Using Fibonacci Extensions to set profit targets?
fibonacci levels (retracements,expansions, arcs) are all arbitrary numbers with no statistical significance. that said thousands of traders world over use, view and depend on fib numbers in their trading ranging from forex, stock commodities etc the point is if it's traded a fibonacci number has been used on it, because of this unanimity on their significance & application the fibonacci's thus act as valid anchors since so many traders are looking at the same levels (self-fulfilling prophecy). the values of the fib numbers are all equally significant i.e the 23.6. 38.2, 50, or 61.8 are statistically all equally likely to occur. you just have to be vigilant as your trade approaches the fib levels. I have never seen a backtest showing that prices tended to be attracted by / to revert around Fibonacci levels. The fact that many people use them doesn't mean that they can be turned into a profitable system... I have on the other hand seen many backtests showing that they don't do anything, such as the one described in this article: At least in this sample of market data, using this particularly specification for swings, we find no evidence that Fibonacci ratios are significant in the market.   Perhaps I have missed something significant, or perhaps I am merely completely wrong in my analysis, but one thing should be clear—the burden of proof should lie on the people offering arcane and complex methodologies, when simpler methods work just as well or better in the marketplace. If Fibonacci ratios are the key to the markets, where are the quantitative tests? Where’s the proof?
This is how I've understood this concept. Fibonacci nos/levels/ratios/%s is based on concept of sequential increment. You may find lot of info about Fibonacci on net. In stock market this concept is used to predict psychological level. While a trend is form, usually price tend to accumulate/consolidate at these level. How the percentage/ ratio make impact is  - check any long trend...Now draw a fibbo retracement from immediate previous high and connect it's low. You will see new levels of intermediate trend. In broader term you will find after reversal a leg (trend) is formed, then body and then head which is smaller; then price reverses. The first leg that forms if it refuses to break 23.6% or 38.2% then the previous trend may continue. 50% is normal; usually this level is indecision phase. Even 61.8% is seen as indecision but it is crucial level as it is breakout level towards 100%. Now if the stock retraces 100% then it is sign a new big trend is forming. Now for day trader 23.6%,38.2% and 50% level are very crucial from trading purpose. This concept is so realistic that every level is considered and respected. Suppose if a candle or bar starts at 23.6% level and crosses 38.2% and directly hits 50%. Then the next bar or candle will revert and first hit 38.2% and then continue with the trend. It means price comes back, forms it area at this level and then continue whichever direction the force directs it. You never trade fibo alone, you need help of oscillators or other tools to confirm it. "John Bensin's answer covers the math, but I like the plain-English examples of the theory from William Bernstein's fine book, The Intelligent Asset Allocator.  At the author's web site, you can find the complete chapter 1 and chapter 2, though not chapter 3, which is the one with the ""multiple coin toss"" portfolio example I want to highlight. I'll summarize Bernstein's multiple coin toss example here with some excerpts from the book.  (Another top user, @JoeTaxpayer, has also written about the coin flip on his blog, also mentioning Bernstein's book.) Bernstein begins Chapter 1 by describing an offer from a fictitious ""Uncle Fred"": Imagine that you work for your rich but eccentric Uncle Fred. [...] he   decides to let you in on the company pension plan. [...] you must pick   ahead of time one of two investment choices for the duration of your   employment: Certificates of deposit with a 3% annualized rate of return, or, A most peculiar option: At the end of each year Uncle Fred flips a coin. Heads you receive a 30% investment return for that year, tails a   minus 10% (loss) for the year. This will be hereafter referred to as   ""Uncle Fred’s coin toss,"" or simply, the ""coin toss."" In effect, choosing option 2 results in a higher expected return than option 1, but it is certainly riskier, having a high standard deviation and being especially prone to a series of bad tosses.  Chapters 1 and 2 continue to expand on the idea of risk, and take a look at various assets/markets over time.  Chapter 3 then begins by introducing the multiple coin toss example: Time passes. You have spent several more years in the employ of your   Uncle Fred, and have truly grown to dread the annual coin-toss   sessions. [...] He makes you another offer. At the end of each year,   he will divide your pension account into two equal parts and conduct a   separate coin toss for each half [...] there are four possible   outcomes [...]: [...]   