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Algorithms for VWAP and Limit Order Trading
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... • say after interval I_j, algo. places order at level (1-ε)^m • Key Idea: after interval j, if price ever rises above the price (1-ε)^m, then our limit order is executed • Hence, at end of trading, can’t “strand” more than one order at any given price level ...
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Short (finance)



In finance, short selling (also known as shorting or going short) is the practice of selling securities or other financial instruments that are not currently owned, and subsequently repurchasing them (""covering""). In the event of an interim price decline, the short seller will profit, since the cost of (re)purchase will be less than the proceeds which were received upon the initial (short) sale. Conversely, the short position will be closed out at a loss in the event that the price of a shorted instrument should rise prior to repurchase. The potential loss on a short sale is theoretically unlimited in the event of an unlimited rise in the price of the instrument, however in practice the short seller will be required to post margin or collateral to cover losses, and any inability to do so on a timely basis would cause its broker or counterparty to liquidate the position. In the securities markets, the seller generally must borrow the securities in order to effect delivery in the short sale. In some cases, the short seller must pay a fee to borrow the securities and must additionally reimburse the lender for cash returns the lender would have received had the securities not been loaned out.Short selling is most commonly done with instruments traded in public securities, futures or currency markets, due to the liquidity and real-time price dissemination characteristic of such markets and because the instruments defined within each class are fungible.In practical terms, going short can be considered the opposite of the conventional practice of ""going long"", whereby an investor profits from an increase in the price of the asset. Mathematically, the return from a short position is equivalent to that of owning (being ""long"") a negative amount of the instrument. A short sale may be motivated by a variety of objectives. Speculators may sell short in the hope of realizing a profit on an instrument which appears to be overvalued, just as long investors or speculators hope to profit from a rise in the price of an instrument which appears undervalued. Traders or fund managers may hedge a long position or a portfolio through one or more short positions.
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