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.

Strategy for Trading Overvalued Stocks

Many retail investors should still remember the 2021 GME frency. The stock GME raised from single digit share price months ago to over 500 dollars (after 1-to-4 stock split >125 dollars as of February 2025) at the peak. The share price soared fastest before reaching the peaK, from below 50 dollars to over 500 dollars in just a few days. It also dropped fast afterwards. From the lowest single digit share price to the peak it took around one year. It is an increase of nearly 10,000%. But the most eye catching is the 10X multiple around the peak in a few days. Investor can make huge profit either when the stocking price is rising or falling. For the rising trend, investor does not know where is the peak. For example, at 50 dollars per share, it was already considered overvalued at that time. Though GME current price is around 27 dollars (equivalent to 108 dollars in 2021 before stock split). The reason to buoy the stock price was because GME issued new shares soon after the peak and for more than one time. This significantly boosted the cash holding. The board made clever decision to take advantage of the frenzy. Retail investors should also know the fair stock value but they would still buy the momentum. This is similar to gambling because everybody knows that it can start to fall at any time. Couple of years before the GME frenzy, another stock TLRY exhibited similar price spike. From IPO price of 17 dollars to the peak of exactly 300 dollars, it took less than two years. The stock soared 400% in just a few days before reaching the peak. Although the peak happened after the IPO lockup period, the board did not issue new shares to take advantage of the overvalued stock price. As of this writing the price of TLRY is just under a dollar. There is no stock split since the peak. The merger with Aphria should have no effect on the stock price since no cash is involved. On the other hand, betting on the fall almost guarantees a win. "The market can remain irrational longer than you can remain solvent". To ensure that a trade can survive margin call at the peak, retail investors can only use a small fraction of the fund on hand to short sell the stock. A thousand dollars can only generate a small profit of a few dollars although in just a few days. Otherwise a greedy investor may lose the whole investment due to forced liquidation by margin call. Theoretically speaking there is still enough time to trade the stock after the peak is passed. But in reality, there would be no shares available to borrow at that time because everybody is selling shares. There is much more sellers than buyers and there is T+2 time lag for each stock transaction. To ensure availability, stock has to be borrowed before the peak and investor has to endure the temporary loss during the spike. Following table shows the percentage usage of fund to survive the margin call of a stock price spike. fixed share count leverage spike safety 1X 5X 11% 1X 10X 5% 3X 5X 17% 3X 10X 8% If there is no leverage for the portfolio, investor can only use 11% for trading to survive margin call of a 5X price spike. For 10X price spike, only 5% can be used. Leverage can improve fund usage but not as much as it appears. 3X leveraging can only increase the safety margin from 11% to 17% for 5X price spike and from 5% to 8% for 10X price spike. An approach for better usage of available fund is to actively monitor the stock to maintain a constant NAV. If the stock rises, NAV will also rise (short selling refers to negative value). This means that stock will be purchased to reduce borrowing. If the stock falls, NAV will also fall. This means that stock will be sold to increase borrowing. Such method can significantly improve the fund usage but at some cost. Without active monitoring, if the porfolio can survive the price spike, when the price falls back to original selling price, there will be no loss. If the price drops further, there will be profit. With active monitoring, if the porfolio can survive the price spike, when the price falls back to original selling price, there will be some loss. This can be compared to the loss in NAV for leveraged ETF. If after price fluctuation, the underlying stock remains the original price, the leveraged ETF will incur minor damage in NAV. For simplicity, assuming that after initial transaction, the stock price rises linearly from 1 to X and then drops back to 1 and below. Two price spike and two fund leveraging are considered, namely 5X/10X and 1X/3X respectively. Using spreadsheet to model the price change during the stock price fluctuation, the safety margin, gain/loss, and breakeven level can be estimated. Note that the results are only approximation using 10% steps for various scenario. The safety margin and gain are slightly undervalued due to the average NAV in calculation being below 100%. This means that if the sale or purchase of a share of stock results in the NAV becoming larger than the assigned value (100% or other designated value), the transaction will not proceed. This can be explained by the fact that if NAV of more than 100% of initial amount is used in the fallback process, the gain will be boosted. The following table shows the in crease in safety margin for fund usage and a 8%¬9% loss in initial capital. fixed shared value leverage spike safety gain/loss breakeven 1X 5X 38% -8% 1.0~0.9 1X 10X 30% -9% 1.0~0.9 3X 5X 50% -8% 1.0~0.9 3X 10X 37% -9% 1.0~0.9 If the stock NAV is increased after the peak has passed, there will be profit when the stock drops back to the initial transaction price. It is 7% for 5X price spike and 13% for 10X price spike. That means the breakeven point occurs at a higher price. For 5X price spike, it is 1.1~1.0 of original price. For 10X price spike, it is 1.2~1.1. Note that borrowing of stock may be difficult during the fall. fixed shared value (110% NAV during fallback) leverage spike safety gain/loss breakeven 1X 5X 38% 7% 1.1~1.0 1X 10X 30% 13% 1.2~1.1 3X 5X 50% 7% 1.1~1.0 3X 10X 37% 13% 1.2~1.1 If the stock NAV is increased further to 120%, the gain will be improved. Since the stock price is dropping , there is no concern of margin call. fixed shared value (120% NAV during fallback) leverage spike safety gain/loss breakeven 1X 5X 38% 23% 1.3~1.2 1X 10X 30% 36% 1.4~1.3 3X 5X 50% 23% 1.3~1.2 3X 10X 37% 36% 1.4~1.3 The risk reward is significant by increasing the stock NAV, more than linear proportion. In reality, borrowing may be difficult and there is usually a large borrowing interest fee depending on particular stock. Also, broker may impose a margin leverage of less than 1X such as in the case of GME frenzy. fixed shared value (150% NAV during fallback) leverage spike safety gain/loss breakeven 1X 5X 38% 69% 1.7~1.6 1X 10X 30% 103% 2.1~2.0 3X 5X 50% 69% 1.7~1.6 3X 10X 37% 103% 2.1~2.0 The trading scenario discussed here is overly simplified. There is irregular stock price fluctuation and it may be difficult to determine the peak until much later. These will be discussed in later posts.

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