استراتژی سرمایه گذاری بهینه برای برنامه های بازنشستگی مشارکتی تعریف شده
|کد مقاله||سال انتشار||مقاله انگلیسی||ترجمه فارسی||تعداد کلمات|
|9773||2001||30 صفحه PDF||سفارش دهید||محاسبه نشده|
Publisher : Elsevier - Science Direct (الزویر - ساینس دایرکت)
Journal : Insurance: Mathematics and Economics, 28 (2001) 233–262
We analyse the financial risk in a defined contribution pension scheme, applying dynamic programming techniques to find an optimal investment strategy for the scheme member. We use a series of interim targets and a target at retirement linked to the desired net replacement ratio. We consider both the investment risk and the annuitisation risk faced by the individual and specifically consider the properties of the so-called “lifestyle” investment strategies. The principal results concern the suitability of the lifestyle strategy and the large variability of the level of pension achieved at retirement in the case of a variable annuity conversion rate. © 2001 Elsevier Science B.V. All rights reserved.
The present work analyses the financial risk in defined contribution pension schemes and uses stochastic dynamic programming in an attempt to find an optimal investment strategy, given a final target linked to the net replacement ratio and a set of interim targets. 2 The use of dynamic programming is not new in the actuarial context. Haberman and Sung (1994) use Bellman’s optimality principle to minimise simultaneously the contribution risk and the solvency risk in a defined benefit pension scheme, and derive the optimal contribution rate. Cairns (1997), in a continuous time framework, and Owadally (1998), in a discrete time framework, apply this principle to a defined benefit scheme in order to derive the optimal contribution rate and the optimal allocation decision in a two-asset world. Thomson (1998) has applied multi-period methods to defined contribution pension schemes, and has determined the optimal investment strategy maximising the member’s expected utility. In the analysis that follows, both the investment risk and the annuity risk borne by the member of the pension scheme are studied, where by “investment risk”, we mean the risk that a poor investment performance during the active membership leads to a lower than expected accumulated fund, and by “annuity risk”, we mean the risk that a low conversion rate used in buying the annuity at retirement leads to a lower than expected pension rate. 3 The suitability of the lifestyle policy is also discussed. (This is clearly described by Sze (1993) in the discussion of Knox’s paper: in a “lifestyle” investment strategy, the fund is invested predominantly in equities when the member is young and it is gradually switched into bonds and cash as the member approaches retirement.)
نتیجه گیری انگلیسی
In this research, the financial risk in defined contribution pension schemes has been investigated in both its components, the investment risk borne by the member during the accumulation period, and the annuity risk when the annuity is bought at retirement. The results found seem to suggest the appropriateness of the lifestyle strategy, in order to reduce the investment risk. They contradict the corresponding results of Booth and Yakoubov (2000), but confirm through a scientific and rigorous approach, the validity of the actual investment strategy usually adopted by actuaries and investment managers of defined contribution schemes in UK. By looking at the annuity risk, the main result found is the large variability of the level of pension achieved at retirement in the case of a variable conversion rate in calculating the annuity, stressing the impact of the annuity risk on the final benefit. The present research does not make any proposal in reducing annuity risk in defined contribution pension schemes and it is our intention to continue in further research in order to approach this relevant problem, as we believe that defined contribution schemes will play a central role in the future in the pension systems of most countries. The model presented has been constructed with a number of simplifying assumptions and can be improved. Unlike other researchers (e.g. Knox, 1993; Ludvik, 1994; Khorasanee, 1995; Booth andYakoubov, 2000), we have not attempted to use a model of asset returns where the parameters have been estimated from actual observations.Our approach has attempted to be more general and considers two independent assets with representative parameter values which are then modified in order to test the sensitivity of the results to these inputs. In the real world, asset returns are not necessarily i.i.d. and lognormally distributed, returns from different assets may not be uncorrelated 5 and returns on the same asset in different periods are not independent as in our model (see, e.g. Khorasanee, 1995; Booth and Yakoubov, 2000). The assumption of having two assets for the whole working life period seems also to be very strong. 6 The different scenarios of volatility may represent different classes of assets. It may be reasonable to assume that for a certain period of time, the fund can be invested in two assets only, diversifying between two different risky assets. It is certainly a simplification to assume that the two assets, in which the funds are invested, should remain the same for the whole period of membership. Therefore, it would also be of interest to investigate the optimal investment strategy in an n-asset model. A simplifying assumption is also the coincidence of asset allocation decisions and targets (both yearly), an assumption which could be relaxed choosing, say, interim targets less frequent than yearly (as every 3 years or even less frequently until the extreme position with only the final target). In addition, the definition of the targets Ft themselves can be changed, including for example also other constraints, like the guarantee of a minimum benefit for the member. A more general model can be made also by varying the level of the contribution rate during the membership, considering for example the contribution rate as a step-function c(t) such that c(t) = cj for Ij ≤ t ≤ Ij+1, where the intervals [Ij, Ij+1] (j = 0, . . . ,K − 1, with I0 = 0 and IK = N) are the partition of the interval [0,N]. It could be of interest to test the response of the model to positive values of the transfer value f0, which would apply to the case of members transferring in from other schemes. However, it is worth noting that some further results about transfer values can be found using the results of the simulations carried out. In fact, if we consider, e.g. the N = 40 case and isolate the last, say, 10 years, considering the simulated f30 as a transfer-in value we would have the case N = 10 with f0 > 0 (exactly, f0 = f30). The same reasoning would apply if we isolate the last 10 years in the N = 30 and 20 cases (with f0 = f20 and f0 = f10, respectively). Similarly, we could have the results relative to N = 20 and f0 > 0 if we isolate the last 20 years in the N = 40 (in this case, f0 = f20) and N = 30 (in this case, f0 = f10) cases. Finally, we would have results relative to N = 30 and f0 > 0 if we limit our attention to the last 30 years in the N = 40 case (in this case, obviously f0 = f10). Other limitations are the absence of expenses and other loadings in the pricing of annuities, and the failure to consider decrements other than retirement. It has also to be mentioned the choice of using the whole final fund to buy an annuity at retirement whereas a more general model would include other uses of that fund, e.g. a lump sum.An important assumption in this research is the choice of the objective. The loss function chosen in this work penalises the fund accumulated above the target, leading to possible distortions in the realistic objectives of the trustees of a defined contribution pension scheme—increase as much as possible the accumulated fund—and possibly limiting the real potentiality of this kind of pension scheme, which consists in giving the member the possibility of gaining higher than expected market returns. However, this problem can be easily solved if we consider an unrealistically high final target (like a pension equal to 400% of the final salary), the objective becoming in practice the maximisation of the final fund. Another way of overcoming this problem is to modify the loss function in such a way that the increase in the fund above a certain benchmark is not penalised: we believe that this approach could be more realistic in treating problems related to defined contribution pension schemes, and we are currently developing further research in this direction.