Why is the difference between adjusted close and close price slightly different between each day?
Prices are adjusted for return and not payout.  So if you take the ratio of the close price and the adjusted close price, it should remain constant. The idea behind a total return (back-)adjustment is to give you a feeling how much money you would have needed back then to reach the price today under the premise that all distributions (dividends, spin-offs, etc.) are reinvested instantly and that reinvestment doesn't cost anything.
This is often the case where traders are closing out short positions they don't want to hold overnight, for a variety of reasons that matter to them.  Most frequently, this is from day traders or high-frequency traders settling their accounts before the markets close. "When you buy a put on a stock, you buy the right to sell the stock at fixed price, F, that his usually different from the market price, M. You paid a price, P, for the put.  Your potential profit, going forward, is represented by the DIFFERENCE you get to collect between your fixed price F, and that market price M, plus the price you paid for the put, or F-(M+P). (This assumes that F>(M+P). P is fixed, but the smaller M gets, the larger the term F-(M+P), and therefore the higher your potential profit from owning the put. So when M ""tanks,"" the put goes higher.  The $395 put is already in the money. If it were settled today, the value would be $395-$376 or $19. This, minus the cost of the put itself, represents your profit. The $365 put is ""out of the money."" The stock has to fall $11 more before the put is exercised. But if the stock went down 8 points today, that is less than the $19 difference at the start of the day. Because there is time between now and October, there is a chance for the stock to go down further, thereby going into the money. The current value of the put is represented by this ""chance."" Obviously, the chances of the stock going down $11 more (from today) is greater than the chance of it going down $19 more. On the other hand, the closer it gets to the expiration date, the less an out of the money put is worth. It's a race between the stock's fall, and the time to expiration." The last column in the source data is volume (the number of stocks that was exchanged during the day), and it also has a value of zero for that day, meaning that nobody bought or sold the stocks on that day. And since the prices are prices of transactions (the first and the last one on a particular day, and the ones with the highest/lowest price), the prices cannot be established, and are irrelevant as there was not a single transaction on that day. Only the close price is assumed equal to its previous day counterpart because this is the most important value serving as a basis to determine the daily price change (and we assume no change in this case). Continuous-line charts also use this single value. Bar and candle charts usually display a blank space for a day where no trade occurred. If you're talking about just Theta, the amount of decay due to the passage of time (all else being equal), then theoretically, the time value is a continuous function, so it would decay throughout the day (although by the day of expiry the time value is very, very small).  Which makes sense, since even with 15 minutes to go, there's still a 50/50 shot of an ATM option expiring in-the-money, so there should be some time value associated with that one-sided probability. The further away from ATM the option is, the smaller the time value will be, and will be virtually zero for options that are deep in- or out-of-the-money. If you're talking about total time value, then yes it will definitely change during the day, since the underlying components (volatility, underlying price, etc.) change more or less continuously. It does sometimes open one day the same as it closed the previous day.  Take a look at ESCA, it closed October 29th at 4.50, at opened November 1st at 4.50.  It's more likely to change prices overnight than it is between two successive ticks during the day, because a lot more time passes, in which news can come out, and in which people can reevaluate the stock. My instinct says that there should be no difference. Your instincts are right. Your understanding of math is not so much. You sold $100K at the current price of 7500000RUB, but ended up buying at 3500000, you earned 3500000RUB. That's 100% in USD (50% in RUB). You bought 7500000RUB for the current price of $100K, but sold later for $200K. You earned $100K (100% in USD), which at that time was equal 3500000RUB. You earned 3500000RUB. That's 50% in RUB. So, as your instincts were saying - no difference. The reason percentages are different is because you're coming from different angles. For the first case your currency is RUB, for the second case your currency is USD, and in both cases you earned 100%. If you use the same currency for your calculations, percentages change, but the bottom line - is the same. NO. All the leveraged ETFs are designed to multiply the performance of the underlying asset FOR THAT DAY, read the prospectus. Their price is adjusted at the end of the day to reflect what is called a NAV unit. Basically, they know that their price is subject to fluctuations due to supply and demand throughout the day - simply because they trade in a quote driven system. But the price is automatically corrected at the end of the day regardless. In practice though, all sorts of crazy things happen with leveraged ETFs that will simply make them more and more unfavorable to hold long term, the longer you look at it. "According to Yahoo, AAPL was trading at $113.26 at 1:10 PM on 11/13/15, which is the approximate time of your option quote.  You provided a quote for AAPL at 4:15, and the stock happened to keep going down most of the that afternoon.  To make a sensible comparison, you need to take contemporary prices on both the stock and the option.  The quote on the option also shows the ""price"" being outside of the bid-ask range, which suggests that the option was trading thinly and that the last price occurred sometime earlier in the day.  If you use a price in the bid-ask range ($21.90-$22.30) and use the price of AAPL at the time of the put quote, you'll come up with a price that's much closer to your expectation." "Company values (and thus stock prices) rely on a much larger time frame than ""a weekend"".  First, markets are not efficient enough to know what a companies sales were over the past 2-3 days (many companies do not even know that for several weeks).  