"How much do I sell at each step. . .if I would not want to let the profits run?
One Level Cost amount is added after each step down in stock price and one level cost amount is removed after each step up in stock price (buy-low/sell-high).
The top and bottom would generally be set quite wide, perhaps inflation uplifted historic high and low price values. I prefer to use dividend yield as that is more time independent and identifying the historic high and lows is easier.
Take as a simple example a range of the UK FT100 index, from a high of 10% yield down to a low of 2% yield (approximations).
Let's assume we're happy to trade at 10% proportionate stock price changes
Start with 2% dividend yield, multiply by 1.1 = next step is 2.2% yield, multiply 2.2 by 1.1 = 2.42, ... etc.
2
2.2
2.42
2.662
2.928
3.221
3.543
3.897
4.287
4.715
5.187
5.706
6.276
6.904
7.594
8.354
9.189
10.10
In total there's 18 steps. So we divide our total fund by one less than the number of steps. If we were investing $40,000 then $40,000 / 17 = $2352 which is our level cost.
To identify the initial amount of stock to buy we start at the top price with $0 stock and add on one Level Cost amount for each subsequent step i.e.
Yield $$$ stock
2.00 0
2.20 2352
2.42 4704
2.66 7056
2.93 9408
3.22 11760
3.54 14112
3.90 16464
4.29 18816
4.72 21168
5.19 23520
5.71 25872
6.28 28224
6.90 30576
7.59 32928
8.35 35280
9.19 37632
10.11 39984
If we start when the yield is 4.29% we might buy $18816 of stock. If then later the yield declines to 3.9% (i.e. stock price has risen) we sell one Level Cost worth $2352 of stock. If it rebounds to 4.29% yield we buy $2352 stock. Across that 10% price up/down move we in effect make $2352 * 0.1 = $235.2.
Our d'Alembert unit stake is the level cost multiplied by the step interval, which is 10% in this case, so our D'A here is $2352 * 0.1 = $235.2 Knock two trade costs of that (one buy and one sell per pair) and our net d'A is $210 (assuming $12.50 per trade cost).
Having set the top and bottom to historic high/low's then if the price runs out the top to make new highs we're all in cash and have to reconstruct a new Ladder to account for the new high. If the price runs out the bottom to new lows, then we're all-in anyway and have to sit it out until the price rebounds back into the Ladders top/bottom range.
Generally for the UK FT100, 10% price cycles (pairs) on average occur 1.6 times p.a. So in this particular example $210 net profit per cycle x 1.6 = $336, which relative to the $40,000 allocated = 0.84%. That 0.84% however is relative to the total allocated amount, much of which will likely be in cash. Compared to the stock exposure amount the gain might be twice that (assuming 50/50 average stock/cash exposure levels) = 1.68%.
More usually however we don't get nice up/down sequential pairs, but runs in one direction followed by a reversal and a sequence of runs in the other direction. The overall effect/benefit is still the same however.
It's relatively easy to set up a spreadsheet to create a Ladder, which in turn is useful as you can tweak the amount allocated, step size intervals etc. to get to a net d'A unit stake amount that best fits with the amount of funds you're investing (i.e. you don't want the net d'A amount to be less than two trade costs otherwise you're trading for nothing (or at a loss)).
If you narrow the range between top and bottom you'll increase the d'A unit stake amount, but run the risk of breaching the top or bottom levels. Set too wide and your d'A gain is smaller (less profit) than it might have been.
You of course don't have to trade at each and every step. If you defer a trade believing the trend might continue further you might trade 2 Level Costs at the next step ($4704) and if then the price reverts back through two levels (20% price move) and you sell $4704, you've made $940.80 across that set move (a 2.35% gain relative to the total allocated fund value).
AI
