the mean you would need to go so that the area and the tail is equal to 5%. So I've gone back to the demo sheet on the statistics we'll find its template workbook and I've gone to the last section called calculating distance from mean. I want to work out what a really bad trading day would look like. And so these are all the returns that are in the orange shaded section of my bell shaped curve, because those are all my biggest losses, and I'm going to assume that the area under the curve is 5%. So I want to calculate what the worst 5% of daily losses might be. Now, 5% is a one and 20 day trading loss. So I can use that information to work out what that might be, but we do need a current price of the stock. So let's assume that the current price of the stock is 100, we know that the daily standard deviation is 2.35%. Now, we know that the area under the curve is 5%. And 5% means the loss that we might incur 1 in every 20 days. And so the orange shaded area as a percentage is 1 out of 20 trading days or 5%. I need to figure out how many standard deviations from the mean I need to go so that the area to the left of that point, that area under the curve is 5%. So I'm going to use a different normal distribution function this time, I'm gonna use a norm is inverse function. Alright. And so what this function does it says well for a given probability or area under the curve, how many standard deviations from the mean would you have to move to find that area? Now, I want to find the area, so that area under the curve is only 5%. How many standard deviations from the mean would I have to travel to get to that point? I'd have to travel 1.64 standard deviations below the mean. And it's below the mean, so it's a negative number. So what does this mean for my stock that's currently sitting at $100? Well, I know that one standard deviation is 2.35% and I know that if I move 1.64 standard deviations, I'm going to get to a point so that the area to the left is 5%. So 1.64 standard deviations, when one standard deviation is 2.35 means the area under the curve, if I have a daily return of 3.87%, there's a 5% chance that I will lose more than that on any given day. Now, what does that mean if the current stock price is a 100? Well, what is 3.87% of 100? I can take my 100 and times it by 3.87. So there's a 5% chance that on any given trading day I may lose more than $3.87. The current price of the security is $100 and the returns are normally distributed.2. Let's practice!
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