After my post last night, I was asked how I make corrections in analyzing premium versus discount bonds.? (Note: if a bond trades at a higher price than the final amount of principal to be paid at maturity, it is called a premium bond.? If lower, it is called a discount bond.)? Happily, there is a story attached to it.? Here it is:

In early 2002, most investment banks placed their cash and CDS traders next to each other. It improved the ability of Wall Street to trade against the rest of us significantly.? By the end of 2002, every major investment bank was doing this.? Many were publishing data on CDS premiums.

I had a habit where I would go out for Chinese food once a week — get out of the office, clear my mind, bring stuff that was important to think about.? One week there was a piece about using CDS spreads to correct for premiums and discounts to par.

The idea was this: if a bond trades at a premium to par, pretend you have bought CDS protection on the amount of the premium.? Deduct the cost of that from the coupons you are paid and re-estimate the yield.? When a bond bought at a premium defaults, guess what? You will never get the premium back — thus using CDS to estimate the insurance cost.? You might not seek the default protection, but it would be valuable to know how much it was worth.

Vice-versa for discount bonds: pretend you have sold CDS protection on the amount of the discount.? Add the the premiums you might receive to the coupons you are paid and re-estimate the yield.? When a bond bought at a discount defaults, guess what? You will fare better than those that bought at par or a premium — thus using CDS to estimate the added yield from that benefit.? You might not sell the default protection, but it would be valuable to know how much it was worth.

Then one day I asked on of my dealers where the CDS was trading on a medium-sized company.? After a pause to talk to the trader he came back, there was no CDS trading on that company.

Okay, what to do? Then it struck me.? Use the credit spread (yield difference over a similar length Treasury Note) as the proxy for the CDS premium.? Bing! problem solved, and more relevant because I didn’t use CDS — it gave me a standard to use in many situations where bonds with different levels of premium or discount were being compared.? I could use this for any bond.

Here are two examples for how it would work.? Here is the analysis for a premium bond:

Year	Cash flows	Swap pmts	Adjusted Cash Flow
0	? (1,100.00)	?????????? (0.65)	?????????????? (1,100.65)
1	?????????? 70.00	?????????? (0.65)	?????????????????????? 69.35
2	?????????? 70.00	?????????? (0.65)	?????????????????????? 69.35
3	?????????? 70.00	?????????? (0.65)	?????????????????????? 69.35
4	?????????? 70.00	?????????? (0.65)	?????????????????????? 69.35
5	???? 1,070.00		???????????????? 1,070.00
Premium/(Discount) to immunize —>		???????? 100.00
	Yield		Spread over Treasuries
Initial	4.71%		0.71%
Treasury rate	4.00%
Comparison	4.65%		0.65%
Initial Price	???? 1,100.00
Coupon Rate	7.00%

And then what it looks like for a discount bond:

Year	Cash flows	Swap pmts	Adj Cash Flow
0	????? (900.00)	???????????? 0.66	?????????????????? (899.34)
1	?????????? 23.00	???????????? 0.66	?????????????????????? 23.66
2	?????????? 23.00	???????????? 0.66	?????????????????????? 23.66
3	?????????? 23.00	???????????? 0.66	?????????????????????? 23.66
4	?????????? 23.00	???????????? 0.66	?????????????????????? 23.66
5	???? 1,023.00		???????????????? 1,023.00
Premium/(Discount) to immunize —>		????? (100.00)
	Yield		Spread over Treasuries
Initial	4.58%		0.58%
Treasury rate	4.00%
Comparison	4.66%		0.66%
Initial Price	??????? 900.00
Coupon Rate	2.30%

So if I had two annual five-year bonds from the same issuer: 10% discount, 2.3% coupon versus 10% premium, 7% coupon, with the equivalent Treasury at a 4% yield, I would be indifferent between the two, even though the yield to maturity on the premium bond is 0.13% higher than that of the discount bond.

If you want to download the simple spreadsheet (be sure to allow for calculations to iterate) you can find it here: Premium-discount adjustment calculator.

That’s all, and for those that try it, I hope you enjoy it.? Wait, one last story:

In late 2002, a broker proposed a relatively complex swap trade.? I suspect he was trying to get an odd bit of paper off of the balance sheet for something more liquid.? As I recall there were premium/discount differences, but also, liquidity, subordination, duration, deal size, and credit rating.? The swap almost looked good, so I decided to “bid him back,” offering the swap at terms more advantageous to my client (and adding in a margin for error — ya wanta rent our balance sheet for illiquidity purposes, ya gotsta pay).

The broker was a little surprised, because the trade looked optically good by most common standards, but as I described to him all of the yield tradeoffs in the swap, he said, “Wow, never hear a trade taken apart like that before. I’ll take it to the trader.? Are you firm at your level? (I.e. will you hold to your terms proposed, or is this just the start of negotiations?)” I assented, and he went to the trader, who agreed to the swap at my terms.? You always have to blink when they do that, because you may have made an error, but my adjustment carved 1% of par off of the swap terms.

I suspect that I got a good trade off, and he needed to get rid of illiquid security that had overstayed its welcome.

In any case, that’s how to do swap trades.? Have fun.? I certainly did.