The creditworthiness of an investor is the most pertinent factor when buying stock on margin without the involvement of a CCP. This is because the investor is essentially borrowing money from a broker to buy the shares. The investor's creditworthiness will determine the interest rate they will be charged on the borrowed funds, the amount they can borrow, and the terms of the margin agreement. Therefore, an investor with a high credit score may be able to borrow more money at a lower interest rate, while an investor with a low credit score may face higher interest rates or stricter terms. This can significantly impact the profitability of the investment and the risk of a margin call, where the broker demands the investor deposit more money or securities into their account to cover potential losses.

Choice A is incorrect. The stock's historical dividend yield, while important in assessing the potential return on investment, does not directly relate to the risks associated with purchasing shares on margin without a central counterparty. It is more relevant when considering the income generation potential of an investment rather than its risk profile.

Choice C is incorrect. The stock's beta coefficient measures its volatility in relation to the market as a whole and can be useful in assessing market risk. However, it does not address the specific risks tied to purchasing shares on margin without using a CCP such as counterparty risk or credit risk which are more pertinent in this context.

Choice D is incorrect. The stock's price-to-earnings (P/E) ratio can provide insight into whether a stock is overvalued or undervalued relative to its earnings, but it does not directly assess the risks associated with margin trading without a CCP—particularly the credit and counterparty risks inherent in such transactions.