Chapter Two Cashflow Models PDF

Chapter two CASH FLOW MODELS 1.Definition ❑ A cashflow model is a mathematical projection of the payments arising from a financial transaction, eg a loan, a share or a capital project. Payments received are referred to as income and are shown as positive cashflows. Payments made are referre...

Chapter two CASH FLOW MODELS 1.Definition ❑ A cashflow model is a mathematical projection of the payments arising from a financial transaction, eg a loan, a share or a capital project. Payments received are referred to as income and are shown as positive cashflows. Payments made are referred to as outgo and are shown as negative cashflows. The difference at a single point in time (income less outgo) is called the net cashflow at that point in time. ❑ 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 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). ❑ Cash inflows are indicated by entering positive values. ❑ Cash outflows are indicated by entering negative values. Future Value versus Present Value Cash Flow Matching ► The means by which providers deliver benefits is through the investment of assets. A key decision for the provider is whether or not to invest in such a way that the expected cashflows from the assets held match the expected cashflows from the liabilities it has taken on. If the decision is taken to match the assets to the liabilities then the optimal matched position will need to be determined. If the decision is taken not to match the assets to the liabilities then additional capital will need to be held to cover the possibility that there are insufficient assets to meet the liabilities when they fall due. Additional capital, also called free assets, provides a cushion against adverse market movements. ASSETS VALUATION TERM ► BOOK VALUE : The value at which the assets is held in a company's accounts. ► Market value : Market value of an assets is the amount that can be realized by selling it at that time on the open market. Many assets are actively traded ,So their market price can be easily identified. Examples include listed company stocks and government and corporate Bonds. ► Experts valuers can estimate the market value of assets , Such as Property ,to which there is no objective market price.Valuations are typically based on the recent sales of Similar assets. ► Mark-to Model : when an assets is valued with reference to pricing model , the valuation is refeed to mark-to model. ► Mark-to-model valuations are used where no obvious market value exists ,perhaps because the assets is complex or unusual.Arguably, they should also be used when market value is clearly different from fair value. 2. Examples of cashflow scenarios ► cashflows that are assumed to be certain are classified as the following : The first few examples considered below are types of security or investment. A security is a tradeable financial instrument, ie a financial contract that can be bought and sold. 2.1 A zero-coupon bond The term zero-coupon bond is used to describe a security that is simply a contract to provide a specified lump sum at some specified future date. For the investor there is a negative cashflow at the point of investment and a single known positive cashflow on the specified future date. 2.2 A fixed-interest security ❑ A body such as an industrial company, a local authority, or the government of a country may raise money by floating a loan on the stock exchange. ❑ 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 2.3 An index-linked security ❑ If inflationary pressures in the economy are not kept under control, the purchasing power of a given sum of money diminishes with the passage of time, significantly so when the rate of inflation is high. For this reason some investors are attracted by a security for which the actual cash amount of interest payments and of the final capital repayment are linked to an ‘index’ which reflects the effects of inflation. ❑ 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. Hence these cashflows are said to be known 2.4 An equity ❑ Equity shares (also known as shares or equities in the UK and as common stock in the USA) are securities that are held by the owners of an organization. Equity shareholders own the company that issued the shares. ❑ Equity shares do not earn a fixed rate of interest as fixed-interest securities do. Instead the shareholders are entitled to a share in the company’s profits, in proportion to the number of shares owned. ❑ 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, and also, therefore, expected 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. 2.5 An annuity-certain ❑ An annuity-certain provides a series of regular payments in return for a single premium (ie a lump sum) paid at the outset. 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. 2.6 An ‘interest-only’ loan ❑ An ‘interest-only’ loan is a loan that is repayable by a series of interest payments followed by a return of the initial loan amount. ❑ The regular repayments only cover the interest owed, so the full capital amount borrowed remains outstanding throughout the term of the loan. ❑ In the simplest of cases, the cashflows are the reverse of those for a fixed-interest security. The provider of the loan effectively buys a fixed-interest security from the borrower. 3- Insurance Products The cashflows for the examples covered in this section differ from those in the previous section in that the frequency, severity, and/or timing of the cashflows may be unknown. severity’ is referring to the benefit or claim amount paid out by the insurer. 3.1 A pure endowment ❑ A pure endowment is an insurance policy which provides a lump sum benefit on survival to the end of a specified term usually in return for a series of regular premiums. ❑ The cashflows for the policyholder will be a series of negative cashflows throughout the specified term or until death, if earlier. A large, positive cashflow occurs at the end of the term, only if the policyholder has survived. If the policyholder dies before the end of the term there is no positive cashflow. ❑ From the perspective of the insurer, there is a stream of regular positive cashflows which cease at a specified point (or earlier, if the policyholder dies) followed by a large negative cashflow, contingent on policyholder survival. 