How can I calculate the volatility(standard deviation) of a stock price? and/or ROI (return on investment) of a stock?
"the ""how"" all depends on your level of computer savvy. Are you an Excel spreadsheet user or can you write in programming languages such as python? Either approach have math functions that make the calculation of ROI and Volatility trivial. If you're a python coder, then look up ""pandas"" (http://pandas.pydata.org/) - it handles a lot of the book-keeping and downloading of end of day equities data. With a dozen lines of code, you can compute ROI and volatility." Use the Black-Scholes formula. If you know the current price, an options strike price, time until expiration, and risk-free interest rate, then knowing the market price of the option will tell you what the market's estimation of the volatility is. This does rely on a few assumptions, such as Gaussian random walk, but those are reasonable assumptions for most stocks. You can also get a list of past stock prices, put them in Excel, and ask Excel to calculate the standard deviation with stdev.s(), but that gives you the past volatility. The market's estimate of future volatility is more relevant. ROI and volatility should be calculated over a representative period of time, for example 3 or 5 years, depending on data availability.  The ROI is simple, for example, over 5 years:- For the 5 year annualised volatility you can refer to the ESMA SRRI methodology. Box 1 (page 3)  m is the annualisation factor. Stock volatility calculated from weekly data should not be compared with volatility calculated from monthly data. Also, for reference: How to Calculate your Portfolio's Rate of Return
My level of analysis is not quite that advanced. Can you share what that would show and why that particular measure is the one to use?  I've run regression on prices between the two. VIX prices have no correlation to the s&amp;p500 prices. Shouldn't true volatility result in the prices (more people putting options on the VIX during the bad times and driving that price up) correlate to the selloff that occurs within the S&amp;P500 during recessions and other events that would cause significant or minor volatility? My r2 showed no significance within a measurement of regression within Excel.  But, *gasp* I could be wrong, but would love to learn more about better ways of measurement :) 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. "Standard deviation from Wikipedia : In statistics and probability theory, the standard deviation   (represented by the Greek letter sigma, σ) shows how much variation or   dispersion from the average exists.1 A low standard deviation   indicates that the data points tend to be very close to the mean (also   called expected value); a high standard deviation indicates that the   data points are spread out over a large range of values. In the case of stock returns, a lower value would indicate less volatility while a higher value would mean more volatility, which could be interpreted as high much change does the stock's price go through over time. Mean would be interpreted as if all the figures had to be the same, what would they be? So if a stock returns 10% each year for 3 years in a row, then 10% would be the mean or average return. Now, it is worth noting that there are more than a few calculations that may be done to derive a mean. First, there is the straight forward sum and division by the number of elements idea. For example, if the returns by year were 0%, 10%, and 20% then one may take the sum of 30% and divide by 3 to get a simple mean of 10%. However, some people would rather look at a Compound Annual Growth Rate which in this case would mean multiplying the returns together so 1*(1+.1)*(1+.2)=1.1*1.2=1.32 or 32% since there is some compounding here. Now, instead of dividing a cubic root is taken to get approximately 9.7% average annual return that is a bit lower yet if you compound it over 3 years it will get up to 32% as 10% compounded over 3 years would be 33.1% as (1.1)^3=1.331. Sharpe Ratio from Investopedia: A ratio developed by Nobel laureate William F. Sharpe to measure   risk-adjusted performance. The Sharpe ratio is calculated by   subtracting the risk-free rate - such as that of the 10-year U.S.   