Topic: A risk/reward analysis of insured pirate: YARR, PPT.X, GIPPT, Hashking, Goat (Read 3708 times)

Those investors who correctly judged counterparty risk and read this thread have not lost any money.

Edit: all the images are gone, but that shouldn't be a problem since there is virtually no BTC lending economy right now...
More math is available upon request

Bump for Goat's upcoming bond

Hashking's 50% insured deposit vs other methods. Compounding using (1+interest rate)^x

-We assume a starting capital of 100 BTC. This is marked as the black line.
-The pink line is putting everything into Hashking's 6.75% and compounding it.
-The green lines are: 50 BTC in 6.75% and 50 BTC in cold storage
---The top green line is total capital, the bottom green line is what you'd have if pirate defaulted
-The orange lines are: 50 BTC in 6.75%, 50 BTC in 1.019% (hashking offers this) fully insured
---The top orange line is total capital, the bottom orange line is what you'd have if pirate defaulted.
-The brown line is 100 BTC in hashking's 3.30% weekly 50% insured deposit
---Again, the top line is total capital; the bottom what you'd have on a pirate default.

This shows something interesting for an investor: after 22 weeks, your principal is 100% guaranteed.

Now, let's keep the 3.30% weekly 50% insured lines compounding, and start paying out interest with other methods.


-With the pink lines, we put all 100 BTC into Hashking's 6.75% uninsured deposit and take out our interest weekly.
-With the orange lines, we put 50 into Hashking's 1.9% weekly for compounding, and take weekly payouts on 50 BTC in 6.75%.

Now, as an investor, we look at the intersections. For the short term (< 4 months), we know that the best total capital is obviously to put everything into uninsured pirate, compounding or taking payouts. The best guarantee of capital is the 50/50 scheme in the short term.

At 19 weeks, hashking's insured deposit finally becomes a higher return than the 50/50 scheme (though the risk has always been higher since day 2)

The final scheme, which will have both a higher return and a higher guaranteed capital, goes like this:
50 into hashking's pirate operation, payouts weekly
50 into someone's insured operation, compounding
I say someone because hashking uses lock-in times, and it would be better for this scheme to get someone like PatrickHarnett who can take more every week.
Whenever you get a payout from pirate, add it to the compounding principle. I'm slightly confused on how to make this into an non-recursive equation right now The compounding part would look like:
50
53.875
57.7888
Each week you have 1.01 * lastweek + 3.375
more formally:
f(x) = 1.01 * f(x-1) + 3.375
f(0) = 50

If anyone here can graph recursive functions I'd appreciate it. Or turn the recursive function above into an exponential one.

I am proud to announce the possibility of...
A Pirate-Pass-Through paying MORE than 7% Weekly!

Here's how it works. Two investors get together, or are matched through a third-party. One is the low-risk seeker, and one wants huge returns. Here's an example:

Lender A wants low-risk returns. He has 300 BTC.
Lender B wants high-risk PPT returns. He has 195 BTC.

The two pool their money for a total of 495 BTC. They purchase 300 shares of YARR for 1.65 BTC each (yes, the market depth is there as of the time of this writing.) Every week, they get 18 BTC in dividends. They split it up in this way:

Lender A gets 3.375 BTC
Lender B gets 14.625 BTC

This means that their returns are:
Lender A: 3.375 / 300 = 1.125% weekly
Lender B: 14.625 / 195 = 7.5% weekly

If pirate defaults, Lender A gets the 300 BTC; Lender B gets nothing. Therefore, this scheme entitles one person to risk-free 1.125% weekly returns, and the other person to 7.5% weekly returns with the same risk as pirate-direct.

This is evidenced by my earlier analysis. At a price of 1.71 BTC, Lender A gets about 1% weekly and Lender B gets about 7% weekly.

There are at least 3 opportunities that this provides:
1. Get-together, as above
2. Just buy shares of YARR yourself and be both people
3. A third-party service which offers 1.1% and 7.1% returns, matches up depositors, covers the unmatched bits, and takes a cut.

Bump for Hashking's deposit and the GIPPT security.

I decided to exclude compounding from the calculations. This is because of scalability. Compounding one share of YARR will take you 25 weeks. Compounding 1000 shares of YARR can be done daily, but not perfectly. It makes for a nicer assessment if we assume taking the payouts. If you have an algorithm which can be used on compounding when compounding can only be done with multiples of 1.55, that would be very cool. I suspect, however, that it would make for some wonky graphs, due to the higher the initial capital, the easier the compounding.

