BED back test (IIP-22)

OK, There have been some discussions within the Discord, Discourse and Product Working Group over whether a balancer pool, or a Set Protocol structure is better.

So, I’ve done some spreadsheet calculations with the following parameters:

  • $10,000 initial investment on 09 October 2020
  • 1/3 BTC, 1/3 ETH, 1/3 DPI
  • 28 day period between rebalances (Fridays, so likely to avoid the 1st working day of the month used by other products).
  • Final date is 23rd April 2021.
  • Coingecko opening prices used.

First the relative performance of each:

HOLD without rebalance
First we can consider buying $3,333.33 of each and holding:

Hold Strategy Value (1:1:1: portfolio)
Date BTC ETH DPI Total
09 Oct 2020 $3,333 $3,333 $3,333 $10,000
06 Nov 2020 $4,761 $3,961 $2,475 $11,197
04 Dec 2020 $5,950 $5,871 $4,446 $16,266
01 Jan 2021 $8,885 $7,033 $4,535 $20,453
29 Jan 2021 $10,142 $12,653 $11,209 $34,004
26 Feb 2021 $14,386 $13,987 $14,733 $43,106
26 Mar 2021 $15,740 $15,115 $14,499 $45,353
23 Apr 2021 $15,908 $23,102 $18,242 $57,252

The composition of the funds over the 7 periods is:

A different way to look at this, is to calculate the value at the end date (23 Apr 21), based on $10,000 invested on each start date (this is a little counter-intuitive !):

Value of Hold Strategy on 23 Apr 21
Entry date BTC ETH DPI Total
09 Oct 2020 $15,908 $23,102 $18,242 $57,252
06 Nov 2020 $11,137 $19,443 $24,567 $55,147
04 Dec 2020 $8,913 $13,117 $13,676 $35,706
01 Jan 2021 $5,968 $10,949 $13,409 $30,326
29 Jan 2021 $5,229 $6,086 $5,425 $16,739
26 Feb 2021 $3,686 $5,506 $4,127 $13,319
26 Mar 2021 $3,369 $5,095 $4,194 $12,658
23 Apr 2021 $3,333 $3,333 $3,333 $10,000

A couple of comments:

  • As the market is going up, a later investment is worth less on the 23 Apr 21.
  • Investment on the 6th Nov results in more of your portfolio being in DPI with a Hold Strategy (which ties in with the low DPI value in early Nov).

The advantage of this visualisation si that we can do the same for a balancer pool, and the periodic rebalance and get a comparable figure.

Balancer pool
I’ve had to fudge the balancer calculations. What I’ve done is:

  1. Take the value at each time point.
  2. Calculate the % change between that time point and the endpoint
  3. I could not find a 3-way impermanence loss calculator. So I’ve used the coin gecko AAM calculator with a 33:67 split between each token and the average of the other 2 tokens.
  4. Then I multiple the Hold value of each token (i.e. the value at 23 Apr 21), but its respective impermanence loss top calculate the value after IL.
  5. Then I sum the modified value to give the pool value on the 23 Apr 21 if $10,000 was invested on the start date.

I think that this is correct/close enough to what the pool would, but if anyone has a better approach I would love to hear it.

