{"blocks": [{"key": "566ef678", "text": "Question", "type": "header-two", "depth": 0, "inlineStyleRanges": [], "entityRanges": [], "data": {}}, {"key": "925441b7", "text": "Consider a stock price that starts at 0 and evolves as a simple symmetric random walk, moving +1 or -1 each discrete time step. At each time T you:", "type": "unstyled", "depth": 0, "inlineStyleRanges": [], "entityRanges": [], "data": {}}, {"key": "5f776e27", "text": "Buy one share if the price change from T−1 to T is +1.", "type": "unordered-list-item", "depth": 0, "inlineStyleRanges": [], "entityRanges": [], "data": {}}, {"key": "d2e24dd1", "text": "Short (sell) one share if the price change is −1.", "type": "unordered-list-item", "depth": 0, "inlineStyleRanges": [], "entityRanges": [], "data": {}}, {"key": "96ea0670", "text": "Assuming you can accumulate multiple positions purchased at different prices, derive the variance of the cumulative profit of your holdings at time T.", "type": "unstyled", "depth": 0, "inlineStyleRanges": [], "entityRanges": [], "data": {}}, {"key": "6b672f11", "text": "Follow-up: What is the expected profit and why? How would the answer extend if the random walk is replaced by continuous-time Brownian motion?", "type": "unstyled", "depth": 0, "inlineStyleRanges": [], "entityRanges": [], "data": {}}], "entityMap": {}}