If someone wants to compound, BitcoinMax is probably a better idea than YARR, even at the current price of 1.55 BTC.

That's the sweet spot for 7% weekly. The sweet spot for 6.9% weekly is slightly higher; take away the ability to compound and it's slightly lower.

You did not factor in the possibility to compound after dividend payments/buybacks though...

Especially for the PPT calculations: These don't pay 7% a week, they pay 28% in 4 weeks. YARR is even more extreme and pays out daily (except sundays).

I guess the sweet spot for PPT.X is still at ~1.07, but probably a bit below.

This is my last attempt at a very formal representation of my model. I will post a series of consecutive numbered statements (some premises, some conclusions, and some if-then statements. Maybe I'll even use 'iff'). Where a conclusion depends on a premise, the premise will have a lower number than the conclusion, and the premise's number will be in parenthesis before the conclusion.

If anyone has a problem with the following document, I request that he or she address individual points.

Emotional denouncement and disclaimer: I have used the following model to make investment choices, which included buying shares of YARR. The following model is not an attack on usagi, CPA, YARR, pirateat40, Bitcoin Savings and Trust, or the GLBSE.com platform.

(0)This document will ignore the "face value" of bonds, because bonds cannot be purchased by an investor at face value. It will similarly ignore no longer relevant market data.

Definitions
1. "pirate" is the colloquial name for bitcointalk.org user pirateat40. In this document, 'pirate' refers to the service he operates, "Bitcoin Savings and Trust." This service offers a maximum of 7% per week.
2. "GLBSE" is a securities exchange located at glbse.com
3. (1)(2)"YARR" is a fixed-return instrument distributed via GLBSE. It provides dividends of 0.06 BTC/unit/week by investing coins with pirate.
4. (1)"pirate-exposed capital" is capital (denominated in Bitcoin) which will be completely lost by an investor if pirate defaults.
5. (1)"Insured Capital" is capital (denominated in Bitcoin) which will not be lost if pirate defaults.

Premises
6. (3)The current market price of YARR is 1.5499.
7. (3)An investor who wishes to buy a unit of YARR must pay close to the market price.
8. (3)(5)Regardless of YARR's market price, the Insured Capital per unit of YARR is 1 Bitcoin.
9. (3)(4)The pirate-exposed capital can be determined by subtracting the Insured Capital from the market price of YARR. To reiterate, this operation will result in the amount of capital which will be lost if pirate defaults.
10. (4) The pirate-exposed capital when investing directly in pirate without insurance is equal to the amount invested.

If-then and conclusions
(Logic refresher: An if-then statement can be considered an entity and evaluated to be true or false. An if-then statement is only false if there is a situation in which the premise is true and the conclusion is false. Thus, the statement "if Kevin Bacon is Bill Gates, then the world has already ended" is true.)
11. (9)The pirate-exposed capital of one share of YARR is currently .5499 BTC.
12. (10)(11)The pirate-exposed capital of .5499 BTC invested directly in pirate is equal to the pirate exposed capital of one share of YARR. To reiterate, this means that if (pirate defaults, and the investor had .5499 BTC in pirate) or (pirate defaults, and the investor had one share of YARR), then the investor will lose .5499 BTC.
13. (12) Another way of phrasing 12 is that the risk of one share of YARR is currently .5499 BTC, which is equal to the risk of .5499 BTC directly invested in pirate.
14. (3)(11)An investor in YARR is gaining 0.06 BTC per week by putting .5499 BTC at risk of a pirate default.
15. (14)The return divided by the risk is 0.109111 per week.
16. 0.109111 can be represented as 10.9111%
17. The Insured Capital of 1 BTC cannot be invested in other opportunities.
18. It is feasible to expect 1% per week return on near zero-risk bitcoin deposits.
19. (17)(18)Therefore, the 1 BTC Insured Capital represents a loss of 0.01 BTC in time value per week.
20. (14)(19)The true return on risk is 0.05 BTC.
21. (6)The return on total capital is 0.06 / 1.5499 =0.0387122
22. 0.0387122 can be represented as 3.87122%
23. (20)The true return on risk is 0.05 / .5499 = 0.0909256
24. 0.0909256 can be represented as 9.09256%
25. (23)(24)Given a time value of 1% per week, YARR represents a return on risked capital of over 9.09% per week. This is greater than the maximum 7% per week that pirate offers.


