Solve and Explain

1. Describe the key findings in behavioural finance

2.

An investor has taken out a $100,000 loan at a 10% per annum rate of interest, annually compounded. The investor uses the loan to buy a portfolio of stocks whose value follows a lognormal distribution, with parameters u = 12% per annum and 02 = 25% per annum. The investor plans to sell the stocks and repay the loan after five years. (i) Calculate the mean and the variance of the lognormal distribution. [1] (ii) Calculate the probability that the investor will have enough money to repay the loan plus interest. [2] After five years the stocks are only worth $120,000 so the investor cannot afford to repay the loan plus interest. (iii) Calculate the one-year 95% value at risk of the investor's stock portfolio from time t = 5 to time t = 6. [2] The annual standard deviation of the investor's stock portfolio at time t = 5 is $81,708. The bank agrees to continue the loan for another five years, as long as the investor can prove that the annual standard deviation of his portfolio is no higher than $40,000 at time t = 5. (iv) Calculate the proportion of the investor's stock portfolio he would have to sell in order to bring the value at risk down to a level acceptable to the bank. [1] The bank also offers a cash deposit account returning a 6% per annum rate of interest, annually compounded. The investor sells the proportion of the stock portfolio in part (iv) and invests the funds in the cash deposit account. The bank therefore continues the loan for another five years. (v) Calculate the probability that the investor's stocks and cash deposit combined are sufficient to repay the loan plus interest at time 10. [3] (vi) (a) Comment on this result. (b) Propose an alternative course of action for the investor. [2]The cumulative claim amounts incurred on a portfolio of motor insurance policies are as follows: Accident Year Development Year 0 2 3 2014 3,907 5,606 6.061 6,145 2015 4,831 7,319 7.470 2016 6,042 8,282 2017 7,061 The cumulative number of reported claims are as follows Accident Year Development Year 0 1 2 3 2014 435 469 528 534 2015 485 525 541 2016 509 558 2017 544 (i) Estimate the ultimate number of claims, for each accident year, using the chain-ladder technique. [4] (ii) Estimate the ultimate average incurred cost per claim, for each accident year, using the grossing-up method. [5] (iii) Calculate the total reserve required, using the results from (i) and (ii), assuming that claims paid to date are 19,544. [2]The trustees of a large defined benefit pension scheme, which is open to future benefit accrual, have instructed their actuary to carry out a funding valuation of the scheme. Pension increases are in line with price inflation. The pension scheme's assets are currently invested 60% in equities and 40% in bonds. (i) Set out the information the actuary will need to carry out the valuation (in addition to member data). [6] (ii) List the financial and demographic assumptions the actuary will need to make. [4] (iii) Explain how each of the assumptions in part (ii) may be derived. [12] (iv) Outline the considerations to be made when determining the valuation basis. [4]