# Present value of expected loss

The present value of the expected loss is conceptually the largest price one would be willing to pay on a bond to a third party (e.g., an insurer) to entirely remove the credit risk of purchasing and holding the bond. Paying this fee transforms a “credit risky” bond to a “riskless bond,” assuming, of course, that the third-party insurer is free of default risk.

My question is who is the third party i.e. insurer. Is the insurer the company issuing the bond or someone else. And who is the person paying to the insurer. Also Why are we paying this amount to the insurer?

Sounds like a CDS? The insurer is one of the parties of the contract.

The third party is the CDS seller.

Its not about CDS. Its from the Fixed Income reading Credit Analysis Models. In other words I need someone to explain me the present value of expected loss.

It is much simpler that you think.

The present value of expected loss is simply the price difference between a risky bond and a riskless bond.

The risk-free bond cash flows are discounted at the risk-free rate of return, and the risky bond cash flows are discounted at a yield higher than the risk-free rate. Have you spotted you confusion already?

If I have two investment options: (1) a risky bond, and (2) a risk-free bond; their prices differ by 5 dollars, and I buy the risky bond, then I would be willing to pay up to 5 dollars to an insurer in order to transfer the risk of the risky bond to the insurer. If the insurer is a riskless institution, then I would have a synthetic riskless bond despite of the fact I actually onw a risky bond and an insurance together.

How pays to who? Let’s make it clearer:

General Motors (GM) issues a corporate note yielding 5% at a price of 900 dollars.

T-bills of the US Treasury are currently yielding 3.5% at a price of 1,000 dollars.

As an investor, If I buy a GM note for 900 dollars, then the maximum price I would be willing to pay to an insurer in order to quit the risky component of GM note would be 100 dollars (1,000 - 900).

100 dollars is the present value of expected loss, also the price difference of the mentioned investment options.

Even though the text is from Credit Analysis, I beleive they are still refering to a CDS (which is the very next section).