Treasury bond - from the rate of return for a portfolio and dividing   the result by the standard deviation of the portfolio returns. Thus, this is a way to think about given the volatility how much better did the portfolio do than the 10 year bond. R-squared, Alpha and Beta: These are all around the idea of ""linear regression"" modelling. The idea is to take some standard like say the ""S & P 500"" in the case of US stocks and see how well does the portfolio follow this and what if one were to use a linear model are the multipliers and addition components to it. R-squared can be thought of it as a measure as to how good is the fit on a scale of 0 to 1. An S & P 500 index fund may well have an R-squared of 1.00 or 0.99 to the index as it will track it extremely closely while other investments may not follow that well at all. Part of modern portfolio theory would be to have asset classes that move independently of each other and thus would have a lower R-squared so that the movement of the index doesn't indicate how an investment will do. Now, as for alpha and beta, do you remember the formula for a line in slope-intercept form, where y is the portfolio's return and x is the index's return: y=mx+b In this situation m is beta which is the multiple of the return, and b is the alpha or how much additional return one gets without the multiple. Going back to an index fund example, m will be near 1 and b will be near 0 and there isn't anything being done and so the portfolio's return computed based on the index's return is simply y=x. Other mutual funds may try to have a high alpha as this is seen as the risk-free return as there isn't the ups and downs of the market here. Other mutual funds may go for a high beta so that there is volatility for investors to handle." "Certainly no one knows in advance how much a stock is going to swing around. However, there are measures of how much it has swung around in the past, and there are people who will estimate the probability. First of all, there's a measure of an individual stock's volatility, commonly referred to as ""beta"". A stock with a beta of 1 tends to rise and fall about as much as the market at large. A stock with a beta of 2, in the meantime, would rise 10% when the market is up 5%. These are, of course, historical averages. See Wikipedia: http://en.wikipedia.org/wiki/Beta_(finance) Secondly, you can get an implied measure of volatility expectations by looking at options pricing. If a stock is particularly volatile, the chance of a big price move will be baked into the price of the stock options. (Note also that other things affect options pricing, such as the time value of money.) For an options-based measure of the volatility of the whole market, see the Volatility Index aka the ""Fear Gauge"", VIX.  Wikipedia: http://en.wikipedia.org/wiki/VIX Chart: http://finance.yahoo.com/q?s=%5EVIX Looking at individual stocks as a group (and there's an oxymoron for you), individual stocks are definitely much more likely to have big moves than the market. Besides Netflix, consider the BP oil spill, or the Tokyo Electric Power Company's Fukushima incident (yow!). I don't have any detailed statistics on quantitatively how much, mind you, but in application, a standard piece of advice says not to put more than 5% of your portfolio in a single company's stock. Diversification protects you. (Alternatively, if you're trying to play Mr. Sophisticated Stock-Picker instead of just buying an index fund, you can also buy insurance through stock options: hedging your bets. Naturally, this will eat up part of your returns if your pick was a good one)." "Volume is really only valuable when compared to some other volume, either from a historical value, or from some other stock.  The article you linked to doesn't provide specific numbers for you to evaluate whether volume is high or low. Many people simply look at the charts and use a gut feel for whether a day's volume is ""high"" or ""low"" in their estimation. Typically, if a day's volume is not significantly taller than the usual volume, you wouldn't call it high. The same goes for low volume. If you want a more quantitative approach, a simple approach would be to use the normal distribution statistics: Calculate the mean volume and the standard deviation. Anything outside of 1.5 to 2.0 standard deviations (either high or low) could be significant in your analysis. You'll need to pick your own numbers (1.5 or 2.0 are just numbers I pulled out of thin air.) It's hard to read anything specific into volume, since for every seller, there's a buyer, and each has their reasons for doing so. The article you link to has some good examples of using volume as a basis for strengthening conclusions drawn using other factors." "As I understand it, Implied Volatility represents the expected gyrations of an options contract over it's lifetime.  No, it represents that expected movement of the underlying stock, not the option itself.  Yes, the value of the option will move roughly in the same direction the value of the stock, but that's not what IV is measuring. I even tried staring at the math behind the Options pricing model to see if that could make more sense for me but that didn't help. That formula is correct for the Black-Scholes model - and it is not possible (or at least no one has done it yet) to solve for s to create a closed-form equation for implied volatility.  