j***b
发帖数: 5901 | 1 Let's assume we have some index which is strictly Brownian motion, and we
have 3x positive and reverse etf on this index. There are three persons A, B
, and C. They all start with $1,000 dollars, but they used different
strategy.
A All in long 3x position etf.
B All in long 3x reverse etf.
C's strategy is more complicated, which involves combination shorting both
3x etf with positions that adjusted regularly.
Question: After 50 years, what are the expectations of these three person's
accounts? | j***b
发帖数: 5901 | 2 Since BM can go to negative, lets assume that once that happens, trading
stops and the account will stay at that amount till the 50th year.
Let's assume that the BM starts from some positive value.
And also, if anyone is wiped out, he's out.
B
s
【在 j***b 的大作中提到】
: Let's assume we have some index which is strictly Brownian motion, and we
: have 3x positive and reverse etf on this index. There are three persons A, B
: , and C. They all start with $1,000 dollars, but they used different
: strategy.
: A All in long 3x position etf.
: B All in long 3x reverse etf.
: C's strategy is more complicated, which involves combination shorting both
: 3x etf with positions that adjusted regularly.
: Question: After 50 years, what are the expectations of these three person's
: accounts?
| n***r
发帖数: 2074 | 3 For common stock, assume the expectation of return is u, the expectation
price of the stock is S*Exp(u*T), the volatility is S**2*Exp(2*u*T)*(exp(...
.)), for 3x etf, the volatility has exponential enlargement。
First, this kind of ETF will not last that long time without reverse split.
Second, for long position, no margin, goes to zero
for short position, you will get margin call some time, suppose the
margin is 25%, then stop at $400, then take interest until 50 years.
for combination shorting position, it's also very possible to get
margin call first without any adjusted regularly. If you adjust by yourself,
for most of people, it will go to zero finally.
B
s
【在 j***b 的大作中提到】
: Let's assume we have some index which is strictly Brownian motion, and we
: have 3x positive and reverse etf on this index. There are three persons A, B
: , and C. They all start with $1,000 dollars, but they used different
: strategy.
: A All in long 3x position etf.
: B All in long 3x reverse etf.
: C's strategy is more complicated, which involves combination shorting both
: 3x etf with positions that adjusted regularly.
: Question: After 50 years, what are the expectations of these three person's
: accounts?
| j***b
发帖数: 5901 | 4 Wrong answer.
The correct answer is:
A, $1,000
B, $1,000
C, $1,000
This is the simple situation of integration with respect to a martingale up
to a stopping time. You simply can't make or lose money out of a martingale.
If anyone can prove otherwise. Go to publish your results and overturn the
long proven theorem about integration with respect to a martingale and
become a big name in math.
And because of this. I seriously doubt there is a rigorous definition of "volatility decay" for leveraged etfs. | n***r
发帖数: 2074 | 5 you should put this assumption in the real market, you have $1000 investment
total, you get margin call first under high volatility, then everything
stop. Pure math does not work under real market, that's why we use the
implied volatility based on the market price to pricing option.
Additionally, if you do adjustment of you portfolio, it's not martingale any
more.
up
martingale.
【在 j***b 的大作中提到】
: Wrong answer.
: The correct answer is:
: A, $1,000
: B, $1,000
: C, $1,000
: This is the simple situation of integration with respect to a martingale up
: to a stopping time. You simply can't make or lose money out of a martingale.
: If anyone can prove otherwise. Go to publish your results and overturn the
: long proven theorem about integration with respect to a martingale and
: become a big name in math.
| j***b
发帖数: 5901 | 6 Everything doesn't stop when you get margin call.
When you get margin call, you reduce position.
-- Says a person who had got margin called multiple times.
And I'm talking about integration with respect to a martingale.
Of course, such integration processes themselves are also martingale, no matter how you adjust your position, as long as it's based on past information, it won't affect the martingale property.
investment
any
【在 n***r 的大作中提到】
: you should put this assumption in the real market, you have $1000 investment
: total, you get margin call first under high volatility, then everything
: stop. Pure math does not work under real market, that's why we use the
: implied volatility based on the market price to pricing option.
