Question 6. On January 1 a share is priced at $1,000. The share pays a dividend every 6 months. The last dividend payment was $20. The dividend amount increases 6% per annum convertible half-yearly. The first receivable dividend payment is due in 3 months. The continuously compounded risk-free rate of interest is 4% per annum. On January 1, an investor enters into a short position in a 12-month forward contract for delivery of one unit of the share. The forward price is determined so that his position is worth zero. (a) Calculate the forward price. (b) After 6 months, i.e. on July 1, the share price becomes $1,050. What is the value of the investor's position on July 1? (c) Comment on the reasons for a non-zero investor's position on July 1. Explain, without carrying out any further calculation, under which condition the investor's position will change towards zero in a month, assuming the interest rate and divi- dend scheme do not change. Question 6. On January 1 a share is priced at $1,000. The share pays a dividend every 6 months. The last dividend payment was $20. The dividend amount increases 6% per annum convertible half-yearly. The first receivable dividend payment is due in 3 months. The continuously compounded risk-free rate of interest is 4% per annum. On January 1, an investor enters into a short position in a 12-month forward contract for delivery of one unit of the share. The forward price is determined so that his position is worth zero. (a) Calculate the forward price. (b) After 6 months, i.e. on July 1, the share price becomes $1,050. What is the value of the investor's position on July 1? (c) Comment on the reasons for a non-zero investor's position on July 1. Explain, without carrying out any further calculation, under which condition the investor's position will change towards zero in a month, assuming the interest rate and divi- dend scheme do not change