VaR for the issuer of debt instruments

Graeme · Post by **Graeme** » Wed Oct 24, 2007 9:59 am

I'm calculating VaR, ETL, attribution etc. etc. etc. for a treasury which has quite a lot of issued debt.

Their intention is to see where the greatest risk lies - more or less so that going forward they can say 'ok, we want to issue/redeem such and such debt because that type of debt is the one whose value is the least/most variable'.

I have only ever done this type of thing for the long side of debt instruments. Do you think that because we are the issuers of the debt that we should modify our MtM calculations (I refer here to experimental MtM in the historical VaR calculation). I'm thinking mainly of

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[*]what credit spread, if any, do I apply to my issued instruments. I intend to survive....
[*]what to do with the convertible bonds I have issued? For the long party these are quite sensitive to changes in share price. But from my perspective is this just a bond, or just the bond component in a bond + equity split (ala Tsiveriotis and Fernandes. or Ayache, Forsyth and Vetzal).
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I'd like to think that because of some sort of symmetry I'm overthinking this, and should just apply the pricing formula unmolested, but would appreciate input to help clarify my thinking.

aaron · Post by **aaron** » Fri Oct 26, 2007 4:48 pm

If you don't spell this out clearly at the beginning, you'll end up with meaningless results that provoke pointless arguments.

For example, suppose you issue long-term unsecured debt. That has a lot of price volatility, due to the duration and credit spread variability. Short-term secured debt has little price volatility. But the secured short-term debt poses much more risk to the firm.

Or, suppose you are choosing between a zero-coupon convertible and a full-coupon non-convertible. The zero will have far more price volatility due to its longer duration and convertible feature. But it is less likely to bankrupt the firm. The zero probably reduces shareholder expected return, but also shareholder volatility (on the upside by diluting some gains, on the downside by preventing some bankruptcies).

In the extreme, suppose you were to sell a lot of credit protection on yourself. These securities would have a lot of volatility, but could never cost you anything since if you have to pay off on them, you wouldn't be able to pay.

My advice is to measure VaR against a benchmark. What you should be concerned about is the value of the securities you issue relative to alternatives, say an 80%/20% mix of long-term straight bonds and common equity. Treasury spends most of its efforts trying to fund cheaper than the straightforward method, you want to measure and control the risk that their choices end up being more expensive. You don't care about the market value of the securities, if you did you'd find yourself rooting against the company's common stock. You care about the cost of capital.

Graeme · Post by **Graeme** » Sun Oct 28, 2007 11:17 am

Thanks very much indeed for this.

It seems that the risk measure is still going to be dominated by the convertible bonds issued. For example, with the CBs comprising about 50% of the value of the issued securities, their relative VaR or relative expected shortfall can easily attribute much more than 100% of the total statistic (the full portfolio viz. short issued securities, long a benchmark bond and long benchmark equity) and attribute something like 95% of the issued only subportfolio.

How does this sit with CBs being a reputed source of cheap funding? Can one argue that by funding cheaper one is implicitly taking on more risk?

Johnny · Post by **Johnny** » Sun Oct 28, 2007 4:59 pm

CBs aren't always a source of cheap funding otherwise companies would rationally only ever fund through CBs and not through other sources. CBs can be a good source of funding when there is uncertainty ahead (e.g. a big acquisition or new project that can materially affect the volatility of the firm value or in a restructuring close to bankruptcy). However, the whole "equity at a premium or cheap debt if not converted" line used by CB originators is just simplistic (uh, but effective) nonsense.

zviacha · Post by **zviacha** » Wed Oct 31, 2007 3:12 pm

I don't get what is the objective of calculating VaR (marking to market) [b]for the issuer[/b]?

Graeme · Post by **Graeme** » Wed Oct 31, 2007 7:30 pm

As has been indicated by myself and (most eloquently) by Aaron, you want to know which instruments you have issued might prove to be a more expensive source of funding than you hoped for.

Wannabe · Post by **Wannabe** » Sat Nov 17, 2007 4:09 am

Hi Graeme and Aaron:

Could you elaborate on the link in the price volatility of the issued debt instruments and cost to the company? Is it a accounting issue related to the market price of the outstanding debt? It is unlikely that a company whose debt is trading at a discount will have the cash to buy the discounted debt in the open market.

Thanks.

Graeme · Post by **Graeme** » Wed Nov 21, 2007 5:05 pm

Agreed, a revolutionary realignment of your debt book is impossible, but these figures might give evolutionary information: i. don't issue any more CBs ii. choose floating instead of fixed iii. try to swap fixed in floating iv. the next issue is going to be more of that prime linked stuff etc etc etc