% Increase in single asset to 23 APR 21
Entry date BTC ETH DPI
09 Oct 2020 377% 593% 447%
06 Nov 2020 234% 483% 637%
04 Dec 2020 167% 294% 310%
01 Jan 2021 79% 228% 302%
29 Jan 2021 56.9% 82.6% 62.7%
26 Feb 2021 10.6% 65.2% 23.8%
26 Mar 2021 1.1% 52.8% 25.8%
23 Apr 2021 0.0% 0.0% 0.0%
Impernanece loss for asset
Entry date BTC ETH DPI
09 Oct 2020 1.29% 0.93% 0.05%
06 Nov 2020 4.60% 0.14% 2.57%
04 Dec 2020 1.75% 0.25% 0.53%
01 Jan 2021 5.40% 0.16% 2.42%
29 Jan 2021 0.10% 0.20% 0.02%
26 Feb 2021 0.77% 0.16% 0.13%
26 Mar 2021 1.09% 1.01% 0.00%
23 Apr 2021 0.00% 0.00% 0.00%
Value of Balancer Strategy on 23 Apr 21
Entry date BTC ETH DPI Total Loss to Hold % Loss
09 Oct 2020 $15,703 $22,887 $18,233 $56,823 -$429 -0.75%
06 Nov 2020 $10,625 $19,416 $23,935 $53,976 -$1,171 -2.12%
04 Dec 2020 $8,757 $13,085 $13,604 $35,445 -$261 -0.73%
01 Jan 2021 $5,646 $10,931 $13,084 $29,661 -$664 -2.19%
29 Jan 2021 $5,223 $6,074 $5,424 $16,721 -$18 -0.11%
26 Feb 2021 $3,658 $5,497 $4,122 $13,277 -$42 -0.32%
26 Mar 2021 $3,332 $5,043 $4,194 $12,570 -$88 -0.70%
23 Apr 2021 $3,333 $3,333 $3,333 $10,000 $0 0.00%

Periodic rebalance of Set Protocol
This strategy calculates the total value at each rebalance date, and then redistributes it so it is 1/3 BTC, 1/3 ETH and 1/3 DPI going into the next period.

Looking at the end value with different start dates we get:

Value of Rebalance Strategy on 23 Apr 21
Entry date BTC ETH DPI Total Gain over hold % gain over hold
09 Oct 2020 $17,119 $25,889 $21,312 $64,320 $7,068 12.3%
06 Nov 2020 $15,289 $23,121 $19,034 $57,444 $2,297 4.2%
04 Dec 2020 $10,129 $15,318 $12,610 $38,058 $2,352 6.6%
01 Jan 2021 $8,188 $12,382 $10,193 $30,763 $438 1.4%
29 Jan 2021 $6,351 $9,486 $7,111 $22,948 $6,209 37.1%
26 Feb 2021 $3,547 $5,365 $4,416 $13,328 $9 0.1%
26 Mar 2021 $3,369 $5,095 $4,194 $12,658 $0 0.0%
23 Apr 2021 $3,333 $3,333 $3,333 $10,000 $0 0.0%

Note: I find the 37% improvement for the 29 Jan 21 start date to be counter intuitive, however, I can’t find an error in my calculations.

Comparison
Comparing all three strategies by variable start date:

If we drop the balancer, we can use a simpler figure to compare the hold vs the reblance strategy starting on the 09 Oct 20:

Some final comments:

  1. Excluding fees, A v1 balancer will always underperform a simple hold.
  2. This backtest shows ~1 to 2% loss over periods up to 28 weeks.
  3. Balancer stats show income around 2 to 3% per year (0.4% fee on BTC:ETH, or 0.3% fee on BTC ETH)
  4. The rebalancing strategy outperforms vs hold
  5. However, it can underperform (If 1 asset continues to underperform the other two and the rebalance keeps buying it).
  6. Reblancing Set Protocol contacts costs gas and management time.

Calculations
Can be found here - any review is welcomed. :+1:

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many thanks for doing this, have to set aside some time to dig in further!

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This is great context @overanalyser! Really appreciate your work here.

Thanks for this data, very helpful even if Balancer data is guestimated.

So final result is 11% difference in final asset price between Set rebalances and Balancer?

From what I can see all the extra value comes from the more periodic rebalance’s and “buying the dip” on index assets when one loses relative value to the others. If that is the only difference then shouldn’t we just stick with CGI which has a better methodology around that rebalance strategy and has protection from crypto prices/volatility with gold?

The BED methodology specifies an "equal weighted index ". From the rebalance strategy data the index will never have equal weights (except a brief moment after rebalances). They either need to increase frequency of rebalance to every week/day or modify the methodology weightings/rebalance on their IIP to reflect the reality of how they plan on managing the index,

It definitely adds an extra element to a BED token to have it rebalance, though I was under the impression that it was fixed. Having said that, there was discussion of eventually replacing underlying tokens with safe and solid yield bearing assets such as a rocketpool ETH. So, beyond convenience, it seems there are opportunities to outperform just holding.

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