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). [10]

(b) Calculate the yield to maturity of the bond if it had been purchased for £168 just after the second coupon payment. [7]

(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). [10]

(d) Calculate the following Greeks for this portfolio; p, T, A. [10]

(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. [7]

(f) Explain briefly (in no more than a few sentences) how you would hedge this portfolio against making a large loss. [5]

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). [10]

(b) Calculate the yield to maturity of the bond if it had been purchased for £168 just after the second coupon payment. [7]

(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). [10]

(d) Calculate the following Greeks for this portfolio; p, T, A. [10]

(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. [7]

(f) Explain briefly (in no more than a few sentences) how you would hedge this portfolio against making a large loss. [5]

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