槓桿ETF的蒙地卡羅模擬 - ETF
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By Jake
at 2021-04-23T21:05
at 2021-04-23T21:05
Table of Contents
Blog post:
https://daze68.blogspot.com/2021/04/etf-leveraged-etf-monte-carlo.html
======
假設Daily return滿足normal distribution
令Daily return= 2bp,Daily SD= 125bp
(每年約250交易日,約當年報酬率5%,年標準差20%)
生成十萬筆250日的日回報率
在不考慮ETF cost 的狀況下,250個交易日後,1x、2x、3xETF的回報率:
1xETF median 3.15%,mean 5.11%,SD 21.00%,geomean 3.07%
2xETF median 2.33%,mean 10.48%,SD 45.44%,geomean 2.16%
3xETF median -2.41%,mean 16.13%,SD 75.38%,geomean -2.63%
圖: https://tinyurl.com/3y9ydyrk
加入cost:
(1xETF daily cost = 0, 2xETF daily cost=0.6bp, 3xETF daily cost=0.8bp
,約當ER 1%,借貸成本 0.5%)
1xETF median 3.15%,mean 5.11%,SD 21.00%,geomean 3.07%
2xETF median 0.81%,mean 8.84%,SD 44.77%,geomean 0.64%
3xETF median -4.34%,mean 13.83%,SD 73.90%,geomean -4.56%
圖: https://tinyurl.com/768jma8r
不考慮cost,比較50% 1xETF + 50% 3xETF不再平衡 vs 100% 2xETF:
2xETF median 2.33%,mean 10.48%,SD 45.44%
50% 1xETF + 50% 3xETF不再平衡 median 0.37%,mean 10.62%,SD 47.85%
圖: https://tinyurl.com/tra96brj
加入cost
(1xETF daily cost = 0, 2xETF daily cost=0.6bp, 3xETF daily cost=0.8bp)
比較50% 1xETF + 50% 3xETF不再平衡 vs 100% 2xETF:
2xETF median 0.81%,mean 8.84%,SD 44.77%
50% 1xETF + 50% 3xETF不再平衡 median -0.59%,mean 9.47%,SD 47.11%
圖: https://tinyurl.com/k8nfhh95
======
註: 各張圖的value 大於2的部分被刻意切掉了,否則0附近太擠了
--
Gereulach éü,Sicé dozzote dar carsarr factina.
Farer dozzoth,R'a sotle nilora rÿal dar üaiponéra.
Frybarec éü, gereulach éü,Farh a lomi zacsantto loréïl.
(星たちよ──汝の命短き眷族の望みを聞くがよい。
我らの望みヽそれは──汝の本降ちゆくを看取ること。
帝國よヽ星たちよ──我らヽともに永遠を抱かん。)
--
https://daze68.blogspot.com/2021/04/etf-leveraged-etf-monte-carlo.html
======
假設Daily return滿足normal distribution
令Daily return= 2bp,Daily SD= 125bp
(每年約250交易日,約當年報酬率5%,年標準差20%)
生成十萬筆250日的日回報率
在不考慮ETF cost 的狀況下,250個交易日後,1x、2x、3xETF的回報率:
1xETF median 3.15%,mean 5.11%,SD 21.00%,geomean 3.07%
2xETF median 2.33%,mean 10.48%,SD 45.44%,geomean 2.16%
3xETF median -2.41%,mean 16.13%,SD 75.38%,geomean -2.63%
圖: https://tinyurl.com/3y9ydyrk
加入cost:
(1xETF daily cost = 0, 2xETF daily cost=0.6bp, 3xETF daily cost=0.8bp
,約當ER 1%,借貸成本 0.5%)
1xETF median 3.15%,mean 5.11%,SD 21.00%,geomean 3.07%
2xETF median 0.81%,mean 8.84%,SD 44.77%,geomean 0.64%
3xETF median -4.34%,mean 13.83%,SD 73.90%,geomean -4.56%
圖: https://tinyurl.com/768jma8r
不考慮cost,比較50% 1xETF + 50% 3xETF不再平衡 vs 100% 2xETF:
2xETF median 2.33%,mean 10.48%,SD 45.44%
50% 1xETF + 50% 3xETF不再平衡 median 0.37%,mean 10.62%,SD 47.85%
圖: https://tinyurl.com/tra96brj
加入cost
(1xETF daily cost = 0, 2xETF daily cost=0.6bp, 3xETF daily cost=0.8bp)
比較50% 1xETF + 50% 3xETF不再平衡 vs 100% 2xETF:
2xETF median 0.81%,mean 8.84%,SD 44.77%
50% 1xETF + 50% 3xETF不再平衡 median -0.59%,mean 9.47%,SD 47.11%
圖: https://tinyurl.com/k8nfhh95
======
註: 各張圖的value 大於2的部分被刻意切掉了,否則0附近太擠了
--
Gereulach éü,Sicé dozzote dar carsarr factina.
Farer dozzoth,R'a sotle nilora rÿal dar üaiponéra.
Frybarec éü, gereulach éü,Farh a lomi zacsantto loréïl.
(星たちよ──汝の命短き眷族の望みを聞くがよい。
我らの望みヽそれは──汝の本降ちゆくを看取ること。
帝國よヽ星たちよ──我らヽともに永遠を抱かん。)
--
Tags:
ETF
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