### Recent Question/Assignment

Please show working for the questions and use excel if possible.
1. A portfolio consists of the following instruments:
• 6 bonds with a face value of £200, paying an annual coupon of £5 semiannually that is due to mature in 40 months time. Assume the original term of the bond was 4 years.
• 3 forward contract to buy an investment vehicle, currently worth £500, 2 years from now that provides an income equivalent to a continuous dividend yield at the nominal rate of 2% p.a.
• 1 European Call Option on some stock with the strike price is £42 and an expiry of 9 months. The spot price of the underlying asset is £40 and the volatility in the market is 20%.
Suppose that 12-month, 24-month, 36-month, and 48-month and 60-month zero rates are 2.4%, 2.6%, 2.9%, 3% and 3.3% per annum with continuous compounding
respectively.
(a) Calculate the value of the portfolio (you may wish to write some python or excel code to accomplish this). 
(b) Calculate the yield to maturity of the bond if it had been purchased for £168 just after the second coupon payment. 
(c) If the interest rates shift (upwards and downwards) by 0.1%, calculate the new value of the portfolio (This is much easier if you wrote some code to calculate the value of the portfolio in the previous part). 
(d) Calculate the following Greeks for this portfolio; p, T, A. 
(e) For the interest rates given, optimise the portfolio. You can have a maximum of 10 instruments in the portfolio and can vary the ratio of each. 
(f) Explain briefly (in no more than a few sentences) how you would hedge this portfolio against making a large loss.