Sophie 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, 9.25% bond that has a current market value of $775;
• $100,000 in a 10-year, zero-coupon bond that has a current market value of $510;
• $100,000 in a 15-year, 13.5% bond that has a current market value of $1,170;
• $100,000 in a 12-year, 10.25% bond that has a current market value of $910.
The 4 corporate bonds are investment grade, noncallable, and nonconvertible.
Sophie  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.(Show all steps)
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.(Show all steps)
c) Find the duration of the portfolio. Is Sophie’s portfolio immunised considering her 8-year investment horizon?(Show all steps)
d) How would you lengthen the duration of this portfolio? What is the longest duration you could achieve?(Show all steps)
e) If possible, construct and describe a new, immunised $400,000 bond portfolio for Sophie using 1 or more of the 4 bonds currently in her portfolio.(Show all steps)
f) If you are able to construct a new, immunised portfolio for Sophie, will you then be able to ignore it for 8 years, leaving it as a buy-and-hold portfolio? Explain your answer.