年金購買方式對長壽風險管理的影響 —一次性與漸進式策略之實證比較

Abstract

隨著平均餘命延長，退休者在退休後面臨之長壽風險、市場風險與序列報酬風險日益重要。傳統退休財務規劃多以投資組合提領與資產配置作為主要工具，然而單純依靠流動資產帳戶並無法完全轉嫁個人長壽風險；相反地，雖然生命年金能提供終身保證收入，卻可能因喪失流動性與遺產保留能力而形成年金化悖論。基於此，本研究旨在探討不同年金購買策略與資產配置方式對退休者終身破產機率、破產年齡及期末遺產價值之影響，並檢驗漸進式年金購買策略是否能在破產防禦、流動性與遺產動機之間取得較佳平衡。 本研究採用美國 1965 年至 2025 年之歷史金融資料進行動態回測，並以 1965 年至 1979 年間每日退休之 65 歲退休者作為研究對象。研究中設定三種年金購買策略：完全不購買年金之純提領策略、一次性全額購買年金策略，以及漸進式年金購買策略；同時搭配三種資產配置，包括積極型配置、平衡型配置與保守型配置。年金價格則依生命表存活機率與 10 年期美國公債實質殖利率計算，並假設年金為通膨指數化即期生命年金，所有資產價值與報酬率皆以實質金額衡量。 實證結果顯示，年金機制確實能有效降低退休者之終身破產風險。若僅以極小化破產機率為目標，一次性全額購買年金策略具有最高之終身成功率，為三種策略中最具防禦力者。然而，此策略之代價為退休者幾乎完全喪失流動性與遺產保留能力。相較之下，漸進式年金購買策略雖無法完全取代一次性全額年金化之防破產效果，但能在多數情境下提升終身成功率，並保留高於全額年金化策略之期末遺產價值，顯示其能在財務安全與資產彈性之間取得折衷。 在資產配置方面，本研究發現，若退休者完全不購買年金，平衡型配置較能同時緩衝股市波動與維持長期成長性，因此在純提領策略下呈現較佳之綜合表現。然而，當退休者導入漸進式年金購買後，年金收入逐步承擔基本生活支出，使剩餘流動資產能承受較高投資風險，進而提升期末遺產價值。此結果顯示，年金與風險資產並非互斥，而是具有互補效果。 此外，本研究進一步選取 1973 年退休梯次作為極端市場壓力測試。結果顯示，退休初期遭遇股市重挫與高通膨時，各策略之終身成功率皆明顯下降，純提領策略尤其容易受到序列報酬風險衝擊而提早破產。一次性全額年金化仍具最強防禦效果，但其成功率亦受資產配置與年金化觸發時點影響；漸進式年金購買策略在此極端情境下改善幅度有限，顯示其防護效果受到購買速率與市場衝擊發生時點限制。整體而言，本研究認為，年金應被視為退休資產配置中管理長壽風險與序列報酬風險之保險工具；若退休者同時重視破產防禦、流動性與遺產保留，漸進式年金購買策略相較於完全不年金化或一次性全額年金化，提供較具現實可行性之折衷方案。

As life expectancy continues to increase, retirees face increasingly important risks during retirement, including longevity risk, market risk, and sequence-of-returns risk. Traditional retirement planning often relies on portfolio withdrawals and asset allocation. However, a self-managed withdrawal strategy cannot fully hedge individual longevity risk. Although life annuities can provide guaranteed lifetime income, full annuitization may lead to the loss of liquidity and bequest value, giving rise to the well-known annuitization puzzle. This study therefore examines how different annuity purchase strategies and asset allocation choices affect retirees’ lifetime probability of ruin, bankruptcy age, and terminal bequest value. This study conducts a historical backtest using U.S. financial market data from 1965 to 2025. The sample consists of individuals retiring at age 65 on each day from 1965 to 1979. Three retirement income strategies are considered: Strategy A, a pure withdrawal strategy without annuity purchases; Strategy B, a one-time full annuitization strategy; and Strategy C, a gradual annuity purchase strategy. These strategies are further combined with three asset allocations: an aggressive portfolio, a balanced portfolio, and a conservative portfolio. Annuity prices are calculated using survival probabilities from a life table and real yields on 10-year U.S. Treasury bonds. All returns, wealth values, and annuity payments are measured in real terms, and the annuity is assumed to be an inflation-indexed immediate life annuity. The empirical results show that annuitization can effectively reduce retirees’ lifetime probability of ruin. If the sole objective is to minimize ruin risk, the one-time full annuitization strategy provides the strongest protection and generates the highest lifetime success rate. However, this strategy also comes at the cost of almost completely sacrificing liquidity and bequest value. In contrast, the gradual annuity purchase strategy cannot fully replace the defensive power of full annuitization, but it improves lifetime success rates in most scenarios while preserving a substantially higher bequest value than the full annuitization strategy. These findings suggest that gradual annuity purchases provide a more practical balance among retirement security, liquidity, and bequest motives. The results also indicate that asset allocation and annuity purchases interact with each other. Under the pure withdrawal strategy, the balanced portfolio performs relatively well because it provides both downside protection and long-term growth potential. However, once gradual annuity purchases are introduced, guaranteed annuity income gradually supports basic consumption needs, allowing the remaining liquid assets to take on more investment risk. As a result, the aggressive portfolio can generate higher terminal bequest values when combined with the gradual annuity purchase strategy. This finding implies that annuities and risky assets are not substitutes, but can serve complementary roles in retirement portfolio construction. Finally, this study conducts a stress test using the 1973 retirement cohort. The results show that when retirees encounter severe stock market declines and high inflation early in retirement, lifetime success rates decline substantially across all strategies. The pure withdrawal strategy is especially vulnerable to sequence-of-returns risk. Full annuitization remains the strongest defensive strategy, but its effectiveness depends on whether the annuitization threshold can be reached before the portfolio is severely depleted. The gradual annuity purchase strategy provides only limited improvement in this extreme scenario, indicating that its protective effect is constrained by the purchase speed limit and the timing of market shocks. Overall, this study suggests that annuities should be viewed as an insurance mechanism for managing longevity risk and sequence-of-returns risk. For retirees who value not only ruin prevention but also liquidity and bequest preservation, gradual annuity purchases offer a more realistic and balanced retirement income strategy.