Subject CT1 – Financial Mathematics Core Technical The aim of the Financial Mathematics subject is to provide a grounding in financial mathematics and. CT1 is one of the nine Core Technical (CT) subjects. Previously a non-member could only apply for the CT1 exam. For the April exams, non-members were able to apply for either CT1 (Financial Mathematics) or CT3 (Probability and Mathematical Statistics). exams edition This is the Core Reading for the exams which will be sat in April and September It is sold as hole-punched sheets, for you to add .
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Introduction to mathematical modelling of financial and insurance markets with and Institute of Actuaries CT1 syllabus (Financial Mathematics, core technical). CT1 – Financial Mathematics For Examinations. Define the present value of a future payment. state the inflows and outflows in each future. If you have never done any actuarial mathematics before then you will have quite a lot to learn (if you have done any other financial maths then that will help a lot.
Why do we assume that arbitrage opportunity does not exist?
How is real rate of interest different from money rate of interest? In simple terms, a real rate of interest is the rate that allows for inflation whereas money rates of interest ignore the effect of inflation. So in period of positive inflation, real rate of interest will be lower than the money rate of interest and in period of negative inflation, the real rate of interest will be higher than the money rate of interest. What is a zero coupon bond? A zero coupon bond as the name implies is one that has no coupon payments i.
What is principle of consistency and where does it fail? Principle of consistency states that in a consistent market the proceeds of an investment should not depend on the course of action taken by the investor i.
Principle of consistency fails when the interest rate varies over the period or when the cash flows are deferred. Net present value NPV is calculated as present value of cash inflows less present value of cash outflows.
It gives the value of the project at the outset. The assumption made while calculating NPV is more realistic because IRR may not reflect the true rate at which cash flows can be reinvested. Both the tools are majorly used to evaluate the profits from the investments but the cons associated with IRR makes NPV a much better measure.
Why do we need to immunize and how do we immunize? We immunize our portfolio to protect our fund from any small changes in the interest rate. To immunize our portfolio, three conditions need to be met: Value of the assets at a given rate of interest should be equal to the value of the liabilities The volatility of asset and liability cash flow series is equal.
The convexity of asset cash flow series should be greater than that of the liability cash flow.
Core Reading for the 2018 exams - CT1 Financial Mathematics
Money weighted rate of return MWRR is the yield earned over the investment period. Describe the main factors influencing the term structure of interest rates.
Apply the above results to the calculation of the probability that a simple sequence of payments will accumulate to a given amount at a specific future time.
Show an understanding of the term structure of interest rates. Define the duration and convexity of a cashflow sequence.
CT1 Notes (pdf file)
Derive algebraically. Explain what is meant by the par yield and yield to maturity. Flag for inappropriate content. Related titles. Jump to Page. Search inside document. Documents Similar To CT1.
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Kiran Kumar Kuppa. Diego Gaspar Terra. Arun Akchutha. Arvind Ace. Vishy Bhatia. Akku Chaudhary. Popular in Discounting. Nikhil Khobragade. Masirah Muhammed Zerna. Kristel Bautista. The purpose of Core Reading is to ensure that tutors, students and examiners have a clear shared appreciation of the requirements of the syllabus for the qualification examinations for Fellowship of both the Faculty and Institute.
The manual gives a complete coverage of the syllabus so that the appropriate depth and breadth is apparent. In examinations students will be expected to demonstrate their understanding of the concepts in Core Reading.
Examiners will have this Core Reading manual when setting the papers. In preparing for examinations students are recommended to work through past examination questions and will find additional tuition helpful. The manual will be updated each year to reflect changes in the syllabus, to reflect current practice and in the interest of clarity.
For a given cashflow process, state the inflows and outflows in each future time period and discuss whether the amount or the timing or both is fixed or uncertain. The practical work of the actuary often involves the management of various cashflows.
These are simply sums of money, which are paid or received at different times. The timing of the cashflows may be known or uncertain. The amount of the individual cashflows may also be known or unknown in advance. From a theoretical viewpoint one may also consider a continuously payable cashflow.
For example, a company operating a privately owned bridge, road or tunnel will receive toll payments. The company will pay out money for maintenance, debt repayment and for other management expenses.
Similar cashflows arise in all businesses. In some businesses, such as insurance companies, investment income will be received in relation to positive cashflows premiums received before the negative cashflows claims and expenses.
Where there is uncertainty about the amount or timing of cashflows, an actuary can assign probabilities to both the amount and the existence of a cashflow. In this Subject we will assume that the existence of the future cashflows is certain. For the investor there is a negative cashflow at the point of investment and a single known positive cashflow on the specified future date.
