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Usually stock returns are assumed to be normally distributed: $R\sim N(\mu,\sigma)$ If market goes up 1%, the expected stock return is $\mu = \beta\cdot 0.01 = 0.02$ (since β is the senstivity to market). Stock price going from 100 to over 103 requires a return $R$ of at least 103/100 – 1 = 0.03. As we have from the question σ = 0.02, we get: $$P(R\geq ... 8 In the academic literature it is extremely widely applied in the last 20 years. I would estimate maybe 200 empirical papers, or more. For example a common finding is that higher frequency (daily) wavelet correlations have been high since 2007, attributable either to increasing financial interation or the financial crisis. It is also popular to estimate the ... 7 Ask minus bid has nothing to do with the mid price - it is the spread. Generally you see a collection of bid/offer orders resting on different price levels. In the simplest case, you just see one bid at price p_b and one offer at price p_a. In this case the mid price is$$ p_m = \frac{p_a + p_b}{2} $$That's all there is to it - you don't need to "... 6 I'm not sure how deep of a question you are asking. The dog that did not bark is from a Sherlock Holmes murder mystery. The dog at the house did not bark at the intruder, so Holmes believed the dog knew the intruder. Therefore, the lack of evidence like barking, was itself the evidence. In the Cochrane paper, the introduction mentions that the lack of ... 5 Pring was (probably) simply referring to the fact that most indicators are function of price -- lots of different ways to twist and contort prices to define trends, reversal points, etc. Volume is another parameter entirely, as it doesn't depend on price; the market or share price can have an up day on average, high, or low volume, it can have a down day on ... 5 Yes I would recommend you to plot the log of prices instead of prices. It will re-scale the data while preserving the hierarchy of prices, and more importantly it allows to compare easily the growth among several stocks because a vertical move of 0.01 corresponds to a 1% change of the price at any point in the figure (not matter the price level and the ... 4 Art markets typically have huge transaction costs of the order of 10%, caused by buyers premium and auction fees. Therefore long holding periods are unavoidable, with long-term returns somewhere between those of bonds and equities. By its very nature, art is not easily replicated so arbitrage or derivatives are out. The rationality of agents (aka collectors) ... 4 Since you're asking on a quant finance forum, the mathematical approach would be Decide on a model that the stock price follows, and Compute the expected value of the price, conditional on the most recent price. A famous model, made ubiquitous by Black, Scholes and Merton, is a geometric Brownian motion. Under this model, the stock price S_T at time T ... 4 By definition, modified duration is$$ D_\text{mod} = \frac{1}{P} \frac{dP}{dy} where P is the dirty price of a bond. Clean price is the standard quoting convention for the vast majority of bond markets (though not all), but nearly all analytics, be it yield to maturity, DV01, or duration, are all computed using dirty price. 4 Step 1: Know your distribution Since \int_0^t W_s\mathrm{d}s\sim N\left(0,\frac{1}{3}t^3\right), we have \begin{align*} S_t &= S_0 \exp\left( rt-\frac{1}{6}\sigma^2 t^3 + \sigma \int_0^t W_s\mathrm{d}s \right) \\ &\overset{d}{=} S_0 \exp\left( rt-\frac{1}{6}\sigma^2 t^3 + \sigma \sqrt{\frac{1}{3}t^3} Z \right) \\ &\overset{d}{=} S_0 \exp\left( ... 4 "How do they choose the forex price number's precision?" By convention. And/or by vendor, e.g. BBG has 4dp for some pairs where Oanda has 5. And of course convention for forwards differs from spot, even for the same pair. There is some colour on the move to 'fractional pips' in the book "Why Aren't They Shouting?". EDIT: perhaps also ... 3 Why not just use Geometric Mean Returns? Each time you buy/sell an ETF calculate the holding period return as a percentage and plug into the formula. The answer is a percentage that you can use to calculate the approximate money appreciation (or loss) against your "fixed notional" 3 If anyone else is wondering what the actual answer is, I've figured it out. When viewing as weekly or monthly data, yahoo displays the Open, Low, High, Close, Vol., and Adj. Close "as of the end of the week/month beginning on ____." It is not an average of any kind. Using OP's example, Exxon opened at 60.25 on Jan 19, 1970 and closed at the end of ... 