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A portfolio consists of the following instruments: 3 bonds with a face value of 2 0 0 , paying an annual coupon of 5 semiannually

A portfolio consists of the following instruments:
3 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.
1 forward contract to buy an investment vehicle, currently worth 550,2 years
from now that provides an income equivalent to a continuous dividend yield at
the nominal rate of 2.6% p.a.
6 European Call Option on some stock with the strike price is 420 and an
expiry of 36 months. The spot price of the underlying asset is 400 and the
volatility in the market is 25%.
Suppose that 12-month, 24-month, 36-month, and 48-month and 60-month zero
rates are 4.4%,4.6%,4.9%,5% and 5.3% 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 183
just after the second coupon payment.
(c) If the interest rates shift (upwards and downwards) by 0.5%, 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 for this portfolio; and the , for the option.
(e) Explain briefly (in no more than a few sentences) how you would hedge this
portfolio against making a large loss.
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