Below are the economics model questions
In a particular country, which uses dollars as its national currency, price inflation has been running at 20% pa for the last 20 years. Calculate the average annual real rate of return for each of the following investments: (i) A set of gold coins purchased for $14,000 on 1 January 2015 and sold for $20,000 on 31 December 2017. (ii) A painting purchased for $3,000 on 1 March 2017 and sold for $3,200 on 1 September 2017. (iii) A diamond purchased for $13,000 on 1 July 2016 and sold for $10,000 on 1 July 2018. (iv) A statuette purchased for $7,500 on 1 November 2010 and sold for $19,000 on 31 December 2017. On 1 January 2015 an investor purchased f10,000 nominal of a stock that pays coupons half-yearly on 30 June and 31 December each year at the rate of 6% pa and is redeemable at par on 31 December 2027. The investor is liable for income tax at the rate of 40%, but is not liable for capital gains tax. Calculate the price paid by the investor in order to achieve a net redemption yield of 5% pa effective. A fixed-interest security with a coupon rate of 6% pa payable half-yearly in arrears is purchased by an investor who is subject to capital gains tax at a rate of 30%. The fixed-interest security is redeemable at par after 15 years. The price paid is such that the investment provides a gross redemption yield of 10% pa effective. Calculate the amount of capital gains tax payable by the investor per f100 nominal. A stock with a term of 9% years has a coupon rate of 5% pa payable half-yearly in arrears and is redeemable at 105%. An investor who is not subject to tax purchases f100 nominal of the stock for E85. Calculate the yield obtained by the investor. An investor purchases a bond 6 months after issue. The bond will be redeemed at 105% eight years after issue and pays coupons of 4% per annum annually in arrears. The investor pays tax of 25% on income and 15% on capital gains. (i) Calculate the purchase price of the bond per f100 nominal to provide the investor with a rate of return of 5% per annum effective. [6] The real rate of return expected by the investor from the bond is 2% per annum effective. (ii) Calculate the annual rate of inflation expected by the investor. [2] [Total 8]You want to use Cox regression to estimate the force of mortality for a group of endowment assurance policyholders. You propose using a model that takes account of duration (ie the time that has elapsed since the policy was issued) and the age and sex of the policyholder. You start by investigating the model: "(x, 21, 22 ) = Ho(x) eBZ+ BZz where x denotes the age of the policyholder, Z1 = 0 if the duration is less than 1 year if the duration is at least 1 year 0 for males Zz = 1 1 for females You have estimated the values of the parameters , and B,, and have obtained the following results: Covariate Parameter Standard error Duration 0.416 0.067 Sex -0.030 0.017 (i) State the class of policyholders to which the baseline hazard refers. [1] (ii) Explain whether the duration covariate is significant in determining mortality. [3] (iii) Compare the force of mortality for a new female policyholder to that of a male policyholder of the same age, who took out a policy 2 years ago. [2] [Total 6]
