This post assumes you have an understanding of what is discussed in my post about SBD Printing Code Walkthrough.

Following up STEEM Rewards News Flash, I had stumbled upon this comment by @inquiringtimes which shows a conversation with @timcliff about what happens when the debt ratio hits 10%.

This is something I had read in the whitepaper awhile ago, but was never able to find, and for some reason I never followed up with someone who knew more about what was coded in the blockchain. My post about debt ratios had asked if anyone knew but it never reached the right folks.

I was referred by @inquiringtimes to this post which had the hint I needed about the price feed, though my searching skill was still lacking, and I was directed by @timcliff to the right spot when I asked in a github issue that discussed these caps (Sorry for the derail folks!)

And it's here

price min_price( asset( 9 * gpo.current_sbd_supply.amount, SBD_SYMBOL ), gpo.current_supply ); // This price limits SBD to 10% market cap
if( min_price > fho.current_median_history )
    fho.current_median_history = min_price;

If computed price in min_price is higher per STEEM than the median, it will replace it.

What is this computed price?

9 * sbd_supply / steem_supply

Note that if this is larger than the feed price, we have

9 * sbd_supply / steem_supply > feed_price

Let x = sbd_supply / feed_price be the SBD portion of the virtual supply and y be the STEEM supply. The virtual supply is x+y.

Then this condition is equivalent to

9x > y

and

10x > x+y

and

debt_ratio = x/(x+y) > 1/10

This condition is equivalent to exceeding the 10% debt ratio threshold.

Note that at this time, since we shut off SBD payouts at 5%, the only thing this adjusted feed price affects is the conversion rate. This protection has the effect of reducing the amount of STEEM you get per SBD using the conversion mechanism.

How much does it reduce it by? Well, for 1 SBD, you'd get

(1/9) * (1-d)/d * (1 usd worth of steem)

where d = x / (x+y) is the debt ratio.

When we are at exactly 10%, it's the same, but as the SBD portion of the debt increases, it steadily decreases. For illustrative purposes the relationship in table form looks as follows:

Debt Ratio d	USD worth of STEEM per SBD
<=0.1	1
0.11	0.9
0.12	0.81
0.13	0.74
0.14	0.68
0.15	0.63
0.16	0.58
0.17	0.54
0.18	0.51
0.19	0.47
0.2	0.44
0.3	0.26
0.4	0.17
0.5	0.11
0.6	0.07
0.7	0.05
0.8	0.03
0.9	0.01
1	0

The reason I have this in terms of USD is to illustrate where the effective peg moves to as the price feed jumps off the intended peg of 1 USD. Thus, this can be read as saying that if the debt ratio is 20%, the blockchain code will only give you 0.44 USD worth of STEEM if you convert. And in this scenario, the conversion mechanism should not be used unless 1 SBD is < 0.44 USD.

The other point is that if mass conversions happen, the debt ratio becomes lower, and that increases the amount of STEEM you would get on conversions (in this regime). An interesting dynamic.

Remember, in situations like now where the market price of SBD is > 1 USD, none of what I am saying here matters, because the conversion mechanism will lose you money (and is turned off on the website).

Debt ratio factors

Just to emphasize the influential factors here, the following influence the debt ratio:

1. Steem prices. Because the crypto market is volatile, this can change the debt ratio quite quickly, as we have seen recently.
2. Payouts. Of the steem inflation, some percentage is allocated to rewards, and half of that (at most) is converted to SBD.
3. Conversions. A conversion event destroys SBD and creates Steem.

What does it all mean?

To most of you, this means absolutely nothing. But if Steem price tanks to lower levels, with SBD as well, then there may be a time when this information becomes relevant.

However, this information, as well as the aforementioned debt ratio protections as the ratio exceeds 2%, need to be taken into account when discussing any monetary policy.

There's discussion about removing some of these behaviors, but that requires knowing why these protections were put into place to begin with. I originally planned to write my understanding of this but found that I was not satisfied with my understanding about this. So I will leave it to a later post and follow the witness discussion about this.