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.
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. "The formula you are looking for is pretty complicated. It's given here: http://itl.nist.gov/div898/handbook/eda/section3/eda3661.htm You might prefer to let somebody else do the grunt work for you. This page will calculate the probability for you: http://stattrek.com/online-calculator/normal.aspx. In your case, you'd enter mean=.114, standard deviation=.132, and ""standard score""= ... oh, you didn't say what you're paying on your debt. Let's say it's 6%, i.e. .06. Note that this page will give you the probability that the actual number will be less than or equal to the ""standard score"". Enter all that and click the magic button and the probability that the investment will produce less than 6% is ... .34124, or 34%. The handy rule of thumb is that the probability is about 68% that the actual number will be within 1 standard deviation of the mean, 95% that it will be within 2 standard deviations, and 99.7% that it will be within 3. Which isn't exactly what you want because you don't want ""within"" but ""less than"". But you could get that by just adding half the difference from 100% for each of the above, i.e. instead of 68-95-99.7 it would be 84-98-99.9. Oh, I missed that in a follow-up comment you say you are paying 4% on a mortgage which you are adjusting to 3% because of tax implications. Probability based on mean and SD you gave of getting less than 3% is 26%. I didn't read the article you cite. I assume the standard deviation given is for the rate of return for one year. If you stretch that over many years, the SD goes down, as many factors tend to even out. So while the probability that money in a given, say, mutual fund will grow by less than 3% in one year is fairly high -- the 25 - 35% we're talking here sounds plausible to me -- the probability that it will grow by an average of less than 3% over a period of 10 or 15 or 20 years is much less. Further Thought There is, of course, no provably-true formula for what makes a reasonable risk. Suppose I offered you an investment that had a 99% chance of showing a $5,000 profit and a 1% chance of a $495,000 loss. Would you take it? I wouldn't. Even though the chance of a loss is small, if it happened, I'd lose everything I have. Is it worth that risk for the modest potential profit? I'd say no. Of course to someone who has a billion dollars, this might be a very reasonable risk. If it fails, oh well, that could really cut in to what he can spend on lunch tomorrow." Yes, it's a risk. To put it in perspective, If we look at the data for S&P returns since 1871, we get a CAGR of 10.72%. But, that comes with a SDev (Standard deviation) of 18.67%. This results in 53 of the 146 years returning less than 4%.  Now if we repeat the exercise over rolling 8 year periods, the CAGR drops to 9.22%, but the SDev drops to 5.74%. This results in just 31 of the 139 periods returning less than 4%. On the flip side, 26 periods had an 8 year return of over 15% CAGR.  From the anti-DS article you linked, I see that you like a good analogy. For me, the returns of the S&P over the long term are like going to Vegas, and finding that after you run the math of their craps (dice rolling game) you find the expected return is 10%. You can still lose on a given roll. But over a series of a larger number of rolls, you're far ahead.  To D Stanley - I agree that returns are not quite normal, but they are not so far off. Of the 139 rolling returns, we'd expect about 68% or 95 results to be 1 SDev away. We get 88 returns +/-1SDev. 2 SDevs? We'd expect only 5% to lie outside this range, and in fact, I only get one result on the low side and 4 on the high side, 5 results vs the 7 total we'd expect. The results are a bit better (more profitable) than the Normal Bell Curve fit would suggest. "Not specifically a ""stream"", but there are royalty companies that operate based on a similar concept. With a royalty, a party will pay upfront to a another party, usually a product manufacturer, oil & gas producer, or miner, and in return they will receive a percentage of the proceeds from the sale of the goods.  For example, Company A owns 100 sections of land which carry mineral rights and they would like to drill on the land to produce oil & gas. However, Company A does not have the capital to produce the resource. Company B, a royalty company, agrees to provide upfront capital to Company A in return for a royalty, sometimes fixed, sometimes sliding scale based on other factors. The royalty is calculated based on a percentage of the sales proceeds that Company A receives from the sale of their oil & gas production.  In this way, royalty companies act similarly to streaming companies, where they provide upfront capital and in return receive a cash flow stream that is dependant on another party's actions. What is different is that the selling price is not fixed. Instead, it is the % of proceeds that is fixed, at least in the short term.  In Canada, PrairieSky Royalty and Freehold Royalties do exactly this." "There are some good answers about the benefits of diversification, but I'm going to go into what is going on mathematically with what you are attempting. I was always under the assumption that as long as two securities are less than perfectly correlated (i.e. 1), that the standard deviation/risk would be less than if I had put 100% into either of the securities. While there does exist a minimum variance portfolio that is a combination of the two with lower vol than 100% of either individually, this portfolio is not necessarily the portfolio with highest utility under your metric.  Your metric includes returns not just volatility/variance so the different returns bias the result away from the min-vol portfolio. Using the utility function: E[x] - .5*A*sig^2 results in the highest utility of 100% VTSAX. So here the Sharpe ratio (risk adjusted return) of the U.S. portfolio is so much higher than the international portfolio over the period tracked that the loss of returns from adding more international stocks outweigh the lower risk that you would get from both just adding the lower vol international stocks and the diversification effects from having a correlation less than one. The key point in the above is ""over the period tracked"".  When you do this type of analysis you implicitly assume that the returns/risk observed in the past will be similar to the returns/risk in the future.   Certainly, if you had invested 100% in the U.S. recently you would have done better than investing in a mix of US/Intl.  However, while the risk and correlations of assets can be (somewhat) stable over time relative returns can vary wildly! This uncertainty of future returns is why most people use a diversified portfolio of assets.  What is the exact right amount is a very hard question though." See the Moneychimp site. From 1934 to 2006, the S&P returned an 'average' 12.81%. But the CAGR was 11.26%.  I wrote an article Average Return vs Compound Annual Growth to address this issue.  Interesting that over time only a few funds have managed to get anywhere near this return, but the low cost indexer can get the long term CAGR minus .05% or so, if they wish. 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. If past is prologue, I'd say $20, give or take, inflation adjusted of course. http://www.antagoniste.net/WP-Uploads/2007/01/oil_prices_1861_2006.jpg If supplies are at nightmare oversupply, say, as an absurd unlikely scenario, 82 year high in US oil supplies or an all time record in EIA weekly inventories, it looks like the oil price could be capped at the cost of oil sands:  This one's just plain scary.  Unless if there were some changes refinery laws or technology that I'm not aware of, refineries cutting 50% of the retail gasoline volumes looks bad: