# 7 – M3L608 Optimization SC PT3 V1

Let’s assume I have a total of 12 stocks and that the initial price of each stock is a $100. I will choose to sell my shares in four traits. Then each trade, I will sell three shares. For illustration purposes, we will assume that the stock price decreases$10 every time we sell three shares. Let’s now calculate the difference between my initial holdings and the money I made by selling the stocks in this fashion. My initial holdings amounts to $1,200 and the money that I made by selling the stocks is$1,020. This gives a difference of a $180. This means that we lost a$180 due to the costs of trading. This difference between the initial holdings and the money that I made by selling the stocks also known as the capture is called the implementation shortfall, which I will denote with I sub s. Now in reality, the stock price fluctuates in-between traits and is that as smooth as it is shown here. So, let’s take a look at a more realistic price model. Stock prices often fluctuate and are not smooth as we saw previously. So, if we perform the same four traits as we did before, we can see that the price at which each trade was executed is now different due to the fluctuations in stock price. So, let’s calculate the implementation shortfall for this case. Again, we’ll have a total of 12 stocks with an initial price per share of a $100. We’re still going to perform the same four traits and we’re still going to sell three shares at every trade. If we calculate the implementation shortfall for this case, we see that now we get$267.