개인의 은퇴자산 부족가능성에 영향을 미치는 요인에 관한 분석적 연구

The retirement of baby boomers in Korea is just beginning and their life expectancy is growing. Studies have focused on optimal accumulation strategy to adequately face the retirement needs however, few studies discussed about optimum spending behavior after retirement and few guidelines on sustainable spending are introduced in Korea. This study is different from other studies by i. focusing on spending rather than investment opportunities to minimize the ruin probability and ii. studying the optimum consumption strategy affected by investment risk and longevity risk jointly. Moreover, this paper measures the ruin probability by implementing analytical method shown in Milevsky and Robinson (2005) using Korean data. This analytical method provides advantage of estimating the ruin probability with less cost and easy replication compared to the Monte Carlo simulations or historical bootstrap studies. In this paper, we applied ruin probability of retirement asset to be affected by three fundamental variables; withdrawal rate, mortality rate,and expected rate of return. The ruin probability is definedas the probability that a retiree lives without resources. If present value of total net future annual consumption is greater than the initial retirement asset, the shortfall may occur in the retireeʼs assets and the retiree will have no financial support to live. Given stochastic rate of return and non-deterministic mortality rate,it is assumed that the life expectancy follows exponential distribution and total investment return follows log-normal distribution. To apply ruin probability, this paper uses the parameter for uncertain life expectancy obtained from the 2008 Korean life table. Also, the expected mean and volatility parameter for investment return is obtained from KOSPI andbond return from 2002 to 2010. The spending rate during retirement period is rep-resented by ʻwithdrawal rate (c/W0)ʼ, which is the annual fixed withdrawal amount over the initial retirement asset. The stochastic present value(SPV)of consumption is known to be a reciprocal gamma distribution as shown in Milevsky and Rbinson (2005). If SPVis greater than the initial investment wealth, the probability of ruin is then obtained by evaluating one minus the cumulative density function of the SPV at the initial wealth level. The numerical test provided using Korean mortality and capital market parameters, suggests that the withdrawal rate has greater impact on the ruin probability when the life expectancy is longer, holding the investment risk. Hence, controlling withdrawal rate becomes more effective to minimize the ruin probability of retirement asset, when longevity risk increases. Moreover, the study finds that ʻjointʼ strategy between well-diversified portfolio and withdrawal control is more effective to minimize the ruin probability of retirement asset rather than maintaining optimal asset allocation alone. Above all the factors that affect the ruin probability, consumption withdrawal rate is the only variable that can be controlled and should be noted to coming retiring baby boomers. In addition, following financial institutionʼs risk management concept like VaR, the study sets ruin tolerance levelto be 5 percent and 10 percent and estimates maximum spending rate accordingly. The spending rate wasestimated jointly by using investment risk and longevity risk under the 5 percent and 10 percent tolerance level. This different tolerance levels are important for the sustainable withdrawal strategy as the paper found that sustainable spending rate differs by as much as two times depending on not only retirement age but also on the tolerance level. The joint strategy in a given 5 percent or 10 percent ruin probability level can suggest maximum annual withdrawal amount for self-annuitization decision making. This optimal withdrawal rate that is equal to the life annuity payout can also give practical implications for the design of life annuity products in insurance market.