What is the standard deviation and mean return of oil?
Oil as a commodity or investing in oil companies as a stock?  As a commodity, I'd recommend none. The article Commodities – They Have (Almost) No Place in Your Portfolio and The Case Against Commodities explain why commodities are not good investments. Your question is a moving target. And my answer will be subject to revision. I disagree with the votes to close, as you are asking (imho) what role commodities and specifically oil, play in one's asset allocation. Right? How much may be opinion, but there's a place to ask if.  I'm looking at this chart, and thinking, long term, the real return is zero. The discussion regarding gold has been pretty exhausted. For oil, it's not tough to make the case that it will fluctuate, but long term, there's no compelling reason to believe its price will rise any faster than inflation over the really long term.
There is no right way but changing your methodology to suit your situation is   a problem. They were happy to use a 4 years period during the crazy times to lower the VAR and then switch to 1 year afterwards to do the same. It is picking and choosing your measures to suit the situation and that is statistical heresy. While there may not be a right way to measure VAR choosing the measure that is suits your situation is bad methodology.    And of course there is such a thing as bad statistical methodology, you see it everyday.   I also pointed out above that it vairies from bank to bank what confidence interval you use. "Wow, this analysis really surprised me. Very complete and useful, but i think my teacher request was easier. He just said: ""Try to build a diversified portfolio. Then try to add a commodity (like silver or gold) and understand how the risk vary introducing an asset like this."" So, i'm basically making a stocks portfolio and i'm calculating its expected return and risk. (for example 40%FB, 10%JNJ, 20%GS, 10%F and 20%MCD) then i'm adding GLD (so now i have something like 20%FB, 10%JNJ, 10%GS, 10%F and 20%MCD 30%GLD) and i'm actually making an excel spreadsheet where i calculate all the: -Expected returns -St Deviation -Covariance  At the end i compare the returns and the risks on the 2 different portfolios." "This page from simplestockinvesting.com gives details of total returns for the S&P500 for each decade over the last 60 years, including total returns for the entire 60 year period. It is important to understand that, from an investors point of view, the total return includes both the change in index value (capital gain) plus dividends received.  This total then needs to be adjusted for inflation to give the ""total real return"". As noted in the analysis provided, 44% of the total return from the S&P500 over the last 80 years comes from dividends.  For the DowJones30, this site provides a calculator for total returns and inflation adjusted total returns for user selected periods. Finding comparable analysis for the NASDAQ market is more difficult.  The NASDAQ market site provides gross values for total returns over fixed periods, but you will then need to do the arithmetic to calculate the equivalent average annual total returns.  No inflation adjusted values for ""real"" returns are provided, so again you will need to combine inflation data from elsewhere and do the arithmetic." "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." This has zero impact on spot prices or anywhere on a reasonably scaled forward curve.  Reddit can be such an echo chamber spouting bullshit sometimes.  Yes, it'll eventually reduce oil use, but it's at least 20 years down the line.  The whole issue with the oil market these days is US tight oil production being able to ramp up quickly and reduce costs. "My question is, using previous data how do I calculate my returns? ""Stupid"" is the person who does not ask. Better to have visited first, but even asking after the fact will get you an education, at a very low cost.  You would only see those returns had you invested at the beginning of the period advertised. ""Past results are not a guarantee of future returns.""  Since we have no idea where you are in life, there's little advice I can give you except to invite you to learn. You can easily spend 100 hours on this Stack reading advice on the beginning investor, and every stage after that. We all needed to start somewhere, and in your case, just showing up was a great first step." Yes E[x] is expected value of x. E[x|y] = expected value of x, given y. c, k are some constants Let E[s_{n+1}|s_n=c] = c, but if  E[s_{n+1}|s_n,s_{n-1},...,s_{n-m}] ->some constant k as m->\infty (call this equation 1) then rebalancing makes sense. Notes: "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." "This is the best tl;dr I could make, [original](https://www.bloomberg.com/news/articles/2017-06-19/oil-s-slide-stalls-as-investors-weigh-stockpiles-against-libya) reduced by 70%. (I'm a bot) ***** &gt; The amount of oil stored in tankers reached a 2017 high of 111.9 million barrels earlier this month, according to Paris-based tracking company Kpler SAS. Oil has slipped below $45 a barrel as supplies in the U.S. remain plentiful and drillers continue to add rigs, raising concerns output cuts by the Organization of Petroleum Exporting Countries and allies including Russia won&amp;#039;t succeed in draining bloated stockpiles.  &gt; Crude stockpiles remain more than 100 million barrels above the five-year average, according to data from the EIA. American production has climbed to 9.33 million barrels a day through June 9, near the highest since August 2015.  &gt; Libya is pumping about 900,000 barrels a day, according to a person with direct knowledge of the matter, who asked not to be identified for lack of authority to speak to the media.   ***** [**Extended Summary**](http://np.reddit.com/r/autotldr/comments/6ietvj/oil_prices_are_tumbling_more_than_2_toward_43/) | [FAQ](http://np.reddit.com/r/autotldr/comments/31b9fm/faq_autotldr_bot/ ""Version 1.65, ~148648 tl;drs so far."") | [Feedback](http://np.reddit.com/message/compose?to=%23autotldr ""PM's and comments are monitored, constructive feedback is welcome."") | *Top* *keywords*: **barrel**^#1 **percent**^#2 **August**^#3 **U.S.**^#4 **Oil**^#5" "Option 1 is out. There are no ""safe returns"" that make much money. Besides, if a correction does come along how will you know when to invest? There is no signal that says when the bottom is reached, and you emotions could keep you from acting. Option 2 (dollar cost averaging) is prudent and comforting. There are always some bargains about. You could start with an energy ETF or a few ""big oil"" company stocks right now." "So, there is no truly ""correct"" way to calculate return.  Professionals will often calculate many different rates of return depending on what they wish to understand about their portfolio.  However, the two most common ways of calculating multi-period return though are time-weighted return and money-weighted return. I'll leave the details to this good Investopeadia article, but the big picture is time-weighted returns help you understand how the stock performed during the period in question independent of how you invested it it.  Whereas money-weighted return helps you understand how you performed investing in the stock in question.  From your question, it appears both methods would be useful in combination to help you evaluate your portfolio. Both methods should be fairly easy to calculate yourself in a spread sheet, but if you are interested there are plenty of examples of both in google docs on the web." Yes, exactly. VaR is just a single tailed confidence interval.  To go from model to strategy, you need to design some kind of indicator (i.e. when to buy and when to short or stay out). In practice, this will look like a large matrix with values ranging from -1 to 1 (corresponding to shorting and holding respectively) for each security and each day (or hour, or minute, or tick, etc.), which you then just multiply with the matrix of the stock returns. The resulting matrix will be your daily returns for each stock, you can then just row sum for daily returns of a portfolio, or calculate a cumulative product for cumulative returns.  A simple example of an indicator would be something like a value of 1 when the price of the stock is below the 30 day moving average, and 0 otherwise. You can use a battery of econometric models to design these indicators, but the rest of the strategy design is essentially the same, and it's *relatively* easy to build a one-size-fits-all back-testing code.  I'll try to edit this post later and link a blog that goes through some of the code.  Edit: [Here](http://www.signalplot.com/simple-machine-learning-model-trade-spy/) is a post that discusses implementing a simple ML strategy. You can ignore most of the content but if you go through the github, you'll see how the ML model is implemented as a strategy.  An even easier example can be found from [the github connected to this post](http://www.signalplot.com/how-to-measure-the-performance-of-a-trading-strategy/), where the author is just using a totally arbitrary signal. As you can see, deriving a signal can be a ton of work, but once you have, actually simulating the strategy can be done in just a few lines of code.  Hopefully the author won't mind me linking his page here, but I find his coding style to be very clean and good for educational purposes. 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). Efficient Frontier has an article from years ago about the small-cap and value premiums out there that would be worth noting here using the Fama and French data. Eugene Fama and Kenneth French (F/F) have shown that one can explain   almost all of the returns of equity portfolios based on only three   factors: market exposure, market capitalization (size), and   price-to-book (value). Wikipedia link to the factor model which was the result of the F/F research. 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.