Both the coupon rate and the reinvestment horizon directly influence the coupon reinvestment risk.

Coupon Rate: The coupon rate is the interest rate that the bond issuer agrees to pay to the bondholder annually, and it is expressed as a percentage of the bond's face value. The higher the coupon rate, the higher the amount of cash flows that need to be reinvested, thereby increasing the reinvestment risk.

Reinvestment Horizon: The reinvestment horizon refers to the time period over which the coupon payments are to be reinvested. The longer the reinvestment horizon, the greater the uncertainty about the future interest rates at which these coupon payments can be reinvested, thereby increasing the reinvestment risk.

Therefore, both the coupon rate and the reinvestment horizon directly correlate with the coupon reinvestment risk.

Why Choice A is incorrect: While the coupon rate does impact the reinvestment risk, it is not the only variable that directly influences this risk. The coupon rate determines the amount of cash flows that need to be reinvested, and thus higher coupon rates may lead to higher reinvestment risk if interest rates fall in future. However, this alone does not fully capture all aspects of reinvestment risk.

Why Choice B is incorrect: Similarly, while the reinvestment horizon also impacts the reinvestment risk, it cannot be considered as a standalone factor influencing this type of risk. Longer investment horizons typically increase exposure to potential changes in interest rates which can affect future cash flows from reinvestments.

Why Choice D is incorrect: This option suggests that neither coupon rate nor investment horizon influence coupon reinvestment risk, which contradicts standard fixed income securities principles where both these factors play a significant role in determining such risks.