Buying on margin involves borrowing money to purchase stocks, which allows an investor to buy more shares than they could with their own funds alone. The return on a stock when buying on margin is affected by the proportion of funds borrowed in the following ways:

Leverage Effect: When you borrow money to invest, you are using leverage. This means that any gains on the stock are amplified because you are controlling a larger amount of stock with a smaller initial investment. If the stock price increases, the return on your equity $($your own invested funds$)$ is higher compared to if you had not borrowed.

Increased Risk: While leverage can amplify gains, it also amplifies losses. If the stock price decreases, the loss on your equity is greater because you still owe the borrowed amount plus interest. This means that a lower initial investment $($and higher loan amount$)$ increases the risk of losing more than your initial investment.

Interest Costs: Borrowing funds incurs interest costs, which can reduce the overall return on the investment. The higher the proportion of funds borrowed, the more interest you will have to pay, which can eat into your profits or increase your losses.

Margin Calls: If the stock price falls significantly, you may face a margin call, which requires you to deposit more funds or sell some of your stock to maintain the required equity level. This can force you to realize losses.

In summary, a lower initial investment and higher loan amount can increase potential returns due to leverage but also increase potential losses and risk due to the same leverage, interest costs, and the possibility of margin calls. The relationship between the proportion of funds borrowed and the return is directly tied to the leverage effect, which magnifies both gains and losses.