A Winning Strategy in Stock Trading: Buy Low, Sell High

The idea is simple, straight forward and executable. In practice, the circumstances is more subtle regarding stock movement and trade transaction. To simplify the scenario, assume the stock price is P with possible movement of one dollar increment in either direction, up or down. Using "buy low, sell high" strategy, when the stock drops to P-1, one share is purchased. Porfolio begins with 1 share and no profit/loss. If the stock drops another increment to P-2, one more share is purchased. The porfolio now incurs a loss of 1 dollar with 2 shares holding. If the stock drops further to P-3, additional share is purchased. The porfolio now consists of 3 shares and a loss of 3 dollars (prvious loss of 1 dollar plus additional loss for 2 shares). The loss for the portfolio can be derived as n(n-1)/2 where n is the price movement. Therefore if stock decreases further to P-4, the loss would be 4(4-1)/2 = 6. Similarly, if the stock price goes up, the loss for each increment would be the same. Since stock movement is not permanently in one direction, there is always a possibility for retrace. Continuing with above scenario, if the stock price retrace back to from P-4 to P-3, one share is sold and the portfolio becomes 3 shares with a accumulated loss of 2 dollars. If the stock increases to P-2, then another share is sold and the portfolio becomes 2 shares with a profit of 1 dollar. If the stock increases further to P-1, another share is sold and the portfolio becomes 1 share with accumulated profit of 3 dollars. Finally if the stock returns to the initial price, the final holding is sold and the accumulated profit becomes 4 dollars. The analysis for stock price risng initially and drops back to original price would give the same amount of profit. It can be seen that the fluctuation of the stock price creates a profit using the "buy low, sell high" strategy. The actual amount is n where n is the total movement of the stock price. This appears to be a free ride but there is a catch. The risk reward is asymmetric meaning that For a specific price movement range, the possible gain versus maximum possible loss is just a small fraction and is in proportion of n^2. In a word, if the stock price does not change value in final holding but with a spike of n dollars, the profit would be n. However if the stock price does not return to initial value, the possible loss would be n(n-1)/2. The maximum possible loss escalates exponentially with the price range. This compares to the "double-up" betting strategy in baccarat casino game. The maximum potential loss escalates proportional to n^2 in both cases. In baccarat, the risk escalates with each game. In stock trade, the risk escalates with price fluation. Even worse for stock, while baccarat limit the loss on table cash, stock allows margin trading which means that loss is not limited only to the initial portfolio value because short selling has unlimited loss potential. Fortunately, in stock trading, the game is continuous thus allowing more control of the risk factor, i.e. n the incremental step for stock transaction. This can be achieved by means of choosing high value stocks meaning that n is a smaller percentage of stock price. Another approach is to use a smaller n unit, e.g. 10 cents instead of a dollar. In short term, stock price movement is inclined to random in nature. Stock price up and down is inevitable. The "buy low, sell high" strategy guarantees profit in price jitter. Consider the portfolio value as a combination of maximum loss from initial stock price to final stock price and a series of stock price jitter in the course. Assuming 0 shares of stock in the beginning, the maximum possible loss at the end is N(N-1)/2 regardless of the stock price going up or down where N is the deviation of final stock price from the beginning. However, the price jitters in the course generate profit n for each individual spike of price flutuation. It is evident that as long as the portfolio can survive the temporary loss for unfavorable price movement, profit can be accumulated with time in the long term. The strategy is most suitable for stocks trading at fair market value where it is not expected to deviate from current price too much, thus reducing the risk of maximum possible loss. For under-valued or over-valued stocks, an initial long or short holding can be used to hedge possible price movement. The strategy is possible on condition that no-commission stock trading is available to retail investors because the individual transaction profit in minute. In theory the strategy works perfectly but the major difficulty for implementation of this strategy is in the timing of trade execution at the desired target price. Since the result is very sensitive to the accuracy of execution, a swift market movement can cause missing operation and easily wipe out significant portion of profit.