INTRODUCTION. DONALD DUVAL Director of Research AON Consulting, United Kingdom

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1 DONALD DUVAL Director of Research AON Consulting, United Kingdom INTRODUCTION I have a rather narrower subject matter than David and inevitably some of what I am going to say actually goes over the grounds that David went over, but possibly from a slightly different viewpoint, and I hope it may be helpful. I am not going to talk about mortality at all. I am going to assume, in effect, that you can successfully predict mortality as an insurer, though there are major difficulties in that because mortality does not only vary by age, it also varies by income level, sex and the choice of whether to buy an annuity. But I am ignoring mortality, assuming it is predictable in this presentation. IMPORTANCE OF INVESTMENT RETURN So, firstly, how important is the investment return: does it really matter? Well, it depends if you have a 5-year annuity payable for five years, the effect of a 2% change in the yield only changes the value of the annuity by 5%. The value of annuity of $1 for 5 years at 5% is $444. If you value at 7% interest it is $424. A bit cheaper but not hugely. The same effect occurs if you are dealing with annuities payable for life. If the people only have a few years to live, then interest rates are not very important. In the developed countries, many of the retirement systems were designed when retirement ages were 65 and expected age of death was 67-7 odd. At that time interest rates really did not matter very much, but the world has changed a bit, and if you look at an annuity payable for years, then obviously the numbers are bigger, the value at 5% interest of an annuity of $1 is now $1,277, for 7% interest it is $1,96. The most important figure is that the effect of a 2% change in yield is now 14%. A 2% change in the investment return changes the price of the annuity by 14%. You can look at this from both sides. From the annuitant's side, if the investment assumption made by the insurance company is unduly conservative, then he will lose a big chunk of his retirement income. If the insurance companies decides to take a 2% margin in the yield then the member loses 15% of his retirement income. That is a lot. On the other hand, if you look at it from the insurance companies side, if they make an estimate of the investment return and get it wrong, again they will make a big loss if they are unduly optimistic on the investment return. That means two things: firstly, it tends to make the insurance companies conservative on investment returns, and secondly, it may tend to require them to have capital. What I am now going to do is to start to construct a pricing model for the investment return part of an annuity. CASHFLOWS Figure 3: Cashflow from annuity portfolio I am assuming in this theoretical model at the moment that this country has government bonds in issue for every term from 1 up to 4 years. I know that is not true in most countries, but if it were true this would be an

2 effective pricing model, and its quite illuminating. However, this is the cash flow you would expect from an annuity. In order to simplify things, I used UK mortality. This is from male aged 65; the cash flow slowly diminishes the level of annuity as the pensioners die off. You see the shape slowly diminishing this is the first eight years of the annuity cash outflow the insurance company will need to provide from selling annuities. And you would normally attempt to back this by government bonds Figure 4: Cashflow from single bond To look at the government bond cash flow, it s a different shape. This is typical government bond cash flow some interest rate payments (quite small in this case it is a 5% coupon bond I have used); and then a big repayment at the end of the period. This form happens to be a 5-year bond. The question for the insurance company is: with the collection of bonds available, can you construct a portfolio of government bonds that would produce exactly the same cash outflow as the annuity payments, as if you can, then all you do is take the price for the annuity, invest in government bonds and the income from the government bonds, both the coupon and the redemption, then goes straight through as the annuity. The answer is you can. On the next slide, this is a collection of government bonds. 1 Figure 5: Cashflow from multiple bonds The total of these gives exactly the same cash outflow as from the original annuity portfolio (a previous slide). At the very left-hand end, there is a 1-year bond (magenta) which is where you get the redemption of the bond coming through in the first year, and then interest payments on all the other components of bonds that you have chosen to buy. You have to buy a certain proportion of bonds for each duration, 1, 2, 3, 4 (in this case up to 8) years as I have truncated the annuity portfolio at 8 years. In fact, if you truncate the annuity portfolio at 8 years, you have got a reasonable spread across the whole 8-year period on those bonds which are fairly similar in value. I have done this in a simplified way with the truncated annuity portfolio so that it is actually visible as to how you build the blocks up. You could, in fact, make a children s game out of this, as to how price annuities: providing children with lots of these different shapes and seeing what they can make with a particular pattern you are aiming to make, which would be a way of making actuaries more entertaining. The next slide shows the whole of the annuity portfolio. Figure 6: Cashflow from annuity portfolio This is the male age 65 running out to age 1, by which stage I assume they are all dead, or practically all dead. This shows the cash flow with a decline slightly steeping in the middle, actually very slightly flattening at the end. That is the characteristic shape of the annuity outflow you expect if you sell annuities to a collection of men aged 65, and you can match that with government bonds, if you have long enough government bonds. On