What most systems do to calculate implied volatility is plug in different values of s (standard deviation) until a value for the option is found that matches the quoted market value ($12.00 in this example).  That's why it's called ""implied"" volatility - the value is implied from market prices, not calculated directly. The thing that sticks out to me is that the ""last"" quoted price of $12 is outside of the bid-ask spread of $9.20 to $10.40, which tells me that the underlying stock has dropped significantly since the last actual trade.   If the Implied Vol is calculated based on the last executed trade, then whatever algorithm they used to solve for a volatility that match that price couldn't find a solution, which then choose to show as a 0% volatility.   In reality, the volatility is somewhere between the two neighbors of 56% and 97%, but with such a short time until expiry, there should be very little chance of the stock dropping below $27.50, and the value of the option should be somewhere around its intrinsic value (strike - stock price) of $9.18." "A stock, at its most basic, is worth exactly what someone else will pay to buy it right now (or in the near future), just like anything else of value. However, what someone's willing to pay for it is typically based on what the person can get from it. There are a couple of ways to value a stock. The first way is on expected earnings per share, most of would normally (but not always) be paid in dividends. This is a metric that can be calculated based on the most recently reported earnings, and can be estimated based on news about the company or the industry its in (or those of suppliers, likely buyers, etc) to predict future earnings. Let's say the stock price is exactly $100 right now, and you buy one share. In one quarter, the company is expected to pay out $2 per share in dividends. That is a 2% ROI realized in 3 months. If you took that $2 and blew it on... coffee, maybe, or you stuffed it in your mattress, you'd realize a total gain of $8 in one year, or in ROI terms an annual rate of 8%. However, if you reinvested the money, you'd be making money on that money, and would have a little more. You can calculate the exact percentage using the ""future value"" formula. Conversely, if you wanted to know what you should pay, given this level of earnings per share, to realize a given rate of return, you can use the ""present value"" formula. If you wanted a 9% return on your money, you'd pay less for the stock than its current value, all other things being equal. Vice-versa if you were happy with a lesser rate of return. The current rate of return based on stock price and current earnings is what the market as a whole is willing to tolerate. This is how bonds are valued, based on a desired rate of return by the market, and it also works for stocks, with the caveat that the dividends, and what you'll get back at the ""end"", are no longer constant as they are with a bond. Now, in your case, the company doesn't pay dividends. Ever. It simply retains all the earnings it's ever made, reinvesting them into doing new things or more things. By the above method, the rate of return from dividends alone is zero, and so the future value of your investment is whatever you paid for it. People don't like it when the best case for their money is that it just sits there. However, there's another way to think of the stock's value, which is it's more core definition; a share of the company itself. If the company is profitable, and keeps all this profit, then a share of the company equals, in part, a share of that retained earnings. This is very simplistic, but if the company's assets are worth 1 billion dollars, and it has one hundred million shares of stock, each share of stock is worth $10, because that's the value of that fraction of the company as divided up among all outstanding shares. If the company then reports earnings of $100 million, the value of the company is now 1.1 billion, and its stock should go up to $11 per share, because that's the new value of one ten-millionth of the company's value. Your ROI on this stock is $1, in whatever time period the reporting happens (typically quarterly, giving this stock a roughly 4% APY). This is a totally valid way to value stocks and to shop for them; it's very similar to how commodities, for instance gold, are bought and sold. Gold never pays you dividends. Doesn't give you voting rights either. Its value at any given time is solely what someone else will pay to have it. That's just fine with a lot of people right now; gold's currently trading at around $1,700 an ounce, and it's been the biggest moneymaker in our economy since the bottom fell out of the housing market (if you'd bought gold in 2008, you would have more than doubled your