Final answer:
The student's question involves determining the dividend $X of a stock using the current stock price, risk-free interest rate, and forward contract price, requiring knowledge of financial mathematics and market principles.
Step-by-step explanation:
The question pertains to calculating the dividend $X of a stock, given its current price, the risk-free rate, and the price of a forward contract expiring in three months. To find $X, one must understand the relationship between dividends, stock prices, and forward contracts. The no-arbitrage price of the forward reflects the value of all benefits and costs associated with owning the stock until the expiration of the forward, including dividends. If we denote the stock price as S, the dividend as D, and the risk-free rate as r, the no-arbitrage forward price F is given by F = (S - D)e^(rT), where T is the time until the forward's expiration, expressed in years.
With the numbers provided, we have S = $50, F = $44.66, r = 5.5%, or 0.055 in decimal form, and T = 3/12 = 0.25 years. We can solve for D with the equation $44.66 = ($50 - D)e^(0.055 * 0.25). By rearranging and solving for D, one can determine the value of the expected dividend.
The understanding of such financial concepts is essential when considering investments in stocks and other securities, and these principles guide decision-making in financial markets. The solution to this problem will involve financial mathematics and understanding of the time value of money and forward contracting.