They look at performance over quarters and years to determine the ""value"" of a company.  They also look forward, not backwards to determine value.  Prior performance only gives a hint of what future performance may be.  If a company shut its doors over a weekend and did no sales, it still would have value based on its future ability to earn profits." The previous day's close on Thursday 10th October was 5,000.00 The close on Friday 11th October is 5,025.92 So the gain on Friday was 25.92 (5025.92 - 5000) or 0.52% (25.92/5000 x 100%). No mystery! The two answers so far are right, but there's a third factor - for many stocks, there's after hours trading. So the official 4PM close is not what the stock's last trade was when they open again. Regardless, even that after hour price is not the starting point as Muro points out. "What most of these answers here seem to be missing is that a stock ""price"" is not exactly what we typically expect a price to be--for example, when we go in to the supermarket and see that the price of a gallon of milk is $2.00, we know that when we go to the cash register that is exactly how much we will pay.  This is not, however, the case for stocks. For stocks, when most people talk about the price or quote, they are really referring to the last price at which that stock traded--which unlike for a gallon of milk at the supermarket, is no guarantee of what the next stock price will be.  Relatively speaking, most stocks are extremely liquid, so they will react to any information which the ""market"" believes has a bearing on the value of their underlying asset almost (if not) immediately.  As an extreme example, if allegations of accounting fraud for a particular company whose stock is trading at $40 come out mid-session, there will not be a gradual decline in the price ($40 -> $39.99 -> $39.97, etc.)-- instead, the price will jump from $40 to say, $20.  In the time between the the $40 trade and the $20 trade, even though we may say the price of the stock was $40, that quote was actually a terrible estimate of the stock's current (post-fraud announcement) price. Considering that the ""price"" of a stock typically does not remain constant even in the span of a few seconds to a few minutes, it should not be hard to believe that this price will not remain constant over the 17.5 hour period from the previous day's close to the current day's open.  Don't forget that as Americans go to bed, the Asian markets are just opening, and by the time US markets have opened, it is already past 2PM in London.  In addition to the information (and therefore new knowledge) gained from these foreign markets' movements, macro factors can also play an important part in a security's price-- perhaps the ECB makes a morning statement that is interpreted as negative news for the markets or a foreign government before the US markets open.  Stock prices on the NYSE, NASDAQ, etc. won't be able to react until 9:30, but the $40 price of the last trade of a broad market ETF at 4PM yesterday probably isn't looking so hot at 6:30 this morning... don't forget either that most individual stocks are correlated with the movement of the broader market, so even news that is not specific to a given security will in all likelihood still have an impact on that security's price. The above are only a few of many examples of things that can impact a stock's valuation between close and open: all sorts of geopolitical events, announcements from large, multi-national companies, macroeconomic stats such as unemployment rates, etc. announced in foreign countries can all play a role in affecting a security's price overnight. As an aside, one of the answers mentioned after hours trading as a reason--in actuality this typically has very little (if any) impact on the next day's prices and is often referred to as ""amateur hour"", due to the fact that trading during this time typically consists of small-time investors.  Prices in AH are very poor predictors of a stock's price at open." "There is a white paper on ""The weekend effect of equity options"" it is a good paper and shows that (for the most part) option values do lose money from Friday to Monday. Which makes sense because it is getting closer to expiration. Of course this not something that can be counted on 100%.  If there is some bad news and the stock opens down on a Monday the puts would have increased and the calls decreased in value. Article Summary (from the authors): ""We find that returns on options on individual equities display markedly lower returns over weekends (Friday close to Monday close) relative to any other day of the week. These patterns are observed both in unhedged and delta-hedged positions, indicating that the effect is not the result of a weekend effect in the underlying securities. We find even stronger weekend effects in implied volatilities, but only after an adjustment to quote implied volatilities in terms of trading days rather than calendar days.""  ""Our results hold for puts and calls over a wide range of maturities and strike prices, for both equally weighted portfolios and for portfolios weighted by the market value of open interest, and also for samples that include only the most liquid options in the market. We find no evidence of a weekly seasonal in bid-ask spreads, trading volume, or open interest that could drive the effect. We also find little evidence that weekend returns are driven by higher levels of risk over the weekend.  ""The effect is particularly strong over expiration weekends, and it is also present to a lesser degree over mid-week holidays. Finally, the effect is stronger when the TED spread and market volatility are high, which we interpret as providing support for a limits to arbitrage explanation for the persistence of the effect."" - Christopher S. Jones & Joshua Shemes You can read more about this at this link for Memphis.edu" The Wikipedia has an article on money flow index. The article which you link to correctly uses the typical price. You state that you are comparing the closing prices, which is incorrect. I'm making no statement on the validity of the money flow index itself, just answering your question. I still can't understand why there is a price discrepancancy.  There isn't. It's the same stock and price differences between such major exchanges will always be minimal. I think you simply haven't paid attention to the date range. It seems Google finance only has data for FRA:BMW reaching back to 2011, so if you try to look at the development of your investment since 2009, you're not getting comparable data.