Question 1

(a) Ten years ago, to supplement their planned retirement, a couple purchased a 25 year flexible savings plan for a target sum of £75,000, which was projected to grow at an annual equivalent rate (AER) of 8%. The insurance company, having reviewed their plan (as they do normally every 10 years), now inform the couple that they will have to increase their monthly premium as the rate of return has turned out to be lower than expected, or face the prospect of receiving a lump sum well below the target.

(i) Calculate the revised monthly premium for the next 15 years in order to meet the target sum of £75,000, based on a projected AER of 6%. (25%)

(ii) What would be the shortfall in the target sum if the couple continued paying their monthly premium as before, but the plan grows at 6% AER for the first 10 years, and then at 5% AER for the next 15 years? (25%)

(b) A householder takes out a mortgage of £75,000 to be repaid over 25 years at an assumed Annual Percentage Rate (APR) of 6.8 %. What would be the reduction in his monthly repayment if £10,000 of the capital were repaid at the end of 10 years, with a part repayment penalty charge of £199 added to the outstanding balance? (30%)

(c) A student loan company will lend you £5,000 now, repayable in 10 years with interest but the repayments will only start after 3 years when you graduate. What will be the end of year annual repayment for the remaining 7 years if the APR on the loan is 3.6%? (20%)

NB: It is better to perform your initial calculations to 6dp to avoid rounding off errors.

Question 2

(a) Using the present value of a fixed term bond, explain the relationship between the price, the par value and the rate of return on this bond. How do you distinguish between a bond that sells at a premium and a bond that sells at a discount? (20%)

(b) A £100 par value bond has a coupon rate of 8.25 per cent, payable semi-annually on 30 June and 31 December. The bond matures on 31 December 2010. Find the quoted price and the market price of this bond on 16 November 2006, given that the yield to maturity was 8 per cent. (20%)

(c) An investor has a portfolio of three assets. The expected returns, expected standard deviations and the correlation matrix of returns are:

Asset Expected Expected Correlation matrix

Return Stand dev A B C

A 2% 10% A 1.0 0.3 0.4

B 3% 12% B 1.0 0.2

C 4% 14% C 1.0

(i) Calculate the portfolio expected return and standard deviation if each asset constitutes one third of the portfolio. (15%)

(ii) Suggest weightings for the assets that would produce a portfolio with lower risk. Explain what risk is and why it is reduced. (15%)

(iii) Trace out the efficient segment for the above data, explaining how this is obtained. What is the expected return on the least risk portfolio? (30%)

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