所得稅法規定「中華民國境內居住之個人」之判定

投資理財淺談

道理基本上 很簡單 就是 多賺錢 多存錢 不要亂花錢 你自然就會變有錢

一般來說 所謂的有錢 一種是看淨資產  另一種是看可用來做投資的淨資產 (自住的房子的價值要先扣掉)

一般小額花費的標準是  萬分之一的消費額度(每日)  不太需要考慮...  萬分之 365  約等於 3.65%...  所以以正常的投資報酬率 就能夠支付

所以有一百萬美金的可投資資產  就大約是一百元美金 約台幣三千元  以這種花錢速度  應該一輩子也花不完

另外 以投資的角度  如果能及早投資在適當的標的  以美國標普500 長期投報率約 6.6%(扣掉通膨) 而言  你從25歲工作40年  65歲退休  預期壽命為85歲

那你從工作開始  每月存台幣一萬元  你退休的時候 平均每月可以有 \(1.066^{40} + 1.066^{20} = 16.48\) 萬元可以花

如果你從一開始只存20年到45歲  後面都不存 每月也有 \(1.066^{40} = 12.89\) 萬元可以花

你存不了一萬  每月存個五千  退休也是有 6~8萬...  所以真的不難

如果你的父母有先見之明 從生下你就每月幫你存台幣一萬元 存20年... 每月就有 \(1.066^{65} = 63.71\)萬元... 存二千就夠了 每月也有12萬

懂得投資理財 比甚麼都重要

Leveraged Portfolio Simulation

Data: $SPY from 1-19-2007
Adjusted by daily closing prices
Starting capital is $10,000.
Neglecting dividends and the borrowing cost.
The blue line is the baseline.

Ultra fund DIY - Constant Leverage Ratio

If we want to create a leveraged portfolio tracking an index, we need to know how to maintain a constant leverage ratio.  The concept is pretty simple.

Say if we want to maintain a leverage ratio, $L = 2$.  If the index $I$ moves $\delta$ percent.  Our portfolio $\pi$ will move $2\delta$ percent.

Assuming the borrowing cost is zero. Our initial capital is $C$.

So at the beginning, our asset is $2C$ and our liability is $C$, the net is $2C-C=C$.

When the index moves $\delta$ percent, then

Asset: $2C*(1+\delta)$

Liability: $C$

Net: $C*(1+2\delta)$

Leverage Ratio: $(2+2\delta)/(1+2\delta) \neq 2$

The leverage ratio is changed due to the index has moved $\delta$ percent.  So we have to adjust our shares to re-balance the leverage ratio to 2.

If our original shares is $S$, the new share price is $2C*(1+\delta)/S$.

Our new net value of the portfolio is $C*(1+2\delta)$, the new shares $T$ is

$T = 2C*(1+2\delta) / (2C*(1+\delta)/S) = (1+2\delta)/(1+\delta)*S = (1+\delta/(1+\delta))*S$

So the percentage of the adjustment is $\delta/(1+\delta)$, when the index moves $\delta$ percent.

If the leverage ratio is $L$, the adjustment is $\dfrac{\delta}{(1+\delta)}(L-1)$.

Let's do some simple calculation for $L=2$

If the index moves up or down 1~5%, the adjustment is listed in the following table.

L=2
1%
2%
3%
4%
5%
down
-1.01%
-2.04%
-3.09%
-4.17%
-5.26%
up
0.99%
1.96%
2.91%
3.85%
4.76%

From the formula $\frac{\delta}{(1+\delta)}(L-1)$, we can also see that when $L>1$, it's similar to a trend following strategy.  Because when the index goes up, we will increase our shares.  When the index goes down, we will decrease our shares.