How do I calculate two standard deviations away from the stock price?
"The formula for standard deviation is fairly simple in both the discrete and continuous cases. It's mostly safe to use the discrete case when working with adjusted closing prices. Once you've calculated the standard deviation for a given time period, the next task (in the simplest case) is to calculate the mean of that same period. This allows you to roughly approximate the distribution, which can give you all sorts of testable hypotheses. Two standard deviations (σ) away from the mean (μ) is given by:  It doesn't make any sense to talk about ""two standard deviations away from the price"" unless that price is the mean or some other statistic for a given time period. Normally you would look at how far the price is from the mean, e.g. does the price fall two or three standard deviations away from the mean or some other technical indicator like the Average True Range (an exponential moving average of the True Range), some support level, another security, etc.  For most of this answer, I'll assume we're using the mean for the chosen time period as a base. However, the answer is still more complicated than many people realize. As I said before, to calculate the standard deviation, you need to decide on a time period. For example, you could use S&P 500 data from Yahoo Finance and calculate the standard deviation for all adjusted closing prices since January 3, 1950. Downloading the data into Stata and applying the summarize command gives me: As you can probably see, however, these numbers don't make much sense. Looking at the data, we can see that the S&P 500 hasn't traded close to 424.4896 since November 1992. Clearly, we can't assume that this mean and standard deviation as representative of current market conditions. Furthermore, these numbers would imply that the S&P 500 is currently trading at almost three standard deviations away from its mean, which for many distribution is a highly improbable event. The Great Recession, quantitative easing, etc. may have changed the market significantly, but not to such a great extent.  The problem arises from the fact that security prices are usually non-stationary.. This means that the underlying distribution from which security prices are ""drawn"" shifts through time and space. For example, prices could be normally distributed in the 50's, then gamma distributed in the 60's because of a shock, then normally distributed again in the 70's. This implies that calculating summary statistics, e.g. mean, standard deviation, etc. are essentially meaningless for time periods in which prices could follow multiple distributions.  For this and other reasons, it's standard practice to look at the standard deviation of returns or differences instead of prices. I covered in detail the reasons for this and various procedures to use in another answer. In short, you can calculate the first difference for each period, which is merely the difference between the closing price of that period and the closing price of the previous period. This will usually give you a stationary process, from which you can obtain more meaningful values of the standard deviation, mean, etc.  Let's use the S&P500 as an example again. This time, however, I'm only using data from 1990 onwards, for the sake of simplicity (and to make the graphs a bit more manageable). The summary statistics look like this: and the graph looks like this; the mean is the central horizontal red line, and the top and bottom lines indicate one standard deviation above and below the mean, respectively.   As you can see, the graph seems to indicate that there were long periods in which the index was priced well outside this range. Although this could be the case, the graph definitely exhibits a trend, along with some seemingly exogenous shocks (see my linked answer).  Taking the first difference, however, yields these summary statistics: with a graph like this:  This looks a lot more reasonable. In periods of recession, the price appears much more volatile, and it breaches the +/- one standard deviation lines indicated on the graph.  This is only a simple summary, but using first differencing as part of the wider process of detrending/decomposing a time series is a good first step.  For some technical indicators, however, stationary isn't as relevant. This is the case for some types of moving averages and their associated indicators. Take Bollinger bands for instance. These are technical indicators that show a number of standard deviations above and below a moving average. Like any calculation of standard deviation, moving average, statistic, etc. they require data over a specified time period. The analyst chooses a certain number of historical periods, e.g. 20, and calculates the moving average for that many previous periods and the moving/rolling standard deviation for those same periods as well. The Bollinger bands represent the values a certain number of standard deviations away from the moving average at a given point in time. At this given point, you can calculate the value two standard deviations ""away from the value,"" but doing so still requires the historical stock price (or at least the historical moving average). If you're only given the price in isolation, you're out of luck.  Moving averages can indirectly sidestep some of the issues of stationarity I described above because it's straightforward to estimate a time series with a process built from a moving average (specifically, an auto-regressive moving average process) but the econometrics of time series is a topic for another day.  The Stata code I used to generate the graphs and summary statistics:" Standard Deviation is a mathematical term that is useful in many areas. It can be considered a measure of how tight the data points are to the average. If there is consistency in the measurement system, then a point that is two standard from the average can be considered an outlier. It doesn't even need to be time based. We can say that a child born weighing less than X pounds is more than 2 standard deviations below the average.  Using it to look at a price or an index value doesn't make a lot of sense because many expect there to be long term growth. For example you would never say that you will buy a new jacket for your child when they are two standard deviations above their average height. You can say you will buy or sell a financial instrument when the P/E ratio is 2 standard deviations from some average. It could be the average of the long term history, or the index, or the sector. You could do the same thing for earnings per share or many other business of financial statistics. A standard deviation calculated from a time series assumes that the measurement will normally stay withing some bounds. And that straying from those bounds is a sign of the right time to buy or sell.
