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
"He's calculating portfolio variance. The general formula for the variance of a portfolio composed of two securities looks like this:  where w_a and w_b are the weights of each stock in the portfolio and the sigmas represent the standard deviation/risk of each asset or portfolio.  In the case of perfect positive or negative correlation, applying some algebra to the formula relating covariance to the correlation coefficient (rho, the Greek letter that looks like ""p""):  tells us that the covariance we need in the original formula is simply the product of the standard deviations and the correlation coefficient (-1 in this case).  Combining that result with our original formula yields this calculation:  Technically we've calculated the portfolio's variance and not it's standard deviation/risk, but since the square root of 0 is still 0, that doesn't matter. The Wikipedia article on Modern Portfolio Theory has a section that describes the mathematical methods I used above. The entire article is worth a read, however." 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. "While derivative pricing models are better modeling reality as academia invests more into the subject, none sufficiently do. If, for example, one assumes that stock returns are lognormal for the purposes of pricing options like Black Scholes does, the only true dependent variable becomes log-standard deviation otherwise known as ""volatility"", producing the infamous ""volatility smile"" which disappears in the cases of models with more factors accounting for other mathematical moments such as mean, skew, and kurtosis, etc.  Still, these more advanced models are flawed, and suffer the same extreme time mispricing as Black Scholes.  In other words, one can model anything however one wants, but the worse the model, the stranger the results since volatility for a given expiration should be constant across all strikes and is with better models. In the case of pricing dividends, these can be adjusted for the many complexities of taxation, but the model becomes ever more complex and extremely computationally expensive for each eventuality.  Furthermore, with more complexity in any model, the likelihood of discovering a closed form in the short run is less. For equities in a low interest rate, not high dividend yield, not low volatility, low dividend tax environment, the standard swap pricing models will not provide results much different from one where a single low tax rate on dividends is assumed. If one is pricing a swap on equity outside of the bounds above, the dividend tax rate could have more of an effect, but for computational efficiency, applying a single assumed dividend tax rate would be optimal with D*(1-x), instead of D in a formula, where D is the dividend paid and x is the tax rate. In short, a closed form model is only as good as its assumptions, so if anomalies appear between the actual prices of swaps in the market and a swap model then that model is less correct than the one with smaller anomalies of the same type.  In other words, if pricing equity swaps without a dividend tax rate factored more closely matches the actual prices than pricing with dividend taxes factored then it could be assumed that pricing without a dividend tax factored is superior.  This all depends upon the data, and there doesn't seem to be much in academia to assist with a conclusion. If equity swaps do truly provide a tax advantage and both parties to a swap transaction are aware of this fact then it seems unlikely swap sellers wouldn't demand some of the tax advantage back in the form of a higher price.  A model is no defense since volatility curves persist despite what Black Scholes says they should be." Here's another attempt at explanation: it's basically because parabolas are flat at the bottom. Let me explain.  As you might know, the variance of the log stock price in Black Scholes is vol^2 * T, in other words, variance of the log stock price is linear in time to expiry. Now, that means that the standard deviation of your log stock price is square root in time. This is consequential.  For normally distributed random variables, in 68% of cases we end up within one standard deviation. So, basically, we expect our log stock price to be within something something times square root of T. So, if your stock has a vol of 16%, it'll be plus/minus 32% in 4 years, plus/minus 16% for one year, plus/minus 8% for 3m, plus/minus 4% for 3-ish weeks, and plus/minus 1% for a business day. As you see, the decay is slow at first, but much more rapid as we get closer.  How does the square root function look? It's a sideways parabola. As we come closer to zero, the slope of the square root function goes to infinity. (That is related to the fact that Brownian motion is almost surely no-where differentiable - it just shoots off with infinite slope, returning immediately, of course :-) Another way of looking at it is the old traders rule of thumb that an at-the-money option is worth approximately S * 0.4 * vol * sqrt(T). (Just do a Taylor expansion of Black Scholes). Again, you have the square root of time to expiry in there, and as outlined above, as we get closer to zero, the square root drops slowly at first, and then precipitously. How you use the metric is super important.   Because it subtracts cash, it does not represent 'value'.  It represents the ongoing financing that will be necessary if both the equity plus debt is bought by one person, who then pays himself a dividend with that free cash.   So if you are Private Equity, this measures your net investment at t=0.5, not the price you pay at t=0.  If you are a retail investor, who a) won't be buying the debt, b) won't have any control over things like tax jurisdictions, c) won't be receiving any cash dividend, etc etc .... the metric is pointless. Ah, pardon me, so it's not *either* 10x return or zero, but also includes points in between there?  Is it path dependent? Do you have any history on the asset?  The usual crutches for dealing with unknown probabilities are using risk neutrality or arbitrage pricing, but if the market is inefficient then that will be an estimation at best. "You can calculate the ""return on investment"" using libreoffice, for example. Look at the xirr function. You would have 2 columns, one a list of dates (ie the dates of the deposits or dividends or whatever that you want to track, the last entry would be today's date and the value of the investment today. The xirr function calculates the internal rate of return for you. If you add money to the account, and the current value includes the original investment and the added funds, it will be difficult to calculate the ROI. If you add money by purchasing additional shares (or redepositing dividends by buying additional shares), and you only want to track the ROI of the initial investment (ignoring future investments), you would have to calculate the current value of all of the added shares (that you don't want to include in the ROI) and subtract that value from the current total value of the account. But, if you include the dates and values of these additional share purchases in the spreadsheet, xirr will calculate the overall IRR for you." Set your xirr formula to a very tall column, leaving lots of empty rows for future additions. In column C, instead of hardcoding the value, use a formula that tests if it's the current bottom entry, like this: =IF(ISBLANK(A7),-C6, C6) If the next row has no date entered (yet), then this is the latest value, and make it negative. Now, to digress a bit, there are several ways to measure returns. I feel XIRR is good for individual positions, like holding a stock, maybe buying more via DRIP, etc. For the whole portfolio it stinks. XIRR is greatly affected by timing of cash flows. Steady deposits and no withdrawals dramatically skew the return lower. And the opposite is true for steady withdrawals. I prefer to use TWRR (aka TWIRR). Time Weighted Rate of Return. The word 'time' is confusing, because it's the opposite. TWRR is agnostic to timing of cashflows. I have a sample Excel spreadsheet that you're welcome to steal from: http://moosiefinance.com/static/models/spreadsheets.html (it's the top entry in the list). Some people prefer XIRR. TWRR allows an apples-to-apples comparison with indexes and funds. Imagine twin brothers. They both invest in the exact same ideas, but the amount of cash deployed into these ideas is different, solely because one brother gets his salary bonus annually, in January, and the other brother gets no bonus, but has a higher bi-weekly salary to compensate. With TWRR, their percent returns will be identical. With XIRR they will be very different. TWRR separates out investing acumen from the happenstance timing of when you get your money to deposit, and when you retire, when you choose to take withdrawals. Something to think about, if you like. You might find this website interesting, too: http://www.dailyvest.com/