What is the principle of forming an arbitrage strategy?
"Arbitrage is basically taking advantage of a difference in price.  Generally extending to ""in different places for the same thing"". A monetary version would be interlisted stocks, that is stocks in companies that are on both the NYSE/Nasdaq and Toronto stock exchanges.  If somebody comes along and buys a large number of shares in Toronto, that will tend to make the price go up - standard supply and demand. But if someone else can buy shares instead in NY, and then sell them in Toronto where the first person is buying up shares, where the price is higher, they the the arbitrageur (second person) can make pretty easy money. By its very nature, this tends to bring the prices back in line, as NY will then go up and Toronto will then go down (ignoring FX rates and the like for ease of explanation). The same can work for physical goods, although it does tend to get more complex with taxes, duties, and the like." Well, arbitrage is a simple mean reversion strategy which states that any two similar commodity with some price difference (usually not much)  will converge. So either you can bet on difference in prices in different exchanges or also you can bet on difference in futures value.  For example if current price of stock is 14$ and if futures price is 10$.  Then you can buy one futures contract and short one stock at the market price. This would lock in a profit of 4$ per share.
To answer your original question: There is proof out there. Here is a paper from the Federal Reserve Bank of St. Louis that might be worth a read.  It has a lot of references to other publications that might help answer your question(s) about TA.  You can probably read the whole article then research some of the other ones listed there to come up with a conclusion.  Below are some excerpts:  Abstract: This article introduces the subject of technical analysis in the foreign exchange market, with emphasis on its importance for questions of market efficiency.  “Technicians” view their craft, the study of price patterns, as exploiting traders’ psychological regularities.  The literature on technical analysis has established that simple technical trading rules on dollar exchange rates provided 15 years of positive, risk-adjusted returns during the 1970s and 80s before those returns were extinguished.  More recently, more complex and less studied rules have produced    more modest returns for a similar length of time.  Conventional explanations that rely on risk adjustment and/or central bank intervention do not plausibly justify the observed excess returns from following simple technical trading rules.  Psychological biases, however, could contribute to the profitability of these rules. We view the observed pattern of excess returns to technical trading rules as being consistent with an adaptive markets view of the world.    and  The widespread use of technical analysis in foreign exchange (and   other) markets is puzzling because it implies  that either traders are   irrationally making decisions on useless information or that past   prices contain useful  information for trading.  The latter   possibility would contradict the “efficient markets hypothesis,”   which holds that  no trading strategy should be able to generate   unusual profits on publicly available information—such as past    prices—except by bearing unusual risk. And the observed  level of   risk-adjusted profitability measures market  (in)efficiency. Therefore   much research effort has been directed toward determining whether   technical analysis is  indeed profitable or not. One of the earliest   studies, by Fama and Blume (1966), found no evidence that a particular   class of TTRs could earn abnormal profits in the stock market.   However, more recent research by Brock,  Lakonishok and LeBaron (1992)   and Sullivan, Timmermann an d White (1999) has provided contrary   evidence. And  many studies of the foreign exchange market have found   evidence that TTRs can generate persistent profits (Poole  6  (1967),   Dooley and Shafer (1984), Sweeney (1986), Levich and Thomas (1993),   Neely, Weller and Dittmar (1997),  Gençay (1999), Lee, Gleason and   Mathur (2001) and Martin (2001)). Your strategy of longing company(a) and shorting company(b) is flawed as the prices of company(a) and company(b) can both increase and though you are right , you will lose money due to the shorting strategy. You should not engage in pair trading , which is normally used for arbitrage purposes You should just buy company(a) since you believed its a better company compared to company(b) , its as simple as that "You're talking about modern portfolio theory. The wiki article goes into the math. Here's the gist: Modern portfolio theory (MPT) is a theory of finance that attempts to maximize portfolio expected return for a given amount of portfolio risk, or equivalently minimize risk for a given level of expected return, by carefully choosing the proportions of various assets. At the most basic level, you either a) pick a level of risk (standard deviation of your whole portfolio) that you're ok with and find the maximum return you can achieve while not exceeding your risk level, or b) pick a level of expected return that you want and minimize risk (again, the standard deviation of your portfolio). You don't maximize both moments at once. The techniques behind actually solving them in all but the most trivial cases (portfolios of two or three assets are trivial cases) are basically quadratic programming because to be realistic, you might have