3.2 Endowment ❑ An endowment assurance is similar to a pure endowment in that it provides a survival benefit at the end of the term, but it also provides a lump sum benefit on death before the end of the term. The benefits are provided in return for a series of regular premiums. ❑ The cashflows for the policyholder will be a series of negative cashflows throughout the specified term or until death, if earlier, followed by a large positive cashflow at the end of the term (or death, if earlier). Depending on the terms of the policy, the amount payable on death may not be the same as that payable on survival. ❑ From the perspective of the insurer, there is a stream of regular positive cashflows which cease at a specified point (or earlier, if the policyholder dies) followed by a large negative cashflow. The negative cashflow is certain to be paid, but the timing of that payment depends on whether/when the policyholder dies. 3.3 Term Assurance ❑ A term assurance is an insurance policy which provides a lump sum benefit on death before the end of a specified term usually in return for a series of regular premiums. ❑ The cashflows for the policyholder will be a series of negative cashflows throughout the specified term or until death, if earlier, (or one negative cashflow at inception if paid on a lump-sum basis), followed by a large positive cashflow payable on death, if death occurs before the end of the term. If the policyholder survives to the end of the term there is no positive cashflow. ❑ From the perspective of the insurer, there is a stream of regular positive cashflows which cease at a specified point (or earlier, if the policyholder dies) followed by a large negative cashflow, contingent on policyholder death during the term. ❑ Generally, the negative cashflow (death benefit), if it occurs, is significantly higher than the positive cashflow (premiums), when compared to, say, a pure endowment. This is because, for each individual policy, the probability of the benefit being paid is generally lower than for endowments, because it is contingent on death, rather than on survival. 3.4 A contingent annuity Definition : This is a similar contract to the annuity-certain but the payments are contingent upon certain events, such as survival, hence the payment term for the regular cashflows (which will be negative from the perspective of the annuity provider) is uncertain. Typical examples of contingent annuities include: A single life annuity – where the regular payments made to the annuitant are contingent on the survival of that annuitant. A joint life annuity – which covers two lives, where the regular payments are contingent on the survival of one or both of those lives. A reversionary annuity – which is based on two lives, where the regular payments start on the death of the first life if, and only if, the second life is alive at the time. Payments then continue until the death of the second life. 3.5 A car insurance policy ❑ A car insurance policy usually lasts for one year, and provides payments to cover any damage to the insured vehicle (property cover) or any damage caused by the insured vehicle (liability cover). ❑ From the insurer’s perspective, there will be a positive cashflow at the beginning of the policy, followed by a negative cashflow when the claim is settled. The timing of the cashflows will depend on how long the claim takes to be reported and settled. Typically property claims take less time to settle than liability claims. ❑ Cashflows tend to be short-term and are payable within the year. 3.6 A health cash plan ❑ A typical health insurance contract lasts for one year. In return for a premium, the policyholder is entitled to benefits which may include hospital treatment either paid for in full or in part, and/or cash benefits in lieu of treatment, such as a fixed sum per day spent in hospital as an in-patient. ❑ From the policyholder’s perspective, the cashflows will include a negative cashflow at the beginning of the year followed by positive cashflows in the event of a claim in the case of a cash benefit. Where the insurance company pays for hospital treatment directly, the policyholder may experience no more cashflows after paying the initial premium. ❑ From the perspective of the insurer, there will be an initial positive cashflow at the start of the policy followed by negative cashflows in the event of a claim, when those claims are settled. ❑ Cashflows tend to be short-term and are payable within the year.  QUESTIONS Q1: Describe the characteristics of: ► (a) an interest-only loan (or mortgage); and ► (b) a repayment loan (or mortgage). Q2: Outline the similarities and differences between an annuity-certain and a contingent annuity. Q3 : What factors should the provider consider when choosing assets to match its liabilities in the case of a term assurance product? ► Factors for the provider to consider when choosing how to invest the initial positive cashflows to match its liabilities in the case of a term assurance product include: The nature of the sum assured payment is fixed in monetary terms, therefore match with fixed-interest assets. the nature of expenses are real, therefore match with real assets. The term of the sum assured payment is equal to the expectation of life, therefore match with assets of the same term. The timing of the sum assured payment is uncertain and therefore there is a need for liquidity in the assets chosen. The currency – match the denomination of the assets with that of the liabilities.  reinvestment risk – premiums and investment income received on the assets will have to be invested in the future on unknown terms. Diversification – to reduce portfolio risk. The use of free assets as a cushion against adverse movements in the values of the assets and liabilities. Compliance with any statutory constraints on the assets held. In reality, the provider will have a group of term assurance policies to administer so will need to consider the characteristics of the liabilities as a group when choosing assets.