risk neutral mean loss rate

[ajsa]

Hi David,

it seems to me for risk neutral mean loss rate the market value of a bond only reflects default risk. it does not reflect time value of the money, current interest rate or any other risks. for example, how to determine the risk neutral mean loss rate for a premium bond?

according to the example, it looks like its formula is just [1-(market value)/(face value)]?

I am very confused...

thanks.

 

[David Harper CFA FRM]

Hi ajsa,

The example is straight from Canabarro on counterparty risk and, yes, his example is very simplistic; he notes that time value of money is not included; and, to your point, he suggests that spreads will be "infected" (my term) by other factors...so I don't follow you because I think you have it exactly right...i.e.,
in his simple example, the price of $80 on a par of $100 produces a simplified 20% risk-neutral mean loss rate, even though the expected loss (due only to default) is $15 because investors are demanding the additional 5% as risk premia compensation.

put another way, if there is a choice between
$85 riskfree and
$85 with risk

they will prefer the riskless $85 ... (or put another way, if you were truly risk-neutral, you would be indifferent, but any risk version tilts you in favor of the riskfree bond) ... so that the risky bond must be bid down to $80 to make it equally attractive (i.e, to compensate them for the risk; the distribution essentially)

...but otherwise, your point is well taken, I infer his subsequent point to be, in so many words, that it's hard to parse this rate from the other factors that influence spread. (interesting, he suggest that credit default swaps may be a good source of this, due to their isolation on credit risk ... but it's now very clear that the CDS basis is similarily impacted by several fundamental and technical factors)

David

 

[David Harper CFA FRM]

....sorry to append...it just occurs to me there may be an analogy here (just thinking out loud) between:

1. the market risk premia in Hull's forward, and
2. the credit risk premia in Canabarro's example

what i mean is:

1. thy of normal backwardation says forward < expected future spot--i.e., F0 < E(St) because, basically, if F0 = E(st), there is no incentive to assume the risk of a long forward with zero payoff. In order to incent long foward to assume risk, expected payoff must be positive; i.e., F0 < E(St)

2. similarly, here, i think Canabarro is saying, why would you pay $85 when that reflects an expected gain of 0; i.e., why assume risk with no expected gain (pay $85 - receive $100 * 85% = 0). You will only assume risk with some positive exp return: pay < 85 - receive $85 = > 0 expected gain as compensation for assuming risk

David