a portfolio that a) doesn't allow short sales for all instruments, and/or b) has some securities that can't be held in fractional amounts (like ETF's or bonds). Then there isn't a closed form solution and you need computational techniques like mixed integer quadratic programming Plenty of firms and people use these techniques, even in their most basic form. Also your terms are a bit strange: It has correlation table p11, p12, ... pij, pnn for i and j running from 1 to n This is usually called the covariance matrix. I want to maximize 2 variables. Namely the expected return and the additive inverse of the standard deviation of the mixed investments. Like I said above you don't maximize two moments (return and inverse of risk). I realize that you're trying to minimize risk by maximizing ""negative risk"" so to speak but since risk and return are inherently a tradeoff you can't achieve the best of both worlds. Maybe I should point out that although the above sounds nice, and, theoretically, it's sound, as one of the comments points out, it's harder to apply in practice. For example it's easy to calculate a covariance matrix between the returns of two or more assets, but in the simplest case of modern portfolio theory, the assumption is that those covariances don't change over your time horizon. Also coming up with a realistic measure of your level of risk can be tricky. For example you may be ok with a standard deviation of 20% in the positive direction but only be ok with a standard deviation of 5% in the negative direction. Basically in your head, the distribution of returns you want probably has negative skewness:  because on the whole you want more positive returns than negative returns. Like I said this can get complicated because then you start minimizing other forms of risk like value at risk, for example, and then modern portfolio theory doesn't necessarily give you closed form solutions anymore. Any actively managed fund that applies this in practice (since obviously a completely passive fund will just replicate the index and not try to minimize risk or anything like that) will probably be using something like the above, or at least something that's more complicated than the basic undergrad portfolio optimization that I talked about above. We'll quickly get beyond what I know at this rate, so maybe I should stop there." The commenters who referred you to the prisoner's dilemma are exactly correct, but I wanted to give a more detailed explanation because I find game theory quite interesting.  The prisoner's dilemma is a classic scenario in game theory where even though it's in the best interests of two or more players to cooperate, they fail to do so. Wikipedia has a simple example using prisoners, but I'll use a simple example using Fidel and Charles, who are fund managers at Fidelity and Charles Schwab, respectively.  To make the table shorter, I abbreviated a bit: INC = increase fees, KEEP=keep fees the same, DEC=decrease fees. Here is the dilemma itself, in the table that shows the resulting market shares if each fund manager follows the course of action in question.  While this example isn't mathematically rigorous because I completely fabricated the numbers, it makes a good example. The most profitable course of action would be both fund managers agreeing to increase their fees, which would keep their market shares the same but increase their profits as they earn more fees. However, this won't happen for several reasons.  Because economies of scale exist in the market for investment funds, it's reasonable to assume in a simple example that as funds grow larger, their costs decrease, so even though a fund manager decreases his fees (betraying the other players), this decrease won't be enough to reduce their profits. In fact, the increased market share resulting from such a decrease may well dominate the decreased fees and lead to higher profits. The prisoner's dilemma is highly applicable to markets such as these because they exist as oligopolies, i.e. markets where a relatively small number of established sellers possess considerable market power. If you actually wanted to model the market for donor-advised funds using game theory, you need to take a few more things into account. Obviously there are more than two firms. It's probably a valid assumption that the market is an oligopoly with significant economies of scale, but I haven't researched this extensively.  There is more than one time period, so some form of the iterated prisoner's dilemma is needed. The market for donor-advised funds is also complicated by the fact that these are philanthropic funds. This may introduce tax implications or the problem of goodwill and institutional opinion of these funds. Although both funds increasing their fees may increase their profits in theory, institutional investors may look on this as a pure profit-seeking and take their funds elsewhere. For example, they may choose to invest in smaller funds with higher fees but better reputations. While reputation is important for any company, it might make more of a difference when the fund/investment vehicle is philanthropic in nature.  