Question 4 (24% of marks available) Shan owns a successful florist shop. Shes also interested in investing and manages her own portfolio of bonds and other fixed-income securities. Shan once actively managed her portfolio; however, her shop has become increasingly successful, so she would like to you to manage her portfolio instead. Shan has informed you that she would like to cash out part of her portfolio in 8 years and use the proceeds to buy a vacation home in the south of France. Her portfolio has a current market value of $400,000, which is invested in the following 4 corporate bonds: $100,000 in a 12-year, 8.25% bond that has a current market value of $785; $100,000 in a 10-year, zero-coupon bond that has a current market value of $520; $100,000 in a 15-year, 12.5% bond that has a current market value of $1,180; $100,000 in a 12-year, 9.25% bond that has a current market value of $920. The 4 corporate bonds are investment grade, noncallable, and nonconvertible. Shan has also asked that you explore immunising her bond portfolio. a) Find the current yield and yield to maturity for each bond. Use annual compounding. [6 marks] b) Calculate the duration and modified duration of each bond. Indicate how the price of each bond would change if interest rates were to rise by 50 basis points and if interest rates were to fall by 50 basis points. [6 marks] c) Find the duration of the portfolio. Is Shans portfolio immunised considering her 8-year investment horizon? [4 marks] d) How would you lengthen the duration of this portfolio? What is the longest duration you could achieve? [2 marks] e) If possible, construct and describe a new, immunised $400,000 bond portfolio for Shan using 1 or more of the 4 bonds currently in her portfolio. [2 marks] f) If you are able to construct a new, immunised portfolio for Shan, will you then be able to ignore it for 8 years, leaving it as a buy-and-hold portfolio? Explain your answer. [4 marks]