money in 4 years; I challenge you to find anything else that's done nearly as well over the same time). In reality, a combination of both of these valuation methods are used to value stocks. If a stock pays dividends, then each person gets money now, but because there's less retained earnings and thus less change in the total asset value of the company, the actual share price doesn't move (much). If a stock doesn't pay dividends, then people only get money when they cash out the actual stock, but if the company is profitable (Apple, BH, etc) then one share should grow in value as the value of that small fraction of the company continues to grow. Both of these are sources of ROI, and both are seen in a company that will both retain some earnings and pay out dividends on the rest." "First, to mention one thing - better analysis calls for analyzing a range of outcomes, not just one; assigning a probability on each, and comparing the expected values. Then moderating the choice based on risk tolerance. But now, just look at the outcome or scenario of 3% and time frame of 2 days. Let's assume your investable capital is exactly $1000 (multiply everything by 5 for $5,000, etc.). A. Buy stock: the value goes to 103; your investment goes to $1030; net return is $30, minus let's say $20 commission (you should compare these between brokers; I use one that charges 9.99 plus a trivial government fee). B. Buy an call option at 100 for $0.40 per share, with an expiration 30 days away (December 23). This is a more complicated. To evaluate this, you need to estimate the movement of the value of a 100 call, $0 in and out of the money, 30 days remaining, to the value of a 100 call, $3 in the money, 28 days remaining. That movement will vary based on the volatility of the underlying stock, an advanced topic; but there are techniques to estimate that, which become simple to use after you get the hang of it. At any rate, let's say that the expected movement of the option price in this scenario is from $0.40 to $3.20. Since you bought 2500 share options for $1000, the gain would be 2500 times 2.8 = 7000. C. Buy an call option at 102 for $0.125 per share, with an expiration 30 days away (December 23). To evaluate this, you need to estimate the movement of the value of a 102 call, $2 out of the money, 30 days remaining, to the value of a 102 call, $1 in the money, 28 days remaining. That movement will vary based on the volatility of the underlying stock, an advanced topic; but there are techniques to estimate that, which become simple to use after you get the hang of it. At any rate, let's say that the expected movement of the option price in this scenario is from $0.125 to $ 1.50. Since you bought 8000 share options for $1000, the gain would be 8000 times 1.375 = 11000. D. Same thing but starting with a 98 call. E. Same thing but starting with a 101 call expiring 60 days out. F., ... Etc. - other option choices. Again, getting the numbers right for the above is an advanced topic, one reason why brokerages warn you that options are risky (if you do your math wrong, you can lose. Even doing that math right, with a bad outcome, loses). Anyway you need to ""score"" as many options as needed to find the optimal point. But back to the first paragraph, you should then run the whole analysis on a 2% gain. Or 5%. Or 5% in 4 days instead of 2 days. Do as many as are fruitful. Assess likelihoods. Then pull the trigger and buy it. Try these techniques in simulation before diving in! Please! One last point, you don't HAVE to understand how to evaluate projected option price movements if you have software that  does that for you. I'll punt on that process, except to mention it. Get the general idea? Edit P.S. I forgot to mention that brokers need love for handling Options too. Check those commission rates in your analysis as well." Aswath Damodaran's [Investment Valuation 3rd edition](http://www.amazon.com/Investment-Valuation-Techniques-Determining-University/dp/1118130731/ref=sr_1_12?ie=UTF8&amp;qid=1339995852&amp;sr=8-12&amp;keywords=aswath+damodaran) (or save money and go with a used copy of the [2nd edition](http://www.amazon.com/gp/offer-listing/0471414905/ref=dp_olp_used?ie=UTF8&amp;condition=used))  He's a professor at Stern School of Business. His [website](http://pages.stern.nyu.edu/~adamodar/) and [blog](http://aswathdamodaran.blogspot.com/) are good resources as well. [Here is his support page](http://pages.stern.nyu.edu/~adamodar/New_Home_Page/Inv3ed.htm) for his Investment Valuation text. It includes chapter summaries, slides, ect. If you're interested in buying the text you can get an idea of what's in it by checking that site out. For implied volatility it is okey to use Black and scholes but what to do with the historical volatility which carry the effect of past prices as a