I am by no means an expert on game theory, so I'm sure there are other nuances to the situation that I'm unaware of. Academic research into ADRs seems to suggest that pairs-trading ADRs and their underlying shares reveals that there certainly are arbitrage opportunities, but that in most (but not all cases) such opportunities are quickly taken care of by the market. (See this article for the mexican case, the introduction has a list of other articles you could read on the subject). In some cases parity doesn't seem to be reached, which may have to do with transaction costs, the risk of transacting in a foreign market, as well as administrative & legal concerns that can affect the direct holder of a foreign share but don't impact the ADR holder (since those risks and costs are borne by the institution, which presumably has a better idea of how to manage such risks and costs). It's also worth pointing out that there are almost always arbitrage opportunities that get snapped up quickly: the law of one price doesn't apply for very short time-frames, just that if you're not an expert in that particular domain of the market, it might as well be a law since you won't see the arbitrage opportunities fast enough. That is to say, there are always opportunities for arbitrage with ADRs but chances are YOU won't be able to take advantage of it (In the Mexican case, the price divergence seems to have an average half-life of ~3 days). Some price divergence might be expected: ADR holders shouldn't be expected to know as much about the foreign market as the typical foreign share holder, and that uncertainty may also cause some divergence. There does seem to be some opportunity for arbitrage doing what you suggest in markets where it is not legally possible to short shares, but that likely is the value added from being able to short a share that belongs to a market where you can't do that. Basic arbitrage is the (near-)simultaneous purchasing and selling of things that are convertible.   The classic example is the international trading of equities. If someone in London wants to purchase a hundred shares of Shell for 40 GBP ea. and someone in New York wants to sell you a hundred shares of Shell for 61 USD ea., you can buy the shares from the guy in New York, sell them to the guy in London and convert your GBP back in to USD for a profit of $41.60 minus fees.  Now, if after you buy the shares in New York, the price in London goes down, you'll be left holding 100 shares of Shell that you don't want. So instead you should borrow 100 shares in London and sell them at the exact same time that you buy the shares in New York, thus keeping your net position at 0. In fact, you should also borrow 4000GBP and convert them to USD at the same time, so that exchange rate changes don't get you. "Can someone please clarify if Norbert's gambit is the optimal procedure to exchange CAD to USD? I'm not sure I'd call an arbitrage trade the ""optimal procedure,"" because as you point out you're introducing yet another point of risk in to the transaction.  I think buying the foreign currency for an agreed upon price is the ""optimal procedure."" If you must use this arbitrage trade, try with a government bond fund; they're typically very stable." "I'm loving this thread, by the way.  The answer to your question is yes: the PDE method and the martingale method lead to the same result.  I think this is intuitive, since they address the same things (drift, probability, etc).  Heath &amp; Schweizer (2000) have a nice paper in the Journal of Applied Probability that shows the (fairly general) circumstances under which the two methods will always have the same result.  It's titled ""Martingales versus PDEs in Finance: An Equivalence Result with Examples"".  My argument is that Black-Scholes is really an equilibrium model, not an arbitrage-free model.  Despite that, I'm claiming that it is possible to use BS (and any other equilibrium model) in a no-arbitrage manner by incorporating information from other securities, but that this doesn't make the underlying model and its assumptions a no-arbitrage model.  I think, basically, what I'm trying to say is that I don't think market completeness is really the issue, but rather that the issue is the difference between the model and reality.  Equilibrium models make a statement about what reality *should* be, given some parameters that you're supposed to know with certainty (all bets are off if you have to estimate them).  Arbitrage-free models explicitly use external, observed prices, *but do not explain why we observe those prices*.  In this context (and using these definitions), I'd say Black-Scholes is clearly an equilibrium model, albeit one built from some arguments that involve arbitrage." A bullish (or 'long') call spread is actually two separate option trades.  The A/B notation is, respectively, the strike price of each trade. The first 'leg' of the strategy, corresponding to B, is the sale of a call option at a strike price of B (in this case $165).  The proceeds from this sale, after transaction costs, are generally used to offset the cost of the second 'leg'. The second 'leg' of the strategy, corresponding to A, is the purchase of a call option at a strike price of A (in this case $145). Now, the important part: the payoff.  You can visualize it as so. This is where it gets a teeny bit math-y.  Below, P is the profit of the strategy, K1 is the strike price of the long call, K2 is the strike price of the short call, T1 is the premium paid for the long call option at the time of purchase, T2 is the premium received for the short call at the time of sale, and S is the current price of the stock.  For simplicity's sake, we will assume that your position quantity is a single option contract and transaction costs are zero (which they are not). P = (T2 - max(0, S - K2)) + (max(0, S - K1) - T1) Concretely, let's plug in the strikes of the strategy Nathan proposes, and current prices (which I pulled from the screen).  