AI
Tuesday, November 02, 2010 5:37:23 AM
Hi Toofuzzy and Conrad
The price difference per step is 10,26016 % per from the top down.
In that earlier example the steps were around 5% apart. It doesn't matter however as the ladder is just a visual representation of the log stochastic and you might only trade at perhaps moving average cross overs or whatever signal you prefer. At which time you calculate (log(current)-log(bottom))/(log(top)-log(bottom)).
What if on a 10% rise or drop you sold or bought enough to bring the equity value back to where you started?
That's the exact thing we're after Toofuzzy.
Maybe another example might help better. Say gold is currently priced at $1000 and I start a Ladder like the one on the left (that's using 10% price moves between steps). Forget about a separate core holdings for now and lets assume that the only exposure we have is determined by the Ladder, so in this case we start with $10,000 gold and $10,000 cash as depicted by the $1000 gold price.
Lets say that the gold price declines to $909, the ladder says buy $1000 more gold (reduce cash to $9000), which we do (buy-low).
Overall across the Permanent Portfolio gold is down and we've lost nearly $1000 in the value of that gold i.e. $10,000 bought at $1000 price is now worth $9090 and we've lost $910 of value. For simplicity let's assume that we've lost exactly $1000. Stocks, LT's and cash might have gained $1000 between them such that the PP's overall value is still the same as it was before.
If we reset and start afresh then we have a ladder such as the one on the right, i.e. we've re-centralised with a new lower top and lower bottom price levels.
If we repeatedly reset in a similar manner over time then in concept we always stay in the middle of the ladder region and never breach the top or bottom price levels (never move to all in or all out) i.e we never exhaust cash nor shares to sell.
As the price moves around however we buy-low/reduce-high and capture something like the
type potential gains/benefit example that I outlined in an earlier posting.
Its a type of d'Alembert betting sequence, where you start with 1 unit stake and increase the stake by 1 unit after each losing play and reduce by 1 unit after each winning play (minimum of 1 unit stake). In the classic sense the d'Alembert breaks down (loses) when your bankroll is exhausted and you can't match the next stake. In this case however we never encounter that extreme (excepting very exceptional circumstances). And with a d'Alembert sequence you make a profit even at 50/50 outcomes or worse, i.e. for a heads and tails sequence of the following and we back heads
stake outcome
1 T lost 1
2 T lost 2 total loss 3
3 T lost 3 total loss 6
4 H won 4 total loss 2
3 H won 3 total gain 1
If each T was a -10% move and each H was a +10% move then despite there being three down -10% moves and only two up +10% moves overall we're in profit.
A failing of the ladder approach alone was that of topping or bottoming out (all in/all out). All out (topping out) isn't really a problem as you can just use the cash to restart again. Bottoming however is a big problem as you're all in and have to await a re-entry into the price range of the Ladder. In the case of Japan when the Nikkei was 30,000 and maybe we had a bottom of 25,000 then from the current 8000 levels that's a long potential wait (or having to lock in a loss and start afresh with a lower total fund value).
When combined with the PP however and the tendency for the PP to maintain total fund value in a relatively consistent manner over time, ladder becomes much more viable.
The price difference per step is 10,26016 % per from the top down.
In that earlier example the steps were around 5% apart. It doesn't matter however as the ladder is just a visual representation of the log stochastic and you might only trade at perhaps moving average cross overs or whatever signal you prefer. At which time you calculate (log(current)-log(bottom))/(log(top)-log(bottom)).
What if on a 10% rise or drop you sold or bought enough to bring the equity value back to where you started?
That's the exact thing we're after Toofuzzy.
Maybe another example might help better. Say gold is currently priced at $1000 and I start a Ladder like the one on the left (that's using 10% price moves between steps). Forget about a separate core holdings for now and lets assume that the only exposure we have is determined by the Ladder, so in this case we start with $10,000 gold and $10,000 cash as depicted by the $1000 gold price.
Lets say that the gold price declines to $909, the ladder says buy $1000 more gold (reduce cash to $9000), which we do (buy-low).
Overall across the Permanent Portfolio gold is down and we've lost nearly $1000 in the value of that gold i.e. $10,000 bought at $1000 price is now worth $9090 and we've lost $910 of value. For simplicity let's assume that we've lost exactly $1000. Stocks, LT's and cash might have gained $1000 between them such that the PP's overall value is still the same as it was before.
If we reset and start afresh then we have a ladder such as the one on the right, i.e. we've re-centralised with a new lower top and lower bottom price levels.
If we repeatedly reset in a similar manner over time then in concept we always stay in the middle of the ladder region and never breach the top or bottom price levels (never move to all in or all out) i.e we never exhaust cash nor shares to sell.
As the price moves around however we buy-low/reduce-high and capture something like the
type potential gains/benefit example that I outlined in an earlier posting.
Its a type of d'Alembert betting sequence, where you start with 1 unit stake and increase the stake by 1 unit after each losing play and reduce by 1 unit after each winning play (minimum of 1 unit stake). In the classic sense the d'Alembert breaks down (loses) when your bankroll is exhausted and you can't match the next stake. In this case however we never encounter that extreme (excepting very exceptional circumstances). And with a d'Alembert sequence you make a profit even at 50/50 outcomes or worse, i.e. for a heads and tails sequence of the following and we back heads
stake outcome
1 T lost 1
2 T lost 2 total loss 3
3 T lost 3 total loss 6
4 H won 4 total loss 2
3 H won 3 total gain 1
If each T was a -10% move and each H was a +10% move then despite there being three down -10% moves and only two up +10% moves overall we're in profit.
A failing of the ladder approach alone was that of topping or bottoming out (all in/all out). All out (topping out) isn't really a problem as you can just use the cash to restart again. Bottoming however is a big problem as you're all in and have to await a re-entry into the price range of the Ladder. In the case of Japan when the Nikkei was 30,000 and maybe we had a bottom of 25,000 then from the current 8000 levels that's a long potential wait (or having to lock in a loss and start afresh with a lower total fund value).
When combined with the PP however and the tendency for the PP to maintain total fund value in a relatively consistent manner over time, ladder becomes much more viable.
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