In many instances such a loan takes the form of a fixed interest security, which is issued in bonds of a stated nominal amount. The characteristic feature of such a security in its simplest form is that the holder of a bond will receive a lump sum of specified amount at some specified future time together with a series of regular level interest payments until the repayment or redemption of the lump sum.
The investor has an initial negative cashflow, a single known positive cashflow on the specified future date, and a series of smaller known positive cashflows on a regular set of specified future dates. If inflationary pressures in the economy are not kept under control, the downloading power of a given sum of money diminishes with the passage of time, significantly so when the rate of inflation is high. Here the initial negative cashflow is followed by a series of unknown positive cashflows and a single larger unknown positive cashflow, all on specified dates.
However, it is known that the amounts of the future cashflows relate to the inflation index. Note that in practice the operation of an index-linked security will be such that the cashflows do not relate to the inflation index at the time of payment, due to delays in calculating the index. It is also possible that the need of the borrower or perhaps the investors to know the amounts of the payments in advance may lead to the use of an index from an earlier period.
The interest additions will be subject to regular change as determined by the investment provider. These additions may only be known on a day-to-day basis. The amounts and timing of cashflows will therefore be unknown.
Equity shareholders own the company that issued the shares. For example if a company issues 4, shares and an investor downloads 1,, the investor owns 25 per cent of the company. In a large organisation there may be many thousands of shareholders. Equity shares do not earn a fixed rate of interest as fixed interest securities do. The distribution of profits to shareholders takes the form of regular payments of dividends.
Since they are related to the company profits that are not known in advance, dividend rates are variable. It is expected that company profits will increase over time. It is therefore expected also that dividends per share will increase — though there are likely to be fluctuations.
This means that in order to construct a cashflow schedule for an equity it is necessary first to make an assumption about the growth of future dividends. It also means that the entries in the cashflow schedule are uncertain — they are estimates rather than known quantities.
In practice the relationship between dividends and profits is not a simple one. Companies will, from time to time, need to hold back some profits to provide funds for new projects or expansion.
Companies may also hold back profits in good years to subsidise dividends in years with poorer profits. Additionally, companies may be able to distribute profits in a manner other than dividends, such as by downloading back the shares issued to some investors. Since equities do not have a fixed redemption date, but can be held in perpetuity, we may assume that dividends continue indefinitely unless the investor sells the shares or the company downloads them back , but it is important to bear in mind the risk that the company will fail, in which case the dividend income will cease and the shareholders would only be entitled to any assets which remain after creditors are paid.
The future positive cashflows for the investor are therefore uncertain in amount and may even be lower, in total, than the initial negative cashflow. The precise conditions under which the annuity payments will be made will be clearly specified. In particular, the number of years for which the annuity is payable, and the frequency of payment, will be specified. Also, the payment amounts may be level or might be specified to vary — for example in line with an inflation index, or at a constant rate.
The cashflows for the investor will be an initial negative cashflow followed by a series of smaller regular positive cashflows throughout the specified term of payment. In the case of level annuity payments, the cashflows are similar to those for a fixed interest security. From the perspective of the annuity provider, there is an initial positive cashflow followed by a known number of regular negative cashflows.
In Subject CT5, Contingencies, the theory of this Subject will be extended to deal with annuities where the payment term is uncertain, that is, for which payments are made only so long as the annuity policyholder survives.
In the simplest of cases, the cashflows are the reverse of those for a fixed interest security. The provider of the loan effectively downloads a fixed interest security from the borrower.
In practice, however, the interest rate need not be fixed in advance. The regular cashflows may therefore be of unknown amounts. It may also be possible for the loan to be repaid early. The number of cashflows and the timing of the final cashflows may therefore be uncertain.
In its simplest form, the interest rate will be fixed and the payments will be of fixed equal amounts, paid at regular known times. The cashflows are similar to those for an annuity certain. Additionally, it is possible that the regular repayments could be specified to increase or decrease with time.
Such changes could be smooth or discrete.
The first repayment will consist almost entirely of interest and will provide only a very small capital repayment. In contrast, the final repayment will consist almost entirely of capital and will have a small interest content. Define the present value of a future payment. Discount a single investment under the operation of simple commercial discount at a constant rate of discount.
Describe how a compound interest model can be used to represent the effect of investing a sum of money over a period. Interest may be regarded as a reward paid by one person or organisation the borrower for the use of an asset, referred to as capital, belonging to another person or organisation the lender. Capital and interest need to be measured in terms of the same commodity, but when expressed in monetary terms, capital is also referred to as principal.
If there is some risk of default i.The investor has an initial negative cashflow, a single known positive cashflow on the specified future date, and a series of smaller known positive cashflows on a regular set of specified future dates. Instead a more approximate probability, or likelihood, may be determined after careful consideration of the risks. Dawes KPMG. The time 0 and the unit of time may be chosen so as to simplify the calculations.
By formula 1.