You have: P = (1.85 - max(0, 142.50 - 165)) - (max(0, 142.50 - 145)) = -$7.80 If the stock goes to $150, the payoff is -$2.80, which isn't quite break even -- but it may have been at the time he was speaking on TV. If the stock goes to $165, the payoff is $12.20. Please do not neglect the cost of the trades!  Trading options can be pretty expensive depending on the broker.  Had I done this trade (quantity 1) at many popular brokers, I still would've been net negative PnL even if NFLX went to >= $165. The literal answer to your question 'what determines the price of an ETF' is 'the market'; it is whatever price a buyer is willing to pay and a seller is willing to accept. But if the market price of an ETF share deviates significantly from its NAV, the per-share market value of the securities in its portfolio, then an Authorized Participant can make an arbitrage profit by a transaction (creation or redemption) that pushes the market price toward NAV. Thus as long as the markets are operating and the APs don't vanish in a puff of smoke we can expect price will track NAV. That reduces your question to: why does NAV = market value of the holdings underlying a bond ETF share decrease when the market interest rate rises?  Let's consider an example. I'll use US Treasuries because they have very active markets, are treated as risk-free (although that can be debated), and excluding special cases like TIPS and strips are almost perfectly fungible. And I use round numbers for convenience. Let's assume the current market interest rate is 2% and 'Spindoctor 10-year Treasury Fund' opens for business with $100m invested (via APs) in 10-year T-notes with 2% coupon at par and 1m shares issued that are worth $100 each. Now assume the interest rate goes up to 3% (this is an example NOT A PREDICTION); no one wants to pay par for a 2% bond when they can get 3% elsewhere, so its value goes down to about 0.9 of par (not exactly due to the way the arithmetic works but close enough) and Spindoctor shares similarly slide to $90. At this price an investor gets slightly over 2% (coupon*face/basis) plus approximately 1% amortized capital gain (slightly less due to time value) per year so it's competitive with a 3% coupon at par.  As you say new bonds are available that pay 3%. But our fund doesn't hold them; we hold old bonds with a face value of $100m but a market value of only $90m. If we sell those bonds now and buy 3% bonds to (try to) replace them, we only get $90m par value of 3% bonds, so now our fund is paying a competitive 3% but NAV is still only $90.  At the other extreme, say we hold the 2% bonds to maturity, paying out only 2% interest but letting our NAV increase as the remaining term (duration) and thus discount of the bonds decreases -- assuming the market interest rate doesn't change again, which for 10 years is probably unrealistic (ignoring 2009-2016!). At the end of 10 years the 2% bonds are redeemed at par and our NAV is back to $100 -- but from the investor's point of view they've forgone $10 in interest they could have received from an alternative investment over those 10 years, which is effectively an additional investment, so the original share price of $90 was correct. "As you say, the currency carry trade shouldn't work.  The deluge of new cash into a high-interest currency should result in falling exchange rates.  A November 2009 paper by Òscar Jordà and Alan Taylor of the University of California, Davis, may be offer one approach which is more stable.  According to The Economist: They find that a refined carry-trade   strategy—one that incorporates a   measure of long-term value—produces   more consistent profits and is less   prone to huge losses than one that   targets the highest yield. However, exchange rates, central bank interest rates, as well as money supply are all political as well as economic constructs.  An economic driver for arbitrage may be offset by political will (such as US quantative easing) or even social malaise (Japanese continual low inward investment). I wouldn't go so far as calling the carry trade ""free money"" - currencies have proven far too unstable for that - but state interference in markets tends to be clearly telegraphed and a trader with nerves of steel may take advantage of it." "The process of borrowing shares and selling them is called shorting a stock, or ""going short.""  When you use money to buy shares, it is called ""going long."" In general, your strategy of going long and short in the same stock in the same amounts does not gain you anything.  Let's look at your two scenarios to see why. When you start, LOOT is trading at $20 per share.  You purchased 100 shares for $2000, and you borrowed and sold 100 shares for $2000.  You are both long and short in the stock for $2000.  At this point, you have invested $2000, and you got your $2000 back from the short proceeds.  You own and owe 100 shares. Under scenario A, the price goes up to $30 per share.  Your long shares have gone up in value by $1000.  However, you have lost $1000 on your short shares.  Your short is called, and you return your 100 shares, and have to pay interest.  Under this scenario, after it is all done, you have lost whatever the interest charges are. Under scenario B, the prices goes down to $10 per share.  Your long shares have lost $1000 in value.  However, your short has gained $1000 in value, because you can buy the 100 shares for only $1000 and return them, and you are left with the $1000 out of the $2000 you got when you first sold the shorted shares.  However, because your long shares have lost $1000, you still haven't gained anything.  