Being handy with numbers, you calculate that your annualized return   for this two-coin-toss sequence is 9.08%, which is nearly a full   percentage point higher than your previous expected return of 8.17%   with only one coin toss. Even more amazingly, you realize that your   risk has been reduced — with the addition of two returns at the   mean of 10%, your calculated standard deviation is now only 14.14%, as   opposed to 20% for the single coin toss. [...] Dividing your portfolio between assets with uncorrelated results increases return while decreasing risk. [...]   If the second coin toss were perfectly inversely correlated   with the first and always gave the opposite result [hence, outcomes   1 and 4 above never occurring], then our return would always be 10%.   In this case, we would have a 10% annualized long-term return with zero risk! I hope that summarizes the example well.  Of course, in the real world, one of the tricks to building a good portfolio is finding assets that aren't well-correlated, and if you're interested in more on the subject I suggest you check out his books (including The Four Pillars of Investing) and read more about Modern Portfolio Theory (MPT)." "I could not figure out a good way to make XIRR work since it does not support arrays.  However, I think the following should work for you: Insert a column at D and call it ""ratio"" (to be used to calculate your answer in column E).  Use the following equation for D3: =1+(C3-B3-C2)/C2 Drag that down to fill in the column. Set E3 to: =(PRODUCT(D$3:D3)-1)*365/(A3-A$2) Drag that down to fill in the column. Column E is now your annual rate of return." "Your strategy fails to control risk. Your ""inversed crash"" is called a rally. And These kind of things often turn into bigger rallies because of short squeezes, when all the people that are shorting a stock are forced to close their stock because of margin calls - its not that shorts ""scramble"" to close their position, the broker AUTOMATICALLY closes your short positions with market orders and you are stuck with the loss. So no, your ""trick"" is not enough. There are better ways to profit from a bearish outlook." If annualized rate of return is what you are looking for, using a tool would make it a lot easier.   In the post I've also explained how to use the spreadsheet.   Hope this helps. Thanks for the answer/comments! The time-based method was something we mooted and something I almost went with. But just to wrap this up, the method we settled on was this: Every time there is an entry or exit into the fund, we divvy out any unrealised market profits/losses according to each person's profit share (based on % of the asset purchased at buy-in) JUST BEFORE the entry/exit. These realised profits are then locked in for those particpants, and then the unrealised profits/loss counter starts at zero, we do a fresh recalculation of shareholding after the entry/exit, and then we start again. Hope this helps anyone with the same issue! In my experience thanks to algorithmic trading the variation of the spread and the range of trading straight after a major data release will be as random as possible, since we live in an age that if some pattern existed at these times HFT firms would take out any opportunity within nanoseconds. Remember that some firms write algorithms to predict other algorithms, and it is at times like those that this strategy would be most effective. With regards to my own trading experience I have seen orders fill almost €400 per contract outside of the quoted range, but this is only in the most volatile market conditions. Generally speaking, event investing around numbers like these are only for top wall street firms that can use co-location servers and get a ping time to the exchange of less than 5ms. Also, after a data release the market can surge/plummet in either direction, only to recover almost instantly and take out any stops that were in its path. So generally, I would say that slippage is extremely unpredictable in these cases( because it is an advantage to HFT firms to make it so ) and stop-loss orders will only provide limited protection. There is stop-limit orders( which allow you to specify a price limit that is acceptable ) on some markets and as far as I know InteractiveBrokers provide a guaranteed stop-loss fill( For a price of course ) that could be worth looking at, personally I dont use IB.  