Suppose that you sell short 100 shares, now selling at $70 per share.
What is your maximum possible loss?
What happens to the maximum loss if you simultaneously place a stop buy order at $78?
The Max possible loss will be increasingly unbounded if P --> infinite.
If you simultaneously place a stop-buy order at $78, the maximum possible loss per share is $8.
To calculate the maximum possible loss when selling short 100 shares at a price of $70 per share, you need to take into account that when you sell short, you are essentially borrowing the shares to sell them. In this case, you have borrowed and sold 100 shares at $70 per share.
The maximum possible loss when selling short is theoretically unlimited because there is no cap on how high the stock price might rise. However, in order to calculate the maximum possible loss, you can assume that the stock price goes to its highest possible value.
So, let's assume that the stock price increases to the highest possible value, let's say $500 per share. Since you sold short 100 shares, you would need to repurchase them in the market at the new higher price of $500 per share to return the borrowed shares.
The calculation for the maximum loss would be:
Maximum Loss = (New Price - Original Price) * Number of Shares
= ($500 - $70) * 100
= $430 * 100
= $43,000
Therefore, the maximum possible loss would be $43,000.
Now, let's consider what happens to the maximum loss if you simultaneously place a stop buy order at $78. A stop buy order is an order placed to buy the shares if the stock price reaches or exceeds a certain specified price.
Assuming the stop buy order is triggered at $78, this means that you would repurchase the 100 shares at $78 per share, rather than waiting for the stock price to reach its highest possible value of $500.
The new calculation for the maximum loss with the stop buy order would be:
Maximum Loss = (Stop Price - Original Price) * Number of Shares
= ($78 - $70) * 100
= $8 * 100
= $800
Therefore, with the stop buy order in place, the maximum possible loss would be reduced to $800 as compared to the unlimited risk without the order.