: Additionally, if you do adjustment of you portfolio, it's not martingale any
: more.
:
: up
: martingale.
| n***r
发帖数: 2074 | 7 suppose you short 100 shares 3x at 10$, the 3x goes to 20$, you lose
everything, they just close your position with zero balance there. Actually
they did this when you lose 75% of you portfolio value for common stock. For
some high volatility stock, they have more strict rule.
【在 j***b 的大作中提到】
: Everything doesn't stop when you get margin call.
: When you get margin call, you reduce position.
: -- Says a person who had got margin called multiple times.
: And I'm talking about integration with respect to a martingale.
: Of course, such integration processes themselves are also martingale, no matter how you adjust your position, as long as it's based on past information, it won't affect the martingale property.
:
: investment
: any
| j***b
发帖数: 5901 | 8 That's not the case. You will get margin call before it gets to $20. So
margin call will actually save you from getting wiped out.
You won't be allowed to Kong Shou Tao Bai Lang.
Actually
For
【在 n***r 的大作中提到】
: suppose you short 100 shares 3x at 10$, the 3x goes to 20$, you lose
: everything, they just close your position with zero balance there. Actually
: they did this when you lose 75% of you portfolio value for common stock. For
: some high volatility stock, they have more strict rule.
| n***r
发帖数: 2074 | 9 when you are adjusting your portfolio, you put your emotion in it, the
expectation return changed. All the assumption do not work here, that's why
only some good luck person make money, others lost much. Without human
disturbation，all portfolio are supposed to have the same performance based
on your theory.
matter how you adjust your position, as long as it's based on past
information, it won't affect the martingale property.
【在 j***b 的大作中提到】
: Everything doesn't stop when you get margin call.
: When you get margin call, you reduce position.
: -- Says a person who had got margin called multiple times.
: And I'm talking about integration with respect to a martingale.
: Of course, such integration processes themselves are also martingale, no matter how you adjust your position, as long as it's based on past information, it won't affect the martingale property.
:
: investment
: any
| j***b
发帖数: 5901 | 10 1. A and B don't need to adjust their portfolio.
2. C can use a shit barrel to manage his portfolio. No emotion involved.
3. Even is emotion is involved, the future movement of BM is independent of
that emotion. It's still going to be martingale.
why
based
【在 n***r 的大作中提到】
: when you are adjusting your portfolio, you put your emotion in it, the
: expectation return changed. All the assumption do not work here, that's why
: only some good luck person make money, others lost much. Without human
: disturbation，all portfolio are supposed to have the same performance based
: on your theory.
:
: matter how you adjust your position, as long as it's based on past
: information, it won't affect the martingale property.
| n***r
发帖数: 2074 | 11 And, actually, there is a name for this, CAPM
why
based
【在 n***r 的大作中提到】
: when you are adjusting your portfolio, you put your emotion in it, the
: expectation return changed. All the assumption do not work here, that's why
: only some good luck person make money, others lost much. Without human
: disturbation，all portfolio are supposed to have the same performance based
: on your theory.
:
: matter how you adjust your position, as long as it's based on past
: information, it won't affect the martingale property.
| n***r
发帖数: 2074 | 12 the system trading is just another human like strategy executor. The base
line is to make money, not lose money, that's not symmetric.
of
【在 j***b 的大作中提到】
: 1. A and B don't need to adjust their portfolio.
: 2. C can use a shit barrel to manage his portfolio. No emotion involved.
: 3. Even is emotion is involved, the future movement of BM is independent of
: that emotion. It's still going to be martingale.
:
: why
: based
| j***b
发帖数: 5901 | 13 My shit barrel became very emotional after reading your post.
【在 n***r 的大作中提到】
: the system trading is just another human like strategy executor. The base
: line is to make money, not lose money, that's not symmetric.
:
: of
| n***r
发帖数: 2074 | 14 I feel that, you are not serious any more, that's OK.
【在 j***b 的大作中提到】
: My shit barrel became very emotional after reading your post.
|
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