2) What is algorithm?

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1 2) What is algorithm? Step by step procedure designed to perform an operation, and which (like a map or flowchart) will lead to the sought result if followed correctly. Algorithms have a definite beginning and a definite end, and a finite number of steps. An algorithm produces the same output information given the same input information, and several short algorithms can be combined to perform complex tasks such as writing a computer program. A cookbook recipe, a diagnosis, a problem solving routine, are some common examples of simple algorithms. Suitable for solving structured problems (amenable to sequential analysis) algorithms are, however, unsuitable for problems where value judgments are required. Algorithm can be defined as outline of the essence of procedure represented in step by step instructional manner. When you implement this algorithm using any programming language, then it is said to be program. A certain problem can be solved using many different algorithms. Informally, an algorithm is a well defined computational procedure that takes some value or set of values as input and gives or produces some value or set of values as output. That is an algorithm is a sequence of computational steps that transform the input in to output. 7

2 Algorithms help us to understand scalability. Performance often draws the line between what is feasible and what is impossible. Algorithmic mathematics provides a language for talking about program behavior. The lessons of program performance generalize to other computing resources. Two main characteristics of a good algorithm are: 1. Running Time: A good algorithm should have shortest running time when compared with others. 2. Space Utilization: Lesser the amount of space an algorithm uses, the better. Finiteness: An algorithm must terminate after a finite number of steps and further each step must be executable in finite amount of time that it terminates (in finite number of steps) on all allowed inputs. In order to establish a sequence of steps as an algorithm, it should be established Definiteness (no ambiguity): Each steps of an algorithm must be precisely defined; the action to be carried out must be rigorously and unambiguously specified for each case. Inputs: An algorithm has zero or more but only finite, number of inputs. Output: An algorithm has one or more outputs. The requirement of at least one output is obviously essential, because, otherwise Effectiveness cannot know the answer/ solution provided by the algorithm. The outputs have specific relation to the inputs, where the relation is defined by the algorithm. 8

3 Effectiveness: An algorithm should be effective. This means that each of the operation to be performed in an algorithm must be sufficiently basic that it can, in principle, be done exactly and in a finite length of time, by person using pencil and paper. It may be noted that the FINITENESS condition is a special case of EFFECTIVENESS. If a sequence of steps is not finite, then it cannot be effective also. The running time depends on the input: an already sorted sequence is easier to sort. Parameterize the running time by the size of the input, since short sequences are easier to sort than long ones. Kind of Algorithm Analysis: Worst-case: (usually) T(n) = maximum time of algorithm on any input of size n. Average-case: (sometimes) T(n) = expected time of algorithm over all inputs of size n. Need assumption of statistical distribution of inputs. Best-case: Disadvantage for the slow algorithm that works fast on some input. Example: Write an algorithm to find average of two numbers. Step 1: Input two numbers. (Suppose a=6, b=6) Step 2: Do the total of two numbers (i.e a+b=12) Step 3: Find the average by dividing the total by 2 (i.e 12/2=6) Step 4: Display the answer. (6) Step 5: End 9

4 Algorithms: Areas of Concern: 1) Lack of Visibility We know what a specific algorithm is supposed to do, measure its pre-trade analytics and see how the post-trade results match up to that expectation. But if the trader didn t select the most optimal algorithm for that trade little can be done. This problem is caused by a lack of visibility and transparency into the algorithm while it is executing orders. 2) Algorithms Acting on Other Algorithms If fund managers trading pattern is spotted and regular; tracked with the use of algorithms, then these algorithms are liable to be reverse engineered. This implies that their buy and sell orders are pre-empted and used to the maximum effect by their competitors. Here, algorithms are acting on other algorithms. 3) Which Algorithm to Use? With brokers offering many algorithmic strategies, one concern is that buy-side institutions lack the tools to understand which algorithm to use for a particular stock. The lack of a standard benchmark has made it almost impossible to assess the quality of algorithms. Buy-side firms are having a hard time evaluating when to use a particular algorithm. For example, if a portfolio manager tells a trader to sell a mid-cap, semi-illiquid stock within five hours because the manager has to raise cash the trader may be confused about which algorithm would be the best solution, given the constraints on liquidity and time. They need a certain level of sophistication and understanding to use it. Algorithmic trading requires careful real-time performance monitoring as well as pre and post-trade analysis to ensure it is properly applied. Traders must calibrate the algorithms to suit portfolio strategy. Far from the sole or final answer to best execution, algorithmic trading represents an additional tool in a trader s expanding kit. Far more important is aligning execution choices with the level of order difficulty involved in terms of: order size, liquidity, and trade urgency. Low touch venues such as algorithmic trading lend themselves best to easier types of orders such as low-urgency and small orders for large cap stocks. But urgent orders for a large volume of small cap stocks would require a higher-touch approach to ensure best execution and cost efficiency. 4) Missing Ingredient The Trader s Gut Feel Algorithms are simply advanced trading tools and they cannot replace the human elements or make interaction redundant. Algorithms fail to capture a trader s gut feel. It is the intraday trading characteristics of a stock that assist a trader in determining the right strategy, whether to back off or be more aggressive. In order to allow their guts to play a proper role, the traders need to see precisely what actions their algorithms are taking, what venue the orders are being sent to, and where they get filled. It is early in 10

5 the development of trading software to think that the thought process of a human trader can be mimicked by an algorithm. Algorithms cannot compete with the ability of the human brain to react to unanticipated changes and opportunities. Some algorithm providers are trying to addressing this issue by offering instant messaging (IM) services that work with the algorithm. As trades go on, a trader is alerted of issues that arise and the trader can alter the strategy depending on the nature of news. At the end of the day, it s the clients who drive the demand and innovation necessitating next generation algorithms. The next generation of algorithms will be able to speak to the trader, to let the trader know what is going on dynamically, and allow the trader to interact with the algorithm. Soon we will have adaptive algorithms that adjust their execution at each moment in time in response to what they see happening in the Market just as a human trader 11