Standard Deviation with Asset Prices?
You can use google docs to create a spreadsheet. In field A2, I put Google will load the prices into the sheet. At that point, I add the following into C12, then copy that line all the way down to the botton of column C. You can find my spreadsheet here. It calculates the moving 10 day standard deviation as a percentage of average price for that time period. "Almost every online datasources provide historical prices on given company / index's performance; from this, you can easily calculate ""standard deviation"" by yourself. With that said, standard deviation presumes a fixed set of data. Most public corporations have data spanning multiple decades, during which a number of things have changed: For these reasons, I have doubts on simplistic measures, such as ""standard deviation"" measuring any reality on the underlying vehicle. Professional investors usually tend to more time-point data, such as P/E ratio." "Some years ago, two ""academics,"" Ibbotson and Sinquefield did these calculations. (Roger) Ibbotson, is still around. So Google Roger Ibbotson, or Ibbotson Associates. There are a number of entries so I won't provide all the links." James Roth provides a partial solution good for stock picking but let's speed up process a bit, already calculated historical standard deviations: Ibbotson, very good collection of research papers here, examples below Books
"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." This link does it ok:  http://investexcel.net/1979/calculate-historical-volatility-excel/ Basically, you calculate percentage return by doing stock price now / stock price before.  You're not calculating the rate of return hence no subtraction of 100%.  The standard is to do this on a daily basis: stock price today / stock price yesterday. The most important and most misunderstood part is that you now have to analyze the data geometrically not arithmetically.  To easily do this, convert all percentage returns with the natural log, ln(). Next, you take the standard deviation of all of those results, and apply exp().  This answers the title of your question. For convenience's sake, it's best to annualize since volatility (implied or statistical) is now almost always quoted annualized.  There are ~240 trading days each year.  You multiply your stdev() result by (240 / # of trading days per return) ^ 0.5, so if you're doing this for daily returns, multiply the stdev() result by 240^0.5; if you were doing it weekly, you'd want to multiply by (240 / ~5)^0.5; etc.  This is your number for sigma.  This answers the intent of your question. For black-scholes, you do not convert anything back with exp(); BS is already set up for geometric analysis, so you need to stay there. The reason why analysis is done geometrically is because the distribution of stock returns is assumed to be lognormal (even though it's really more like logLaplace). Since the market is in general rather efficient, the price of the ETF will most of the time reflects the prices of the underlying securities. However, there are times when ETF price deviates from its fundamental value. This is called trading at a premium/discount. This creates arbitrage opportunity, which is actually being studied in finance literature. Intuitive? I doubt it. Derivatives are not the simplest thing to understand.  The price is either in the money or it isn't. (by the way, exactly 'at the money' is not 'in the money.') An option that's not in the money has time value only. As the price rises, and the option is more and more in the money, the time value drops. We have a $40 stock. It makes sense to me that a $40 strike price is all just a bet the stock will rise, there's no intrinsic value. The option prices at about $4.00 for one year out, with 25% volatility. But the strike of $30 is at $10.68, with $10 in the money and only .68 in time premium. There's a great calculator on line to tinker with.  Volatility is a key component of options trading. Think about it. If a stock rises 5%/yr but rarely goes up any more or less, just steady up, why would you even buy an option that was even 10% out of the money? The only way I can describe this is to look at a bell curve and how there's a 1/6 chance the event will be above one standard deviation. If that standard deviation is small, the chance of hitting the higher strikes is also small.  I wrote an article Betting on Apple at 9 to 2 in which I describe how a pair of option trades was set up so that a 35% rise in Apple stock would return 354% and Apple had two years to reach its target. I offer this as an example of options trading not being theory, but something that many are engaged in. What I found curious about the trade was that Apple's volatility was high enough that a 35% move didn't seem like the 4.5 to 1 risk the market said it was. As of today, Apple needs to rise 13% in the next 10 months for the trade to pay off. (Disclosure - the long time to expiration was both good and bad, two years to recover 35% seemed reasonable, but 2 years could bring anything in the macro sense. Another recession, some worldwide event that would impact Apple's market, etc. The average investor will not have the patience for these long term option trades.) "P/E alone would not work very well. See for example http://www.hussmanfunds.com/html/peak2pk.htm and http://www.hussmanfunds.com/rsi/profitmargins.htm (in short, P/E is affected too much by cyclical changes in profit margins, or you might say: booms inflate the E beyond sustainable levels, thus making the P/E look more favorable than it is). Here's a random blog post that points to Schiller's normalized earnings measure: http://seekingalpha.com/article/247257-s-p-500-is-expensive-using-normalized-earnings I think even Price to Sales is supposed to work better than P/E for predicting 10-year returns on a broad index, because it effectively normalizes