3 the next slide, is the matching slide exactly the same shape. Figure 7: Cashflow from multiple bonds 6% 5% Figure 8: Distribution of bonds That is the government bonds going all the way out. You can probably just about see in the first year that only half of your cash flow in that year comes from your 1-year bond, the other half of your cash flow is of interest payments from all the later bonds you have bought. That is the cash flow that exactly matches the annuity. You can turn it round another way, that means that the individual who has purchased an annuity, has purchased exactly the cash flow that is shown on this slide, in other words, the cash flow obtainable from this particular portfolio of government bonds. They have effectively invested in this collection of government bonds. That immediately tells you something about the investment decision or risk they have taken from where they were before. Because wherever they were in the pension fund they have now suddenly decided to switch into a portfolio of government bonds, which is represented on this slide, and the market movement risk they are taking, if their previous investment was differently shaped, as it almost certainly was, they are then taking a market decision at the time they purchase the annuity. In effect, they have a market risk, depending on the level of the market at that time, which is probably out of their control, because the purchase of an annuity is normally associated with retirement not with any investment decision. DISTRIBUTION OF BONDS Now, you can decompose that distribution of bonds a different way. 4% 3% 2% 1% % 1 This is the proportion of the portfolio that is to be hold in each input bond. There are just over 5% of the assets in the 1-year bond, and about 5% through a 2-year bond. This is, as I say, the investment portfolio they are buying. For the insurance company, if you can price that investment portfolio you can exactly price the annuities you are selling. The interesting feature of this model is that you do not need to make an assumption about investment returns, you derive it straight from the market, which means that if interest rates vary by term you pick up the term variation directly. 1% 9% % 7% % 5% 4% 3% % 1% % Figure 9: Distribution of bonds by term If you look at that distribution cumulatively (this does not show very well), this is the distribution of bonds by term cumulatively so that the 5% in the 1-year bond (left hand end) and by the time you get to the bonds of term 35 years or less (right hand end), you have 1% of the fund. The 5% line which is, in effect, the average bond duration, is about 11 years. Over half your bonds have duration greater than 11 years, and over half the bonds have duration less than 11 years (about half each side). As Jonathan pointed out, there are not very many countries that have substantial volumes of bonds in issue longer than

4 years, and with selling an ordinary lifetime annuity you want to put half the assets into such bonds you cannot. Therefore, what you have to do is invest them shorter, and then when the bonds mature, those bonds that are too short when they mature, you have to reinvest the proceeds at whatever rate of interest you happen to be able to get at the time. That reinvestment risk is quite significant because you are talking about reinvesting 1-15 years hence and therefore you are talking about making a guess on investment returns or interest rates 1-15 years hence, which is hard to do in developed economies like the UK or US. It is extremely difficult in transitional economies to estimate what interest rates will be that far in advance, and in practice a very prudent estimate is likely to be taken. That very prudent estimate means that the annuity will be very harshly priced. Doing a pricing model that depends on the existence of long term securities, it may appear unrealistic. The reason I am doing that is not because I expect such securities to exist but because it indicates that the risk being taken by the insurance companies is very similar to the risk that the government would take if it chose to issue such long term securities, and the governments in general have chosen not to take that risk. It is interesting that that risk is being forced on private sector insurance companies who are selling annuities. The examples I did, I did incidentally with government bonds that were paying a 5% coupon which is not particularly high. If the government bonds are issued at a higher coupon rate, say 1% coupon, then you need even more long bonds because you get lots of interest coming out of them earlier. IMPACT OF LENGTHENING TERM So, what has been happening: the term of annuities is now quite long and the term of retirement is now quite long and with investment in annuities there are, I think, a number of problems. There is a loss of investment return from the, in effect, forced investment in annuities because these annuities behave like bonds and investment in long term government bonds is not generally particularly high yielding. But, moreover, these have to be very cautiously priced because those bonds simply do not exist and therefore the individual, by being forced into an annuity in a developing country, will normally lose quite a lot of investment return during their retirement years, compared with what they would have been able to obtain if they were not forced into an annuity, or if the annuity were more flexible in pricing and its structure. There is a serious difficulty of matching and it is common in many countries, that the difficulty of matching should be dealt with by, for example, statutory valuation basis at interest rates which seem conservative when they are set. For example, many European countries have statutory valuation bases at 6% interest, which looked very conservative when they were set. However, the best yield you can get on the Euro bond is perhaps 4.5% now, which means that fundamentally the statutory evaluation basis on investment returns is about 25% below what the companies actually need. Any pure annuity company that has been issuing on statutory bases would be indubitably insolvent. I suspect the reason we have not seen insolvencies in Europe is two-fold. One is there are no pure annuity companies in general in Western Europe, and the second one, it is not the practice to mark investments to market and therefore insolvency can exist and be concealed for a long period, and indeed you may be able to trade your way out of it by overcharging new annuitants to pay for the fact that you have undercharged previous ones. This is, of course, the classic banking cycle but it is also a classic part of insurance cycles, particularly as I say when you do not mark your assets and liabilities to market values, which in Europe you normally do not. The next thing that is created is a demand for capital. Insurance companies are taking this very substantial reinvestment risk and they need capital to meet that risk. That capital can come from various places. If they are foreign insurers in a developing country market, or foreign owned, you may get access

