Slow down usagi. This is a math thread, not a heated argument thread.
Edit: it's quite possible that I mistook your tone, or vice-versa
I'm going to be answering the part in bold. The second paragraph merely addresses one of the 5 "additional risks and detractors" and I'm going to concede that point. The third paragraph starts with an incorrect sentence, then moves on to make assumptions about lower than current market prices. It ends with a statement based on the part in bold, which I am going to address. The fourth paragraph does not have much for me to debate. I hope I'm not missing anything.

The second bold sentence is easiest: no, I don't take into account the fluctuating price of YARR, however I do provide general formulas which will work for any price of YARR. I then give one example which uses the "last" price.

Now for the first sentence. Let me quote it again, since I've rambled quite a bit and might have put it above the page scroll.
Here, we have a mis-communication. It actually reflects better on YARR if I don't do that. Here we get into time value.
What happens is that the 0.89 is risked. Pirate defaults --> it's gone. The 1 BTC is not risked. It's almost 100% guaranteed. Therefore, the risk of investing in YARR at a price of 1.89 BTC is mathematically equivalent to the risk of investing 0.89 in pirate and 1 BTC in cold storage. From there I say that it is the 0.89 which is generating about 0.0674% interest, while the 1 is staying safe generating 0% interest. An investor will put 0.89 at risk and 1 safely and enjoy 0.06 week. If, however, the investor puts 0.89 at risk directly with pirate (pretend that this is possible, I'm simply working with the numbers of 1 share although this calculation should be scaled up -- the outcome would not change) and then 1 with PatrickHarnett (now pretend that Patrick is 100% guaranteed; I'd say it's close -- again, the outcome doesn't change much), the investor would enjoy 0.0723 week. Similarly, if the investor put 8.9 with PayB.tc and 10 with PatrickHarnett, he would get 0.7141 week.

I hope I have expressed myself clearly enough to show that giving a "time value" to the guaranteed 1 BTC actually decreases YARR's value. In truth, I was planning on getting to the time value calculations in a later post in this thread, but I decided to leave the time value at 0% for simplicity's sake.

Note that the thread was not intended to bash you, YARR, or CPA. I do math. I enjoy it. And this thread is not professional investment advice.


Edit: oops, I missed your point about fees. The fact is that if you want to invest *right now* or get out *right now* (rather than wait for someone more urgent than you), then you'll pay a fee (is it 0.5%?).
This does not matter in the case of, for example, YARR vs FOO.PPPPT (actually, you'll pay a lower fee in foo because the overall price is lower, but let's ignore that), but it does matter very slightly in the case of YARR vs Bitcoinmax.

Edit2: If I need to make myself more clear, then we can do examples which involve different time values. I also had a graphing tool around here somewhere, and intersections are often more visually clear than algebraic solutions.

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

How dare you nimda to base your post on mathematics?

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.

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

 
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.

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.

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.

Bump for Hashking's deposit and the GIPPT security.