I hope this answer provides some helpful information, and generally speaking, super-short term investing is for algorithms. Your plan won't work. Working 40 hours a week at federal minimum wage (currently $7.25 / hr) for 52 weeks is an annual income of just over $15,000. Even assuming you can reliably get a return of 15% (which you definitely can't), you'd need to start with $100,000 of assets to earn this poverty income. Assuming a more reasonable 7% bumps the required assets up to over $200,000, and even then you're dead the first time you need to make withdrawals after a mistake or after a major market downturn. As a fellow math Ph.D. student, I know your pain. I, too, struggled for a while with boredom in an earlier career, but it's possible to make it work. I think the secret is to find a job that's engaging enough that your mind can't wander too much at work, and set aside some hobby time to work on interesting projects. You likely have some marketable skills that can work for you outside of academia, if you look for them, to allow you to find an interesting job. I think there's not much you can do besides trying not to get fired from your next McJob until you can find something more interesting. There's no magic money-for-nothing in the stock market. "I think that pattern is impossible, since the attempt to apply the second half would seem to prevent executing the first. Could you rewrite that as ""After the stock rises to $X, start watching for a drop of $Y from peak price; if/when that happens, sell."" Or does that not do what you want? (I'm not going to comment on whether the proposed programmed trading makes sense. Trying to manage things at this level of detail has always struck me as glorified guesswork.)" I spent a while looking for something similar a few weeks back and ended up getting frustrated and asking to borrow a friend's Bloombterg.   I wish you the best of luck finding something,  but I wasn't able to.   S&amp;P and Morningstar have some stuff on their site,  but I wasn't able to make use of it.  Edit: Also,  Bloomberg allows shared terminals.  Depending on how much you think as a firm,  these questions might come up,  it might be worth the 20k / year "I'm just trying to visualize the costs of trading. Say I set up an account to trade something (forex, stock, even bitcoin) and I was going to let a random generator determine when I should buy or sell it. If I do this, I would assume I have an equal probability to make a profit or a loss. Your question is what a mathematician would call an ""ill-posed problem.""  It makes it a challenge to answer.  The short answer is ""no.""  We will have to consider three broad cases for types of assets and two time intervals. Let us start with a very short time interval.  The bid-ask spread covers the anticipated cost to the market maker of holding an asset bought in the market equal to the opportunity costs over the half-life of the holding period.  A consequence of this is that you are nearly guaranteed to lose money if your time interval between trades is less than the half-life of the actual portfolio of the market maker.  To use a dice analogy, imagine having to pay a fee per roll before you can gamble.  You can win, but it will be biased toward losing. Now let us go to the extreme opposite time period, which is that you will buy now and sell one minute before you die.  For stocks, you would have received the dividends plus any stocks you sold from mergers.  Conversely, you would have had to pay the dividends on your short sales and received a gain on every short stock that went bankrupt.  Because you have to pay interest on short sales and dividends passed, you will lose money on a net basis to the market maker.  Maybe you are seeing a pattern here.  The phrase ""market maker"" will come up a lot. Now let us look at currencies.  In the long run, if the current fiat money policy regime holds, you will lose a lot of money.  Deflation is not a big deal under a commodity money regime, but it is a problem under fiat money, so central banks avoid it.  So your long currency holdings will depreciate.  Your short would appreciate, except you have to pay interest on them at a rate greater than the rate of inflation to the market maker. Finally, for commodities, no one will allow perpetual holding of short positions in commodities because people want them delivered.  Because insider knowledge is presumed under the commodities trading laws, a random investor would be at a giant disadvantage similar to what a chess player who played randomly would face against a grand master chess player.  There is a very strong information asymmetry in commodity contracts.  There are people who actually do know how much cotton there is in the world, how much is planted in the ground, and what the demand will be and that knowledge is not shared with the world at large.  You would be fleeced. Can I also assume that probabilistically speaking, a trader cannot do   worst than random? Say, if I had to guess the roll of a dice, my   chance of being correct can't be less than 16.667%. A physicist, a con man, a magician and a statistician would tell you that dice rolls and coin tosses are not random.  