Name of the Organisation : Institute Of Actuaries Of India
Exam : Actuarial Common Entrance Test – ACET
Subject : Financial Mathematics
Year : 2016
Document Type : Previous Years’ Question Papers
Website : https://actuariesindia.org/
Download Model/Sample Question Paper :
CT1 : https://www.pdfquestion.in/uploads/13260-CT1QP.pdf
CT2 : https://www.pdfquestion.in/uploads/13260-CT2QP.pdf
CT3 : https://www.pdfquestion.in/uploads/13260-CT3QP.pdf
CT4 : https://www.pdfquestion.in/uploads/13260-CT4QP.pdf
CT5 : https://www.pdfquestion.in/uploads/13260-CT5QP.pdf
CT6 : https://www.pdfquestion.in/uploads/13260-CT6QP.pdf
CT7 : https://www.pdfquestion.in/uploads/13260-CT7QP.pdf
CT8 : https://www.pdfquestion.in/uploads/13260-CT8QP.pdf
ACET Financial Mathematics Question Paper :
Time allowed : Three Hours (10.30 – 13.30 Hrs)
Total Marks : 100
Instructions To The Candidates :
1. Please read the instructions on the front page of answer booklet and instructions to examinees sent along with hall ticket carefully and follow without exception.
Related : Mahatma Gandhi Kashi Vidyapith Combined Pre-AYUSH Test – CPAT Question Paper 2016 : www.pdfquestion.in/13212.html
2. Mark allocations are shown in brackets.
3. Attempt all questions, beginning your answer to each question on a separate sheet.
4. Please check if you have received complete Question Paper and no page is missing. If so, kindly get new set of Question Paper from the Invigilator.
Q. 1) i) Explain and differentiate
a) Static and dynamic hedging
b) Arbitrage and Hedging (3)
ii) The current exchange rates of the INR/EUR, INR/USD, and EUR/USD pairs are 74.321, 67.5790, and 1.07980 respectively. Discuss any arbitrage opportunity that exists for a forex trader, given that a lot for each currency pair is 1,000 units. (3) [6]
Q. 2) Write short notes on the following :
i) Risks faced by the investor of a swap. (2)
ii) Increase in yield margins on the corporate bonds. (2)
iii) Characteristics of property as an investment compared to the bonds. (2) [6]
Q. 3) On 1st November 1985, a man was in receipt of three annuities mentioned below:
Annuity 1: INR 200 p.a. payable annually on 1st February each year, the final payment being 1st February 2007
Annuity 2: INR 320 p.a. payable quarterly on 1st January, 1st April, 1st July and 1st October each year, the final payment being 1st January 2002
Annuity 3: INR 180 p.a. payable monthly on the first day of each month, the final payment being 1st August 2004
Immediately after receiving the monthly payment due on 1st November 1985, the man requested that these three annuities be combined into a single annuity payable half-yearly on 1st February and 1st August in each subsequent year, the final payment being 1st February 2007. The man’s request was granted.
Find the amount of the revised annuity, given that it was calculated at an interest rate of 8% p.a. effective, all months are assumed to have equal length. [6]
Q. 4) i) Explain the relationship d = iv by general reasoning where d is the effective annual rate of discount and i is the effective annual rate of interest. (2)
ii) Given i = 0.08, Calculate
a. d(12)
b.i(365)
c. d
d.i(1/2)
(4) iii) Derive, from the first principles, the formula for for i>0 (2) [8]
Subject CT8 : Financial Economics
Time allowed : Three Hours (10.30 – 13.30 Hrs.)
Total Marks: 100
Q. 1) Comment on which form of market efficiency is supported/contradicted by the following scenarios:
i) Market over reacts to the news and corrects itself over couple of trading sessions. (1)
ii) An investor earns returns that are significantly higher than those predicted by a log-normal model fitted for a particular index using technical analysis. (2)
iii) Equity yields are correlated with the yields implied in the last three trading sessions and show an element of mean revision over a 4-5 year time frame. (2)
Q. 2) i) A stock price is currently Rs. 400. Assume that the expected return from the stock is 17% and that its volatility is 30%. Derive and determine the probability distribution for the rate of return (with continuous compounding) earned over a period of two years? State your assumptions. (4)
ii) Derive the differential equation of stock price S on the basis of your assumption in part 2(i). (3)
iii) Suppose that F is a function of a stock price S. Let are the volatilities of S and F respectively. Show that when the growth rate on S increases by p , the growth rate of F increases by p , where p is a constant (5) [12]
Q. 3) There are two equity stocks with correlation coefficient of ‘-0.6’ listed in a market with the share price, mean return and variance as shown in the following table. Short-selling is not permitted in the market and one cannot have infinitely divisible holdings
An investor wants to invest Rs. 10000 for one year in the market and approached you for advice.
i) Calculate the proportion of funds that you will advise the investor to invest in Share A if the variance on the portfolio is to be minimized. Hence calculate the expected return on the portfolio.
ii) How would your answer change if the correlation coefficient is +0.6 (2)
iii) Comment on risk appetite of the investor for whom the above advice would be appropriate. (1)
Q. 4) A financial advisory company is conducting a survey to check applicability of behavioural finance theories to a particular population and has devised the following questionnaire. According to you which theme of behavioural finance is the advisory trying to survey by asking each of the following questions?
i) Would a prior investment decision that resulted in a loss stop you from making a similar decision, even if the new investment appears to be the best alternative? (1)
ii) How frequently do you review your investment portfolio? (1)
iii) A popular analyst has commented that markets are expected to provide returns in excess of 15% in the coming year. Will you invest in equities with a hope to earn atleast 15% for next year? (1)
iv) Would you prefer to manage your portfolio yourself or rely on views of expert analysts? (1)