This can all be done with PPT.X, but first I'd like to hear some feedback, particularly from PatrickHarnett and usagi. Remember to address individual points that you perceive as incorrect.

I am going to put this here, since I have nowhere else
Hmph. I say it's simply true! You cannot contest historical market price data; that's preposterous.

Just an update:
The price of YARR has dipped to 1.55 thanks to either someone who wanted out or someone who was taking profits.
I don't think I need to go through the math again; you can verify for yourself that this is the best publicly available deal in all of Bitcoin.

When doing math, I often like to take extremes. For example, when dealing with concentric circles, it's often useful to reduce the inner one to a point. Here's a few things to ponder:
-The system even works for calculations when you give everything to pirate. In that case, you value your money's time at 7% weekly, and you think pirate has a 0% chance of defaulting.
-Flip that and say you think pirate has a 100% chance of defaulting right NOW! (wait for it...)
In that case you shouldn't put any of your money in any pass-through.

Hmm... maybe we should do some calculations with defaulting chance. It comes with a few problems -- investors often have a hard time putting a percentage on risk, and the chance is often a curve: 1% chance of defaulting today, 10% by next week... so on until 95% within 2 years etc

Also: to PPT-PR et all: I think this thread focuses a lot on YARR. This is simply because the market rate of YARR varies, and PPT-X has a simple solution: "buy at 1.07 or less to win."
Also, since the insured amount is smaller (0.32), the time value lost is just 0.0128. One could get this amount through faucets in a month.

 
R has too much of a learning curve (get it? ) for me. Apparently, in order to plot two functions, you have to combine them into a matrix and stuff... it's just failing for me.

So... enjoy this :-/

Equations used are 0.05/(X-1) and 0.069*(X-1)+0.01

Now let's just check that math:
Scenario 1:
Alice buys a share of YARR for 1.782 BTC. She gets 0.06 weekly. On default:
1 BTC + 0.06w

Scenario 2:
Alice puts .782 into BitcoinMax and 1 into Starfish BCB. On default:
1 BTC + 0.01w + 0.053889w > 1 BTC + 0.06 w

So I did something wrong. It's actually closer to 1.725 BTC.

Edit: I should probably have given the YARR line a time value of 0%. In any case, this graphic is a "good enough" representation.

Cool. I'm always open to new programming languages/environments.
Then you are a very lucky man
The math can be taken even further if we come up with investors confidence in each party. For example, if the investor thinks YARR, PPT.X, CPA, BitcoinMax etc is more likely to default than pirate himself.

It may be novel, but it is the correct way to go about it. When I gave you money for the 1.5%/week compounding interest, the risk is the same for every satoshi I gave you. Either you default, or you don't, or you say "sorry, here's a partial return."
When Bob gives money to Alice, though, the risk varies. Some BTC is at risk of a pirate default, and some isn't. Some BTC is at risk of Starfish BCB defaulting, and some isn't. To accurately calculate the reward/risk ratio, we need to take that into account. The reason I had Bob give Alice money instead of investing himself is because YARR and PPT.X come as a "bundle:" you give them 1 or 0.32 BTC respectively that you are guaranteed, then you give them .89 or .75 BTC to gain interest, which you won't get back if pirate defaults. Furthermore, if the investor's confidence in usagi/CPA or the "cartel of lenders" is 100%, then the risk on the guaranteed portion is 0. The return can be 0 or negative.

I believe that my examples show that my model is correct. Now off to download R! (Not R-)

You can use R to plot graphs, here are some examples: http://www.sr.bham.ac.uk/~ajrs/R/r-gallery.html

Luckily I picked up 70 shares of YARR for 1.17 not long after the IPO 

France legislated pi = 4 (since corrected)

There are other issues around that require attention too, but it is descending into hysteria like the Salem trials with the newest crusader messing things up rather than applying any logic or thought.  So, this thread is refreshing.

The concept of capital at risk is a bit novel, as you normally look at overall return.  Surely you want to know the result for all funds.  For example, as I progressively cash out my initial seed money, my return becomes higher and higher until it hits infinity.