While we teach ""fair"" coins and ""fair"" dice in introductory college classes to simplify many complex ideas, they also do not exist.  If you want to see a funny version of the dice roll game, watch the 1962 Japanese movie Zatoichi.  It is an action movie, but it begins with a dice game.   Consider adopting a Bayesian perspective on probability as it would be a healthier perspective based on how you are thinking about this problem.  A ""frequency"" approach always assumes the null model is true, which is what you are doing.  Had you tried this will real money, your model would have been falsified, but you still wouldn't know the true model. Yes, you can do much worse than 1/6th of the time.  Even if you are trying to be ""fair,"" you have not accounted for the variance. Extending that logic, then for an inexperienced trader, is it right to   say then that it's equally difficult to purposely make a loss then it   is to purposely make a profit? Because if I can purposely make a loss,   I would purposely just do the opposite of what I'm doing to make a   profit. So in the dice example, if I can somehow lower my chances of   winning below 16.6667%, it means I would simply need to bet on the   other 5 numbers to give myself a better than 83% chance of winning. If the game were ""fair,"" but for things like forex the rules of the game are purposefully changed by the market maker to maximize long-run profitability.  Under US law, forex is not regulated by anything other than common law.  As a result, the market maker can state any price, including prices far from the market, with the intent to make a system used by actors losing systems, such as to trigger margin calls.  The prices quoted by forex dealers in the US move loosely with the global rates, but vary enough that only the dealer should make money systematically.  A fixed strategy would promote loss. You are assuming that only you know the odds and they would let you profit from your 83.33 percentage chance of winning. So then, is the costs of trading from a purely probabilistic point of   view simply the transaction costs? No matter what, my chances cannot   be worse than random and if my trading system has an edge that is   greater than the percentage of the transaction that is transaction   cost, then I am probabilistically likely to make a profit? No, the cost of trading is the opportunity cost of the money.  The transaction costs are explicit costs, but you have ignored the implicit costs of foregone interest and foregone happiness using the money for other things. You will want to be careful here in understanding probability because the distribution of returns for all of these assets lack a first moment and so there cannot be a ""mean return.""  A modal return would be an intellectually more consistent perspective, implying you should use an ""all-or-nothing"" cost function to evaluate your methodology." My reaction to this is that your observation @D.W. is spot on correct: It sounds like long-term market timing: trying to do a better job than   the rest of the market at predicting, based upon a simple formula,   whether the market is over-priced or under-priced. I read the post by the founder of Valuation Informed Indexing, Rob Bennet. Glance at  the comments section. Rob clearly states that he doesn't even use his own strategy, and has not owned, nor traded, any stocks since 1996! As another commenter summarizes it, addressing Rob: This is 2011. You’ve been 100% out of stocks — including indexes —   since 1996? That’s 15 years of taking whatever the bond market, CDs or   TIPS will yield (often and currently less than 2%)... I’m curious how   you defend not following your own program even as you recommend it for   others? Rob basically says that stocks haven't shown the right signals for buying since 1996, so he's stuck with bonds, CD's and fixed-income instead. This is a VERY long-term horizon point of view (a bit of sarcasm edges in from me). Answering your more general question, what do I think of this particular Price/ Earnings based ratio as a way to signal asset allocation change i.e. Valuation Informed Investing? I don't like it much. "Yes, and the math that tells you when is called the Kelly Criterion. The Kelly Criterion is on its face about how much you should bet on a positive-sum game. Imagine you have a game where you flip a coin, and if heads you are given 3 times your bet, and if tails you lose your bet.  Naively you'd think ""great, I should play, and bet every dollar I have!"" -- after all, it has a 50% average return on investment.  You get back on average 1.5$ for every dollar you bet, so every dollar you don't bet is a 0.5$ loss. But if you do this and you play every day for 10 years, you'll almost always end up bankrupt.  Funny that. On the other hand, if you bet nothing, you are losing out on a great investment.  