回測使用網站 https://www.portfoliovisualizer.com/monte-carlo-simulation
回測時間：Jul 2006 - Dec 2023 (QQQ 成立日期 1999/03/10 ; QLD 成立日期 2006/6/18)
Asset1 : QQQ 100%, Beta 1.0Asset2 : QQQ 80% , QLD 10%, CASH 10%, Beta 1.0
Asset3：QQQ 60%, QLD 20%, CASH 20%, Beta 1.0
※Initial Amount：10,000,000
※Withdrawal Frequency：Monthly
※Withdraw amount：80,000
※Rebalancing：rebalance annually
※Performance Summary
同樣是 Beta 1.0 槓桿基金，有較佳的 Sharpe Ratio，年化報酬率也比較高。
若 Withdraw amount 改為 100,000 ，則 QQQ 100% 則會破產。另外持有槓桿基金的則不會。
若每個 profolio 用 蒙地卡羅來模擬分析，30年滾動模擬10000次，存活百分比如下：
Asset1 : QQQ 100%
2247 portfolios out of 10000 simulated portfolios (22.47%) survived all withdrawals.
Asset2 : QQQ 80% , QLD 10%, CASH 10%, Beta 1.0
6298 portfolios out of 10000 simulated portfolios (62.98%) survived all withdrawals.
Asset3：QQQ 60%, QLD 20%, CASH 20%, Beta 1.0
6467 portfolios out of 10000 simulated portfolios (64.67%) survived all withdrawals.
Asset4：QQQ 50%, QLD 25%, CASH 25%, Beta 1.0
6514 portfolios out of 10000 simulated portfolios (65.14%) survived all withdrawals.
Assets 改為 5%提領後，
10000 portfolios out of 10000 simulated portfolios (100.00%) survived all withdrawals.
存活率為 100%
[結論]
1. 從歷史數據來說，投資組合持有部份槓桿基金能提高存活率。
2. 以QQQ的標的來說，5%提領可以滿足30年提領不破產。
