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A line graph is the most suitable visual aid for presenting a report on monthly stock gains and losses over a one-year period. This type of graph effectively displays data points over time, making it ideal for showing trends and patterns across different months. By connecting the data points, a line graph allows viewers to easily track changes in stock performance over the year, highlighting both upward and downward trends.

While a bar chart could illustrate monthly gains and losses, it is more effective for comparing discrete categories rather than illustrating trends over time. Pie charts are generally used to represent parts of a whole and are not ideal for showing changes over time. Scatterplots are useful for showing the relationship between two variables but do not effectively communicate sequential data like stock performance across a year. Therefore, a line graph is the best choice for this specific scenario, providing clarity and immediate understanding of how stock performance fluctuates over time.