So under certain assumptions, you neither want to bet everything, nor do you want to bet nothing (assuming you can repeat the bet almost indefinitely). The question then becomes, what percentage of your bankroll should you bet? Kelly Criterion answers this question.  The typical Kelly Criterion case is where we are making a bet with positive returns, not an insurance against loss; but with a bit of mathematical trickery, we can use it to determine how much you should spend on insuring against loss. An ""easy"" way to undertand the Kelly Criterion is that you want to maximize the logarithm of your worth in a given period.  Such a maximization results in the largest long-term value in some sense. Let us give it a try in an insurance case. Suppose you have a 1 million dollar asset.  It has a 1% chance per year of being destroyed by some random event (flood, fire, taxes, pitchforks). You can buy insurance against this for 2% of its value per year.  It even covers pitchforks. On its face this looks like a bad deal.  Your expected loss is only 1%, but the cost to hide the loss is 2%? If this is your only asset, then the loss makes your net worth 0.  The log of zero is negative infinity.  Under Kelly, any insurance (no matter how inefficient) is worth it.  This is a bit of an extreme case, and we'll cover why it doesn't apply even when it seems like it does elsewhere. Now suppose you have 1 million dollars in other assets.  In the insured case, we always end the year with 1.98 million dollars, regardless of if the disaster happens.  In the non-insured case, 99% of the time we have 2 million dollars, and 1% of the time we have 1 million dollars. We want to maximize the expected log value of our worth.  We have log(2 million - 20,000) (the insured case) vs 1% * log(1 million) + 99% * log(2 million). Or 13.7953 vs 14.49.  The Kelly Criterion says insurance is worth it; note that you could ""afford"" to replace your home, but because it makes up so much of your net worth, Kelly says the ""hit it too painful"" and you should just pay for insurance. Now suppose you are worth 1 billion.  We have log(1 billion - 20k) on the insured side, and 1%*log(999 million) + 99% * log(1 billion) on the uninsured side. The logs of each side are 21.42 vs 20.72.  (Note that the base of the logarithm doesn't matter; so long as you use the same base on each side). According to Kelly, we have found a case where insurance isn't worth it. The Kelly Criterion roughly tells you ""if I took this bet every (period of time), would I be on average richer after (many repeats of this bet) than if I didn't take this bet?""  When the answer is ""no"", it implies self-insurance is more efficient than using external insurance.  The answer is going to be sensitive to the profit margin of the insurance product you are buying, and the size of the asset relative to your total wealth. Now, the Kelly Criterion can easily be misapplied.  Being worth financially zero in current assets can easily ignore non-financial assets (like your ability to work, or friends, or whatever).  And it presumes repeat to infinity, and people tend not to live that long. But it is a good starting spot. Note that the option of bankruptcy can easily make insurance not ""worth it"" for people far poorer; this is one of the reasons why banks insist you have insurance on your proprety. You can use Kelly to calculate how much insurance you should purchase at a given profit margin for the insurance company given your net worth and the risk involved.  This can be used in Finance to work out how much you should hedge your bets in an investment as well; in effect, it quantifies how having money makes it easier to make money." "There are two things going on here, neither of which favors this approach. First, as @JohnFx noted, you should be wary of the sunk-cost fallacy, or throwing good money after bad. You already lost the money you lost, and there's no point in trying to ""win it back"" as opposed to just investing the money you still have as wisely as possible, forgetting your former fortune. Furthermore, the specific strategy you suggest is not a good one. The problem is that you're assuming that, whenever the stock hits $2, it will eventually rebound to $3. While that may often happen, it's far from guaranteed. More specifically, assuming the efficient market hypothesis applies (which it almost certainly does), there are theorems that say you can't increase your expected earning with a strategy like the one you propose: the apparent stability of the steady stream of income is offset by the chance that you lose out if the stock does something you didn't anticipate." Can you give more detail on the problem? If you can model it with a one step binomial tree, then the price is favourable as long as the chance to multiply is P(S^1 = 10 S^0 ) &gt; 0.1.  If you don't know the probabilities, then the usual go-to is to determine what probability space is that would lead to an expected profit (plus an error, and a cushion for risk aversion if the bet is sufficiently large).