Question

Suppose the current value of a popular stock index is 649.50 and the dividend yield on the index is 2.8%. Also, the yield curve is flat at a continuously compounded rate of 5.5%.

If you estimate the volatility factor for the index to be 18%, use the Black-Scholes model to calculate the value of an index call option with an exercise price of 662 and an expiration date in exactly three months. You may use Appendix D to answer the question. Do not round intermediate calculations. Round your answer to the nearest cent.$_____

Answer 1

The question revolves around the S&P 500 index's total annual rate of return, focusing on dividends and capital gains over the decades. Originally, dividends averaged about 4% but have decreased since the 1990s to about 1% to 2%, with capital gains now comprising a larger portion of total returns.

Step-by-step explanation:

The question is related to the historical analysis of the S&P 500 index and its total annual rate of return, including dividends and capital gains. Historically, from the 1950s to the 1980s, companies within the S&P 500 paid an average of 4% in dividends relative to their stock value. However, since the 1990s, there has been a notable decrease in dividends, often yielding closer to 1% to 2% return.

Furthermore, there has been a shift over time with capital gains becoming the more significant component of total returns, particularly during the 1980s and 1990s. The 2000s witnessed fluctuations in stock prices with dividends remaining low, with stock values generally ending the decade roughly where they began. In the 2010s and into the early 2020s, this trend of low dividends continued while stock prices saw increases.