The setup. You think that we are at the peak and the price is about to drop. You want to sell now in order to rebuy later. How much of a drop should you expect in order for it to be worth your while to sell and then attempt to rebuy lower? Considerations:
- risk of selling too early and losing your coins
- taxes
tl;dr. - I think a typical person would need to expect a drop of 65-70% in order for it to be worth their while to sell and attempt to rebuy later at a lower price.
- Interestingly, in the last 2 crashes, price dropped by this amount.
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For the people who trade more frequently - I just do not understand why you do it / how you can justify it. Please explain. Do you make coins?The equations. You buy C0 bitcoins at price Pb at the beginning of a cycle. Once the price peaks, you sell them at Ps, near the top, with the hopes of rebuying more bitcoins at Pr after the crash.
Since the price increased,
Ps = f * Pb, f >> 1.
The fiat gains per bitcoin are:
g = Ps - Pb = (f - 1) * Pb = (1 - 1/f) * Ps
Total fiat gains: G = g * C0 = (1 - 1/f) * Ps * C0
At the end of the year, you'll have to pay taxes on G, at a rate of t. If, after you sell, you reserve the money to pay these taxes, then, post-tax, you gained in fiat G' = (1 - t) * G = (1 - t) * (1 - 1/f) * Ps * C0. [This assumes that you did not have any coins before buying at Pb.]
The total amount of fiat after you sell is the post-tax gains plus what you had invested originally:
L = G' + Pb * C0
L = [(1 - t) * (1 - 1/f) + 1/f] * Ps * C0
L = [1 - t + t / f] * Ps * C0
When you eventually buy back at Pr, you will have C1 coins. The ratio a = C1 / C0 is the coin gain
a = [1 - t + t / f] * Ps / Pr
The price drop from Ps to Pr is d':
d' = 1 - Pr / Ps = 1 - [1 - t + t / f] / a
The actual price drop from the peak to the trough will be greater than d' because you can't pick the exact top and bottom. Peak to trough drop: d = d' + c. Let's say c = 0.15. So
d = 1 - [1 - t + t / f] / a + 0.15.
We are interested in is the price drop d as a function of the tax rate t, the runup f, the coin gain a.
Variable values.t depends on where you live and whether you decide to pay taxes. If you don't pay taxes or live in a country that doesn't tax bitcoin trades, t = 0. Here is the US federal tax bracket:
http://www.moneychimp.com/features/tax_brackets.htm Plus, you'll pay at the state level, maybe 5%. Some reasonable values for t are 0 and (0.25, 0.28, 0.33) + 0.05 = 0.30, 0.33, 0.38.
Based on
previous crashes, some reasonable values for f are 8, 17, and 36*.
a = 1 is interesting because it tells us how much price has to drop just to get all of your coins back. However, selling your coins is very risky, since you might lose them if price keeps rising. For most people, they require a >> 1 to sell. I really think a = 1.25 is the minimum any sane person would require. a = 2 is a very good gain, and a = 1.5 is probably what most people will settle for. -- What do you think are good values of a?
Results.Consider the case when a = 1 -- you just want to get your coins back. This is not realistic. Just a baseline.
t f a d
1 0 8 1 0.15
2 0 17 1 0.15
3 0 36 1 0.15
4 0.3 8 1 0.413
5 0.3 17 1 0.432
6 0.3 36 1 0.442
7 0.33 8 1 0.439
8 0.33 17 1 0.461
9 0.33 36 1 0.471
10 0.38 8 1 0.483
11 0.38 17 1 0.508
12 0.38 36 1 0.519
When t = 0, d' = 0. Meaning, you could sell and rebuy the next instance and keep all your coins. d = 0.15 because that's what I've assumed above -- by the time you notice the price going down, by the time you sell, by the time you rebuy again, with all the slippage and panic, for d' = 0, d has to be > 0.
If you are paying taxes, you would require a drop in the mid-40%, all the way up to 50% if you are in a higher tax bracket. That's just to keep your coins.
a = 1.25 -- you are pretty risk tolerant.
t f a d
1 0 8 1.25 0.35
2 0 17 1.25 0.35
3 0 36 1.25 0.35
4 0.3 8 1.25 0.56
5 0.3 17 1.25 0.576
6 0.3 36 1.25 0.583
7 0.33 8 1.25 0.581
8 0.33 17 1.25 0.598
9 0.33 36 1.25 0.607
10 0.38 8 1.25 0.616
11 0.38 17 1.25 0.636
12 0.38 36 1.25 0.646
Even if you are paying 0 tax, you still want the price to crash at least 35%. Once you figure the taxes in, you require a price drop of 55-65%. For a chance to increase your stash by 25%.
a = 1.5 -- where I think most people are in terms of risk aversion.
t f a d
1 0 8 1.5 0.483
2 0 17 1.5 0.483
3 0 36 1.5 0.483
4 0.3 8 1.5 0.658
5 0.3 17 1.5 0.672
6 0.3 36 1.5 0.678
7 0.33 8 1.5 0.676
8 0.33 17 1.5 0.69
9 0.33 36 1.5 0.697
10 0.38 8 1.5 0.705
11 0.38 17 1.5 0.722
12 0.38 36 1.5 0.73
Even non-tax payers need the price to drop 50%. With taxes, people require a drop of 65-70%.
a = 2 -- what I think is very risk averse.
t f a d
1 0 8 2 0.65
2 0 17 2 0.65
3 0 36 2 0.65
4 0.3 8 2 0.781
5 0.3 17 2 0.791
6 0.3 36 2 0.796
7 0.33 8 2 0.794
8 0.33 17 2 0.805
9 0.33 36 2 0.81
10 0.38 8 2 0.816
11 0.38 17 2 0.829
12 0.38 36 2 0.835
65% required drop even without taxes. With taxes, you would have to expect a drop of ~80% to sell.
For comparison, here are the
actual crashes that we've had:
pk.date pk.price tr.date tr.price drop ft.date ft.price n.dest n.be
1 2010-07-19 0.09 2010-07-24 0.05 44.4 2010-07-27 0.06 NA 83
2 2010-11-07 0.36 2010-12-10 0.19 47.2 2010-12-11 0.22 11 68
3 2011-02-14 1.06 2011-04-05 0.67 36.8 2011-04-07 0.75 14 62
4 2011-06-09 29.6 2011-11-18 2.14 92.8 2011-11-24 2.42 42 617
5 2013-04-09 215 2013-04-16 65.3 69.6 2013-07-08 77 17 209
6 2013-11-30 1,130 2014-04-11 392 65.4 2014-05-07 441 17 NA
Interestingly, the past two crashes were 70%, which is exactly what I think a reasonably risk-averse person who is paying taxes would require in order to attempt to sell at the top and rebuy at the bottom.
Here is what I do not understand -- people trading coins on a more frequent basis. Why would you do this? Are you really so risk tolerant that your a is close to 1? Do you not pay taxes? Do you actually gain coins by frequent trading? Even on an after-tax basis? How?
---
* Appendix: reasonable values of f. See my discussion of
previous crashes for more details.
pk.date pk.price ft.date ft.price r.pk.ft
1 2010-07-19 0.09 2010-07-27 0.06 NA
2 2010-11-07 0.36 2010-12-11 0.22 6
3 2011-02-14 1.06 2011-04-07 0.75 4.82
4 2011-06-09 29.6 2011-11-24 2.42 39.4
5 2013-04-09 215 2013-07-08 77 88.7
6 2013-11-30 1,130 2014-05-07 441 14.7
Based on this, here is a prediction for f (which, in the above table, is r.pk.ft):
p_25 p_50 p_75
1 8.13 17.2 36.2