5 to the parent company capital. If they are domestic insurers then they will need to raise capital on what may be very new domestic capital markets, and any shortage of capital leads into a requirement greater caution in pricing, because if the capital is not really enough, then you need to have a bigger margin in your price. The important effect of the term lengthening is that the inflation risk, if the annuities are not indexed, is increased. If the annuity is indexed, then that is just another risk being thrown on the insurance company. Whether that matters, I think, depends on the country. In many South American countries, in effect, the entire capital market is indexed, so actually to do anything but indexed annuities would probably be seriously difficult. However, in other countries, things are generally expressed in money terms and inflation is a genuine additional risk. OTHER TYPES OF ANNUITY So, given those problems, what about other types of annuity. One or two countries have allowed fixed term annuities. The fixed term annuity simply does not meet the retirement needs that David identified. Frankly, you might as well give people a lump sum in my view. They are more likely to invest the lump sum sensibly, I suspect. They might even be less likely to squander a lump sum than a relatively short fixed term annuity. Index linked annuities: a brief comment relative to the UK one reason index linked annuities in the UK are relatively unpopular in the voluntary market, is that they are mandatory in some areas, and supply of index linked government bonds is effectively inadequate, that has driven real interest rates down below 2% and in consequence index linked annuities are very poor value. The other comment is that in some countries that do not index all capital markets, their price indexes are doubtful, and when indexing purely for pension purposes, the index may still be subject to political manipulation. Unit linked annuities or variable annuities annuities which vary with investment returns represent a solution that I think, may help solve the investment problem because it does not force individuals to invest in what is probably an unsuitable investment portfolio for somebody with 25 or 3 years of life remaining. A couple I have not mentioned on the slide: With-profit annuities. The essential problem with with-profit annuities is that they are more conservatively priced at the beginning in order that you can pay more later. The difficulty with that, from the individual s point of view, is you get all the profits, but you get them when you are almost dead. You actually do not need that; you want the money up-front. It might be nice for your heirs, but that is a different problem! Income draw-down. With income drawdown, effectively, as David said, you must achieve not merely the investment return but the mortality drag. The mortality drag is actually the increase in the cost of annuities, and that is simply the proportion of people that die each year, so to get an equivalent result from income draw-down as you would get from an annuity, you have to manage to earn as much investment return as the annuity provider assumed when they priced it, plus the proportion of people that will die in the next year. If you can get more than that you are better off with income draw-down. One of the fundamental problems with the fixed annuities, including the index linked, is that you are trying to provide certainty over a very long period. Certainty on the interest rates and, in effect, on the mortality. But both of those are fundamentally uncertain things. The cost of certainty is very high because you have to find somebody else prepared to take the risk who has got a lot of capital, and they will demand the corresponding premium. If we are going to force people to pay that price for the certainty, we need to be very confident that it is actually socially desirable. It is not necessarily clear to me that it is, because if we try to protect a group in the economy from any variations in economic performances, we may gear up the impact of economic variability on everybody else, so

6 that if the substantial proportion of the population that is actually retired is receiving their income all in terms of fixed annuities, and the economy goes into a downturn, then the impact on the rest of the population may be geared up. is an excess of supply of capital which is being forced into fixed interest and it is a consequence on the supply of risk capital, and risk capital which generates economic growth, not fixed interest capital. So, I will finish on that thought. CAPITAL MARKET ISSUES Finally, what is the impact on the capital markets? Well, the first capital market question is do appropriate long investments exists. I have mentioned long government bonds, and mortgage instruments. If they don t exist, the annuity providers will ask for them to be created, but it may not be a good idea if interest rates are currently high and the credit risk of the country is not very good. Long government bonds can be a very expensive way of the government raising capital. Conversely, if the government can issue bonds because the annuity providers are being forced to buy them, then it may be a cheap way for the government to raise capital at the expense of its population. The population here, when talking about the part in the mandatory annuity system, may not be the wealthiest part of the population either. So long government bonds may not exist, and there may be very good reasons where you do not want them to exist. Even if they do exist, is that a sensible investment for an individual aged 65 and retiring to put their entire retirement assets into a portfolio of government bonds which is heavily weighted to the long term I am not certain that it is. The problem of the capital for annuity guarantees the life companies will need capital, and therefore the capital markets need to be able to provide it if these annuities are going to be compulsory. If they are going to be effectively provided, and provided securely, then these companies need to be adequately capitalized, which means the capital market needs to be able to raise the capital. So, in general, my conclusion is that there is some fundamental problem with requiring annuities for this large portion of the population and this rich portion of the population, because what we may be creating 21

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