the margins. (Normalized valuation explains the variance in 10-year returns better than the variance in 1-year returns, I think I've read; you can't rely on things ""reverting to mean"" in only 1 year.) Another issue with P/E is that E is more subject to weird accounting effects than for example revenues. For example whether stock compensation is expensed or one-time write-offs are included or whatever can mean you end up with an economically strange earnings number. btw, a simple way to do what you describe here would be to put a chunk of money into funds that vary equity exposure. For example John Hussman's fund has an elaborate model that he uses to decide when to hedge. Say you invest 40% bonds, 40% stocks, and 20% in Hussman Strategic Growth. When Hussman fully hedges his fund, you would effectively have 40% in stocks; and when he fully unhedges it, you would have 60% in stocks. This isn't quite the whole story; he also tries to pick up some gains through stock picking, so when fully hedged the fund isn't quite equivalent to cash, more like a market-neutral fund. (For Hussman Funds in particular, he's considered stocks to be overvalued for most of the last 15 years, and the fund is almost always fully hedged, so you'd want to be comfortable with that.) There are other funds out there doing similar stuff. There are certainly funds that vary equity exposure though most not as dramatically as the Hussman fund. Some possibilities might be PIMCO All-Asset All-Authority, PIMCO Multi-Asset, perhaps. Or just some value-oriented funds with willingness to deviate from benchmarks. Definitely read the prospectus on all these and research other options, I just thought it would be helpful to mention a couple of specific examples. If you wanted to stick to managing ETFs yourself, Morningstar's premium service has an interesting feature where they take the by-hand bottom-up analysis of all the stocks in an ETF, and use that to calculate an over- or under-valuation ratio for the ETF. I don't know if the Morningstar bottom-up stuff necessarily works; I'm sure they make the ""pro"" case on their site. On the ""con"" side, in the financial crisis bubble bursting, they cut their valuation on many companies and they had a high valuation on a lot of the financials that blew up. While I haven't run any stats and don't have the data, in several specific cases it looked like their bottom-up analysis ended up assuming too-high profit margins would continue. Broad-brush normalized valuation measures avoided that mistake by ignoring the details of all the individual companies and assuming the whole index had to revert to mean. If you're rich, I think you can hire GMO to do a varied-equity-exposure strategy for you (http://www.gmo.com/America/).  You could also look at the ""fundamental indexing"" ETFs that weight by dividends or P/E or other measures of value, rather than by market cap. The bottom line is, there are lots of ways to do tactical asset allocation. It seems complex enough that I'm not sure it's something you'd want to manage yourself. There are also a lot of managers doing this that I personally am not comfortable with because they don't seem to have a discipline or method that they explain well enough, or they don't seem to do enough backtesting and math, or they rely on macroeconomic forecasts that probably aren't reliable, or whatever. All of these tactical allocation strategies are flavors of active management. I'm most comfortable with active management when it has a fairly objective, testable, and logical discipline to it, such as Graham&Buffett style value investing, Hussman's statistical methods, or whatever it is.  Many people will argue that all active management is bad and there's no way to distinguish among any of it. I am not in that camp, but I do think a lot of active managers are bad, and that it's pretty hard to distinguish among them, and I think active management is more likely to help with risk control than it is to help with beating the market. Still you should know (and probably already do know, but I'll note for other readers) that there's a strong argument smart people make that you're best off avoiding this whole line of tactical-allocation thinking and just sticking to the pure cap-based index funds." &gt; So: what do i do to have the monthly %change? I was thinking (last day of the mont CP - 1st day of the month OP)/ 1st day of the mont opening price.  No, use the same day (usually month end) of each month (i.e. December 31 vs. January 31). Use closing prices only.   Keep in mind, it may make more mathematical  sense to use LN (natural logs) to determine %-change and standard deviation.   The simplest way to compare the riskiness of each is just to compare St. Dev. You can, of course, go into more detail.   If you want to impress your professor, look up the efficient frontier and make one for each portfolio. "From the Vanguard page -  This seemed the easiest one as S&P data is simple to find. I use MoneyChimp to get -  which confirms that Vanguard's page is offering CAGR, not arithmetic Average. Note: Vanguard states ""For U.S. stock market returns, we use the Standard & Poor's 90 from 1926 through March 3, 1957,"" while the Chimp uses data from Nobel Prize winner, Robert Shiller's site." Annualize quarterly returns:      AR = (1+QR)^4  Where *QR* is a decimal return, e.g. 0.05.  Standard deviations are similar:      Annual SD = SD * sqrt(T)  If you have quarterly deviations, *T=4*, if you have daily, *T=252*, etc.  As an aside, for work with money riding on it, it is *not* okay to aggregate standard deviations if there's autocorrelation amongst observations at a smaller time scale. Volatility is often quoted this way and that's fine, but it is dangerous to do any sort of risk management with this and you'll require more due diligence. It's a good enough approximation for napkin math, though.