predictor of future prices.And then precisely the conditional historical volatility.i suggest that you must go with the process like, for stock returns  1) first download stock prices into excel sheet 2) take the natural log of (P1/po) 3) calculate average of the sample  4) calculate square of (X-Xbar) 5) take square root of this and you will get the standard deviation of your required data. "I looked at data from Sept 2010 to present: Standard deviation is what shows the spread shape of returns over time, and it meanS that about 2/3 of the time, AAPL return was within +/- 1.65 higher/lower than the daily average return which was .21 %. Not sure where to go with this except to suggest that in fact, AAPL is more volatile than the S&P and even another random tech company. With time, I'd probably come up with a list of stock more volatile. I know that when I look at a list of stocks I track on Yahoo, there are always a few that are just as volatile on a given day.  Excel makes the above analysis easy to do for a given stock, and it's actually an interesting exercise, at least for me. Disclaimer - the shape of stock returns is not a bell curve, and STdev is just a best fit.  Edit - given more time to tinker on excel, it would be interesting to see how the stock's volatility tracked over the years, did it increase or does it feel that way due to the high price? A $20 swing on a $600 stock is the same as a $2 swing on a $60 stock, yet ""up $20"" sounds huge." "The key to evaluating book value is return on equity (ROE). That's net profit divided by book value.  The ""value"" of book value is measured by the company's ROE (the higher the better). If the stock is selling below book value, the company's assets aren't earning enough to satisfy most investors. Would you buy a CD that was paying, say two percentage points below the going rate for 100 cents on the dollar? Probably not. You might be willing to buy it only by paying 2% less per year, say 98 cents on the dollar for a one year CD. The two cent discount from ""book value"" is your compensation for a low ""interest"" rate." Risk and return always go hand by hand.*  Risk is a measure of expected return volatility. The best investment at this stage is a good, easy to understand but thorough book on finance. *Applies to efficient markets only. You could take these definitions from MSCI as an example of how to proceed.  They calculate price indices (PR) and total return indices (including dividends).  For performance benchmarks the net total return (NR) indices are usually the most relevant. In your example the gross total return (TR) is 25%. From the MSCI Index Defintions page :- The MSCI Price Indexes measure the price performance of markets   without including dividends. On any given day, the price return of an   index captures the sum of its constituents’ free float-weighted market   capitalization returns. The MSCI Total Return Indexes measure the price performance of markets   with the income from constituent dividend payments. The MSCI Daily   Total Return (DTR) Methodology reinvests an index constituent’s   dividends at the close of trading on the day the security is quoted   ex-dividend (the ex-date). Two variants of MSCI Total Return Indices are calculated: With Gross Dividends: Gross total return indexes reinvest as much as possible of a company’s   dividend distributions. The reinvested amount is equal to the total   dividend amount distributed to persons residing in the country of the   dividend-paying company. Gross total return indexes do not, however,   include any tax credits. With Net Dividends: Net total return indexes reinvest dividends after the deduction of   withholding taxes, using (for international indexes) a tax rate   applicable to non-resident institutional investors who do not benefit   from double taxation treaties. "A minor tangent. One can claim the S&P has a mean return of say 10%, and standard deviation of say 14% or so, but when you run with that, you find that the actual returns aren't such a great fit to the standard bell curve. Market anomalies producing the ""100-year flood"" far more often than predicted over even a 20 year period. This just means that the model doesn't reflect reality at the tails, even if the +/- 2 standard deviations look pretty. This goes for the Black-Sholes (I almost abbreviated it to initials, then thought better, I actually like the model) as well. The distinction between American and European is small enough that the precision of the model is wider than the difference of these two option styles. I believe if you look at the model and actual pricing, you can determine the volatility of a given stock by using prices around the strike price, but when you then model the well out of money options, you often find the market creating its own valuation."