6 – M3L607 Optimization SC PT2 V1

Let’s begin by understanding market impact. Here we have the price of a single stock over a period of time. Market impact is the effect that a market participant has when he buys or sells a number of stocks. Since the optimal liquidation problem only deals with selling stocks, for the rest of this lesson we will only focus on what happens to the stock price when we sell stocks. So, let’s see what happens when we sell a stock. Let’s suppose I sell a particular number of stocks right here. In general, when you sell a stock, its price decreases. In our model, we will assume that the price drops due to two factors. Temporary market impact and permanent market impact, which we’ll talk about in detail in a later lesson. What we see here is the permanent market impact on the stock price due to my action of selling. In this example, my action of selling has caused the stock price to drop from $100 to $90. This permanent impact occurs every time I sell a stock. So, if I sell the same number of stocks right here, then I will see the same market impact as before and similarly, if I sell again here and here. As we can see, by selling stocks in this particular fashion, the stock price has decreased from $100 to $60 due to the induced permanent market impact. Since the stock price decreases every time we sell, this means that we’re going to lose money. Let’s take a look at a concrete example to see how much money we would have lost by selling in this fashion.

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