Quote from: theymos on May 06, 2012, 10:16:03 AM

Quote from: Meni Rosenfeld on May 06, 2012, 09:25:03 AM

The insurance is a gimmick. Buying X bonds with 25% insurance at Y BTC each is equivalent to buying 0.75X uninsured bonds at (4Y/3 - 32/75) BTC each. This means that, all else being equal, buying X PPT bonds at more than 1.07 BTC each is dominated by investing 0.75X BTC in pirate at the same MPR.

The bonds in general are good for people who can't invest in Pirate at all, or too little to enjoy the higher interest rates; but assuming everyone is rational, the insurance shuffles some numbers around but it ultimately has no effect on who should buy them and what they gain for it.

Ah, interesting. I was just intuitively thinking that a lower-risk asset would be more desirable when I want lower risk, despite the lower return.

In general, no matter how risky an investment is and how risk-averse the investor, as long as it has positive expectation, it will be attractive if scaled down enough. Insurance can serve a purpose when it is impossible to scale down the investment (and in some other cases), but simple uninsured pass-through bonds can be scaled down.

Details: Utility is generally considered to be fairly accurately modeled as the logarithm of the total net worth. If the initial net worth is T and the gain from an investment per BTC invested is a random variable X, then the expected gain from investing a is

E[log(T+aX) - log(T)] ~ aE[X]/T - a^2 V[X]/(2T^2)

This is maximized when a = E[X]T/(V[X]). The approximation requires that E[X] is relatively small, so may not be applicable precisely to the problem discussed.