A life insurance company has a portfolio of identical single premium endowment assurances with a combined sum assured of $1.5m. The outstanding term of the portfolio is exactly 20 years. The endowment assurance death benefit is payable at the end of the year of death. The endowment assurances were paid for by single premiums at the outset of the policies. The current age of all policyholders is 30 exact. The company holds three assets (A, B and C) to meet its liabilities in respect of this portfolio. The basis used by the company to value its liabilities, together with details of the assets held, is set out in worksheet ‘Q2 Base’. (i) Determine the present value of the insurance company’s portfolio of endowment assurances and the present value of total assets held in respect of the portfolio. (ii) Determine the volatility of the portfolio of endowment assurances and the volatility of total assets held in respect of the portfolio. The company now wishes to re-balance its holdings of assets B and C such that the portfolio is immunised against small changes in the rate of interest. The holding of asset A will remain unchanged. (iii) (a) Determine the new holdings of assets B and C. (b) Demonstrate that Redington’s conditions for immunisation are met with these new holdings. What is "re-balance its holdings of assets B and C" meaning? I can't understand logic of question (iii)-(a) ask for and answer.
It means you need to choose how much of B to hold and how much of C to hold such that the resulting portfolio is immunised. This will involve solving two simultaneous equations. One equation will set the PV of the assets equal to the PV of the liabilities, and the other will set the duration of the assets equal to the duration of the liabilities.
Could you please explain the logic of solution D10:F18 of Q2(iii)a? I don't quite understand what this area wants to express and what it does.
This is the solving of the simultaneous equations. We start off with the discount factors for B and C. These multiplied by the amounts of B and C must give the present value ie B*v^10 + C*v^25 = 447,803.22 The second equation is the volatility numerator: B*10*v^11 + C*25*v^26 = 8,416.260.08 The examiners then go through the process of isolating B and C ie working out the values that would be gained from holding just B or just C to work out what the amounts of those assets should be.