Actually I was about to ask if it was OK to use your name -- I assumed so, as my posts don't portray you in a negative light -- but it's best to be sure. I should probably PM PayB.tc soon.

As for the logic, I saw theymos' post about "local rules" and decided that there are enough "Pirate is a ponzi" arguments already.

Well... uhhh... how dare you not have defaulted on my deposit with you yet? SO THERE!

I'm open to anyone pointing out math flaws -- a fatal rounding error which when combined with a year of compound interest states that tennis racket companies pay more than pirate, or my algebra being wrong, or it being against U.S. law to use e the way I did etc

Fun Fact: according to this book (which I highly recommend) in one state, a man successfully filed a patent on the "mathematical truth" that pi = 4.

How dare you nimda to base your post on mathematics?

I heard my name, so I'd better sub - plus it's an interesting thread and attempts to cover some of these items more logically than several others.

Here is a multiple-scenario example:

Time Value of 0%, Pirate defaults
Scenario 1:

Bob has 18.995 BTC. He says "here Alice, I trust you. Invest this money in the best possible way."
After taking out 0.0005 for a transaction fee just to be safe, Alice has 18.9945 BTC on the GLBSE to invest. Turns out, that's the perfect amount for 10 shares of YARR at 1.89 each plus the 0.5% trade fee. What a perfect world. Alice now has 10 YARR shares. Every day, she gets 0.1 BTC, except for Sundays. That's 0.6 weekly, or 3.15881% weekly on the 18.9945.

Then one day (dun dun dun) Pirate defaults

Given w weeks have passed since the investment, Alice now has the dividends of 0.6w  plus 10 BTC.

Scenario 2:
Blah blah money changes hands. Alice gives 8.695652174 BTC to Bitcoinmax (earning 6.9%). She puts the rest (about 10.2988) in cold storage. She gets 0.6 BTC weekly, or 3.15881% weekly on the 18.9945.

blah blah pirate defaults in this universe too

Alice now has 0.6w plus 10.2988 BTC. This is the better deal

Time Value of 1% weekly, Pirate defaults
Scenario 1:
Same story as the very first scenario.

Scenario 2:
Same as the original scenario 2, but with 1 modification: instead of cold storage, Alice gives the 10.2988 to PatrickHarnett (earning 1% weekly). That last bit is perfectly reasonable, since Patrick provides some of the "lowest" rates and is one of the most trusted. Besides, like you said, no one is going to keep bitcoins in cold storage not gaining interest anywhere.

When pirate defaults, Alice has 0.6w + 10.2988e^.01w (also expressed as 0.6w + 10.2988 * 1.01^w)
This is the better deal

Hopefully it is now clear why time value is an argument against "insured" pirate bonds (not just YARR).
In another set of hypotheticals, pirate doesn't default, but Bob wants to buy a wikispeed car with his money (it's been many years now, pirates rates have never changed, and pirate owes more bitcoins than can ever exist ). Set 1: BitcoinMax or any other non-bond instrument: 0.0005 max is paid on withdrawal. Set 2: GLBSE, and Bob wants that money NOW: 0.5% fees are paid when selling the shares.

Nope. It's math. If the whole market could do middle school math and the whole market read this post, prices would probably go down some. But that doesn't hurt you, as you've said. Finally, let's look at 2 more sets (these show a cheaper YARR is a mathematical pipe dream ):

Time value of 0%, YARR price is 1.3, Pirate defaults, no fees paid
Scenario 1:
So Bob gives Alice 13.0005 BTC. She puts 3 into BitcoinMax and 10 into cold storage. She gets 0.207 weekly. When pirate defaults, she has:
10 BTC + 0.207w

Scenario 2:
Drop the fee and buy 10 shares @ 1.3 BTC each (bids got filled; Alice wasn't the taker). That's 0.1 daily except Sundays, for 0.6 weekly. When pirate defaults, Alice has:

10 BTC + 0.6w
This time, YARR is the better deal, because it cost 1.3 BTC, not 1.89 BTC.

Time value of 1%, YARR price is 1.3, Pirate defaults, 0.5% GLBSE fee
Scenario 1:
Bob --> Alice 13.0655 BTC. 10 go into PatrickHarnett, 3.065 go into BitcoinMax (actually, we'd need to multiply every number in this last set by 10, since BitcoinMax has a minimum of 5 BTC, but it doesn't matter really). When Pirate defaults:
0.2114w + 10 + .01w (or .2114w + 10 * 1.01 ^ w if the Starfish account was compounding, but that's unfair because YARR wasn't compounding -- it's difficult to compute compounding with multiples and not really relevant)

Scenario 2:
Alice gets 13 YARR shares. When pirate defaults:
0.78w + 13
This is the better deal.