3 This mean that the reason why apple stock price went from 3 to 100 in 10years is the overnight variation in price. This is quite unexpected, if there was no overnight variation the stock price would have died a long time ago... Why is that ? Have we been lying to us ? This is because many business and financial news are reported at market close, either pre-... 3 I would say the financial- and the art market is very different, only the roots of the market / auctions is the same. As the art market is unique and very illiquid, alot of the strategies from the modern financial market simply does not apply. I have been building (and still maintains) a toolbox of models, which mostly try to find trends based on multiple ... 3 Index all the stocks to 100 in the start of the period!That is mulitiply all stock prices with 100 and divide all stock prices with their price in the beginning of the time series! 3 In the first case it is a "race condition": whichever order is received first (even if it is only one microsecond before the other) will populate the Book and the second limit order will execute against it, at the price of the first order. In the second case it is indeterminate and may depend on the details of how the "matching engine" works. Probably when ... 3 That simply means that a bond pays one unit of the currency in any state (regardless what happens in the future, i.e. there is no default risk about the payoff of a bond). So you will receive 1 in the next period (regardless what you paid for it). Of course, today you probably pay less than 1 due to time value of money... 3 A bond repays its notional face value (plus interest sometimes), not the original purchase price. Do not assume the the price you pay for a bond is its face value. Sometimes a law or a regulation (pretty useless, in my humble opinion:) does require that a bond newly issued in primary market be sold at exactly 100% par price (face value). Then the coupon ... 3 You can extract the risk neutral density implied by option prices and have a look at that. The implied probabilities are given by the prices of butterfly spreads in the market. This is common knowledge. Page 241 of this book explains how you could go about doing it in Excel: https://gaussiandotblog.files.wordpress.com/2018/02/wiley-trading-giles-peter-jewitt-... 3 Hi: Based on your question, it sounds like the Diebold-Mariano test might be perfect for your case. It doesn't require any sophisticated assumptions about models or processes etc. All one needs are the two sets of forecasts and the actuals. I can't find the actual paper but below is the reference to it. I imagine that, if you google hard enough, the paper ... 3 Most banks use mid market to compute daily MTM p/l whilst maintaining a reserve to account for liquidation costs. The latter is usually recalculated periodically and is indeed a function of market bid-offers. Market participants may use different methods because the definition of MTM pnl may differ depending on jurisdiction, accounting standards etc. 3 This is an excellent philosophical question. Recall that the goal of mark to market is to predict the P&L if we unwound this position in an orderly market. Suppose that you're in a very convinient world, where for every asset you know at all times the bid and offer (ask) prices, at which you can sell or buy these assets. Suppose you're just long some ... 3 Giving my 2 cents on your questions: I believe the amount of decimal places is dependent on (the exchange and) the type of financial product. However, an Investopedia article writes: In 2005, the Securities and Exchange Commission introduced Rule 612, also known as the Sub-Penny Rule. Rule 612 requires the minimum price increments for stocks over \1.00 to ... 3 An example of typical use of SVD: Suppose you have a square matrix. You would like to apply Cholesky decomposition. But Cholesky complains that the matrix is not positive definite. So you call SVD instead. You can then see whether you can tweak the matrix to obtain a positive definite matrix not materially different from your original matrix, and use ... 2 On exchanges, there is such orderbook with sufficient amount of limitorders, so when you place an order (market or limit), the "best" limitorders for you will be hitted and change the price last traded price. The price you see is actually just the midpoint between the currently best available bid and ask prices in the orderbook. Therefore, this price might ... 2 price went from \200 to \202, this is "one percent change", because \frac{\2}{\200}100=1 2 The state price vector are the prices of securities which pay \1 if and only if that state of the world occurs. This is just a question of being able to replicate the payoffs \begin{pmatrix} 1 \\ 0 \\ 0 \end{pmatrix}, \begin{pmatrix} 0 \\ 1 \\ 0 \end{pmatrix}, \begin{pmatrix} 0 \\ 0 \\ 1 \end{pmatrix}  with payoff vectors $\vec{b} = [1,1,1]^T$ and \$\...