The ETF price quoted on the stock exchange is in principle not referenced to NAV. The fund administrator will calculate and publish the NAV net of all fees, but the ETF price you see is determined by the market just like for any other security.  Having said that, the market will not normally deviate greatly from the NAV of the fund, so you can safely assume that ETF quoted price is net of relevant fees. The nature of options requires you to understand that they are essentially a bet. In one sense, so is investing in stocks. We imagine a bell curve (first mistake) with a median return at 10%/yr and a standard deviation of about 14%. Then we say that odds are that over some period of time a monte-carlo simulation can give us the picture of the likely returns.  Now, when you buy short term options, say one month or so, you are hoping the outcome is a rise in price that will yield some pretty high return, right?  There was a time I noticed a particular stock would move a large percent based on earnings. And earnings were a day before options expiration. So I'd buy the call that was just out of the money and if the surprise was up, I'd make 3-4X my money. But I was always prepared to lose it all and often did. I never called this investing.  I know of no recovery strategy. Sorry. "I strongly suggest you read up the Option Greeks. You can be right about a stocks price movement and still not make money b/c other factors come into play from time or volatility. For a ""free"" option hedge you can look at collars. Buying puts and selling calls to offset the debit you pay for the transaction. Ex: AAPL is 115, You buy the 110 puts and sell the 120 calls. This gives you a collar around he current price. Your hedged below 110 and can still participate in upside move to 120. Also look into time value. Time decays exponentially in the last 30 days. If you are long this hurts you, if you are short(selling) this is good. Be sure to take this into account. Delta: relation of the option to the underlying stock move on a .01-1 scale, .50 is ""normal."" Deep in the money options have higher deltas. It is possible other factors can offset this delta move. This is why people will lose money on earnings plays even though they are right.  EX: Say you buy an AAPL call at 120, earnings comes out and the stock goes to 121. Even though you are ""in the money"" your contract may still have less value than what you paid because of VOLATILITY collapse. The market place knows earnings move a stock and that is factored into the price of the options expected volatility. As mentioned watch out for dividend dates. Always be aware of dividend dates and earnings dates and if your contract is going to cover one of these events. Interest rates have an effect as well but since the Fed has near 0 rates there is little impact at the present. Though this could certainly change if the fed starts raising rates. Research the Black Scholes Pricing model. Whenever you trade always think about what the other guys is thinking. Sometimes we forget their is someone else on the other side of my trade that thinks essentially the exact opposite of me. Its a zero sum game. As far as choosing strikes you can look at calculating the At THe money straddle to see if the options are ""cheap"" [stock Price * Implied Volatility (for 30, 60, 90 days Depending on your holding period)* Sq root of days to expiration] / 19 (which is sq root of days/yr) Add and subtract this number to the current stock price to give you an approximate 1 standard deviation of expected price movement. Keeping with our example. AAPL at 115, lets say your formula spits out a 6; therefore price range is expected to be 109 to 121 for the time period. Helpful for selling options, I would sell the 122  call or the 108 puts. Hope this helps. Start small and get a feel for things." if I have a asset A with expected return of 100% and risk(measured by standard deviation) 1%, and asset B with expected return of 1% and risk 100%, would it be rational to put asset B into the portfolio ? No, because Modern Portfolio Theory would say that if there is another asset (B2) with the same (or higher) return but less risk (which you already have in asset A), you should invest in that. If those are the only two assets you can choose from, you would invest completely in Asset A. The point of diversification is that, so long as two assets aren't perfectly positively correlated (meaning that if one moves up the other always moves up), then losses in one asset will sometimes be offset by gains in another, reducing the overall risk. That is called a 'volume chart'. There are many interactive charts available for the purpose. Here is clear example.  (just for demonstration but this is for India only) 1) Yahoo Finance 2) Google Finance 3) And many more Usually, the stock volume density is presented together (below it) with normal price vs time chart. Note: There is a friendly site about topics like this. Quant.stackexchange.com. Think of checking it out. Let's suppose your friend gave your $100 and you invested all of it (plus your own money, $500) into one stock. Therefore, the total investment becomes $100 + $500 = $600. After few months, when you want to sell the stock or give back the money to your friend, check the percentage of profit/loss. So, let's assume you get 10% return on total investment of $600.  Now, you have two choices. Either you exit the stock entirely, OR you just sell his portion. If you want to exit, sell everything and go home with $600 + 10% of 600 = $660. Out of $660, give you friend his initial capital + 10% of initial capital. Therefore, your friend will get $100 + 10% of $100 = $110. If you choose the later, to sell his portion, then you'll need to work everything opposite. Take his initial capital and add 10% of initial capital to it; which is $100 + 10% of $100 = $110. Sell the stocks that would be worth equivalent to that money and that's it. Similarly, you can apply the same logic if you broke his $100 into parts. Do the maths. id like to start by saying youre still doing this yourself, and i dont actually have all the info required anyway, dont send it but  &gt;[3] Descriptive Statistical Measures: Provide a thorough discussion of the meaning and interpretation of the four descriptive &gt;statistical measures required in your analysis: (1) Arithmetic Mean, (2) Variance, (3) Standard Deviation and (4) Coefficient of &gt;Variation. For example, how are these measures related to each other? In order to develop this discussion, you may want to &gt;consult chapters 2 and 3 of your textbook. This topic is an important part of your report. can be easily interpreted, im guessing the mean is simply just the observed (and then projected stock price for future models) the standard deviation determines the interval in which the stock price fluctuates. so you have like a curve, and then on this curve theirs a bunch of normal distributions modeling the variance of the price plotted against the month  also the coefficient of variation is just r^2 so just read up on that and relate it to the meaning of it to the numbers you have  actually my stats are pretty rusty so make sure you really check into these things  but otherwise the formulas for part 4 is simple too. you can compare means of a certain month using certain equations, but there are different ones for certain situations  you can test for significance by comparing the differences of the means and if its outside of your alpha level then it probably means your company is significantly different from the SP index. (take mu of SP - mu of callaway)  you can also find more info on interpreting the two different coefficients your given if you look up comparing means of linear regression models or something One thing to keep in mind when calculating P/E on an index is that the E (earnings) can be very close to zero.  For example, if you had a stock trading at $100 and the earnings per share was $.01, this would result in a P/E of 10,000, which would dominate the P/E you calculate for the index.  Of course negative earnings also skew results. One way to get around this would be to calculate the average price of the index and the earnings per share of the index separately, and then divide the average price of the index by the average earnings per share of the index. Different sources calculate these numbers in different ways.  Some throw out negative P/Es (or earnings per share) and some don't.  Some calculate the price and earnings per share separate and some don't, etc... You'll need to understand how they are calculating the number in order to compare it to PEs of individual companies.