Conclusion:
YARR is worth more than 1.3 BTC, and less than 1.89 BTC. Those who bought in at 1.3 BTC are getting an amazing deal.

What is that deal though?
WELL!
The capital at risk or "exposed" to a pirate default is only .3 BTC. The other capital is guaranteed. Thus, the risk is identical to giving pirate .3 BTC. The return, however, is huge. The people who bought in at that price are getting 0.06 weekly per .3 BTC risk. That's an ASTOUNDING 20% WEEKLY ON RISKED CAPITAL
There is the small problem of time value: the other btc is at no risk. If one were to invest 1 BTC in PatrickHarnett and  0.3 direct with pirate, one would get 0.031 weekly. Just over HALF of what YARR brings you.
If we treat the lost time value as a detractor, then we're losing a possible 0.01 weekly on that 1 BTC. So... 0.05 weekly on that 0.3 BTC risk. Still an ASTOUNDING 16.67% weekly on risked capital

Conclusion: I should have bought very large amounts of YARR at the IPO. Perhaps I will get a chance when usagi sells down to 1.4 BTC. Even at the worst case estimate, I'd "get" 0.05 weekly on 0.4 risk and 1 BTC which I can't trade or invest. STILL AN ASTOUNDING 12.5%


I think now is the time for the graphs. We'll see visually the exact fair price of YARR. But I have other work to do. See you tomorrow!
P.S. The fair price is about 1.76 BTC.
P.P.S. Does anyone have a nice (command line or GUI) graphing tool for Windows?
P.P.P.S. All of this applies to PPT.X too; 1.07 is the fair price

Well, I guess we need some examples. I'm running out of time, but I'll be back tonight with examples. For now:

I don't know about you, but I like to be able to liquidate my assets and withdraw my deposits. Therefore, said amount is not a payment per-se; I will want it back later. Good news: I can get it back later. Maybe it won't be exactly 0.89 when I decide to get it back, but that won't really be a problem given that I've been getting 0.0053% PER DAY ( ). And maybe that 0.89 will go up. Who knows.

I won't get it back later if Pirate defaults. I'll get 1, not 1.89. Tough luck for me. Next time I won't sell my car for GLBSE assets.

The point is that yes, that 0.89 is risked. It will be lost completely if pirate defaults, lost partially if CPA cancels the contract and buys back at 1.3, and it may rise or fall with the market. It is not a payment, however, because I can get it back later.

This is irrelevant. I didn't accuse you of scamming based on market flux or whatever. Personally, I thought you were going to release more shares rather soon, and you said you were going to release more shares in this thread:
But it's beside the point. In fact, I don't even know why you said that you make nothing and lose nothing on YARR's price.
If I were going to accuse you of scamming, I'd point at that 1.3 clause. But I won't. Most bonds and shares on GLBSE   can be bought back for >= face value, which is almost always <= market price.

Sure, I love the free market. The free market allowed me to buy shares of MOORE for less than 0.5, and I just got a guarantee that it will always be worth at least 0.5.
And sure, people can pay whatever they want for YARR. If YARR were denominated in dollars (and paid $0.09 ~= 0.01 BTC daily except Sundays), people would pay more than $2700 for a single share, because that's about 1% yearly. As my example will show later, though these people you spoke of (back to BTC and GLBSE now) would get a better return/risk if they didn't buy YARR at 1.9.
Furthermore, my mental math leads me to believe that buying YARR at 1.3 is 3 times better than investing directly with pirate.   Whoa. If I get out ye olde graphing calculator, I'll find the 4 spots where YARR is equal to [bitcoinmax, direct pirate] * [time value of 1%/wk, time value of 0%/wk]



Muis: I'll think about that; usagi probably has a better answer than me. I for one have never run an insurance company, let alone one in BTC, but I believe that if Pirate doesn't default in ~65 Sundays (~= 15 months) from IPO, CPA will be just fine.