Here again, you have lost whatever the interest charges are. As explained in the Traders Exclusive article that @RonJohn posted in the comments, there are investors that go long and short on the same stock at the same time.  However, this might be done if the investor believes that the stock will go down in a short-term time frame, but up in the long-term time frame.  The investor might buy and hold for the long term, but go short for a brief time while holding the long position. However, that is not what you are suggesting.  Your proposal makes no prediction on what the stock might do in different periods of time.  You are only attempting to hedge your bets.  And it doesn't work.  A long position and a short position are opposites to each other, and no matter which way the stock moves, you'll lose the same amount with one position that you have gained in the other position.  And you'll be out the interest charges from the borrowed shares every time. With your comment, you have stated that your scenario is that you believe that the stock will go up long term, but you also believe that the stock is at a short-term peak and will drop in the near future.  This, however, doesn't really change things much.  Let's look again at your possible scenarios. You believe that the stock is a long-term buy, but for some reason you are guessing that the stock will drop in the short-term.  Under scenario A, you were incorrect about your short-term guess.  And, although you might have been correct about the long-term prospects, you have missed this gain.  You are out the interest charges, and if you still think the stock is headed up over the long term, you'll need to buy back in at a higher price. Under scenario B, it turns out that you were correct about the short-term drop.  You pocket some cash, but there is no guarantee that the stock will rise anytime soon.  Your investment has lost value, and the gain that you made with your short is still tied up in stocks that are currently down. Your strategy does prevent the possibility of the unlimited loss inherent in the short.  However, it also prevents the possibility of the unlimited gain inherent in the long position.    And this is a shame, since you fundamentally believe that the stock is undervalued and is headed up.  You are sabotaging your long-term gains for a chance at a small short-term gain." "You're mostly correct, although I think you're missing something essential about no-arbitrage versus an arbitrage argument.  Black-Scholes makes an arbitrage argument, which is that the value of an option should be the same as any portfolio that has identical cash flows, and this is generally a sound argument.  Notice, however, that BS is ultimately an equilibrium model: it tells you the ""correct"" price of an option if the assumptions of BS hold, and doesn't necessarily match observed market prices.  A no-arbitrage condition or model deliberately incorporates observed prices (or yields, or whatever) into the model, so that there cannot be an arbitrage opportunity implied by the model.  This comes up a lot in term structure of interest rate problems, where equilibrium models like Vasicek or Cox-Ingersoll-Ross won't perfectly reproduce the current, observed term structure, and so imply an arbitrage opportunity.  No-arbitrage models like Hull-White specifically match the model's term structure to observed yields/prices, so that there is no arbitrage opportunity between the observed term structure and your model of it.  It's important to note that this will still allow for arbitrage involving bonds that are *not* part of the observed term structure.  As for equivalent martingale measures, you might think about it more generally.  The process involves changing the probability distribution from the actual (which is hard to use for pricing) to a different one that's easier to use but will result in the same prices; this is nearly always a risk-neutral probability.  You can think of equivalent martingale  pricing as asking, ""how would this security behave, and be priced, in a world that is completely risk neutral"", and then making an argument that the prices are in fact equivalent.  EDIT: grammar" "Being ""long"" - expecting the price to go up to make a profit - is a two step process:  1) buy 2) sell Being ""short"" - expecting the price to go down to make a profit - is a 5 step process:  1) borrow someone else's asset 2) sell their asset on the open market to somebody else a third party 3) pocket the proceeds of the sell for your own account 4) buy an identical asset for a cheaper price 5) return this identical asset to the person that let you borrow their asset if this is successful you keep the difference between 3) and 4)" "What disconnect? And I'm not even kidding here - where is it? Do you really think that arbitrage that is a pittance compared to long term trading somehow distorts the process that some people claim is actually socially beneficial? Given that there's really no evidence of it causing misallocation or mispricing, what is the problem? That some dumbass day trader (who is, by the way, trying to make money in exactly the same way as the HFT people - he's just worse at it) got screwed over by some not-quite-as-dumbass people working at Goldman Sachs?  And why would you think that HFT (or any other advancement) is somehow related to such a thing; we've had ""speculation"" and foul play of various types for hundreds of years. What is it that is fundamentally different this time that wasn't there in, for example, the 80s?"