## Sunday, 12 July 2015

### Bonds, sovereign and corporate

An interesting thought experiment to get underneath the seeming disparity between a country's treasury securities and its corporate securities.  I want to find a way to see them all as part of the same model, not as essentially different as they are sometimes characterised in the books.  Bonds are ways to leverage something, future tax receipts or future corporate revenue streams.  So just as credit worthiness of companies worsens when the expected revenues (free cash flow) decreases, so too with nations.  The two ways that expectations on tax receipts may worsen.  Either the effective tax takes get worse (the U.S. takes in 26.9%, the UK 39%, Switzerland 29.4%, Germany 40.6%, Norway 43.6%, Denmark 49% versus Afghanistan 6.4%, China 17%, Equatorial Guinea 1.7%, Egypt 15.8%, Indonesia 12%, Saudi Arabia 5.3%, U.A.E. 1.4%, OECD average 34.8% ), all other things being the same, or else the GDP of the nation deteriorates (smaller population, less productive population, reduced output).  Put another way, just how well developed a capital market can a country expect in the face of very low national tax takes.  Compare in passing how oil rich Saudi Arabia compares with oil rich Norway.  Norway doesn't have an unproductive workforce and a tiny cabal of fabulously wealthy Al Saud princelings, it has an enormous sovereign wealth fund.

Each nation state, especially those in the developed world, with mature capital markets tries to reset the meaning of 'risk free' by considering their country's treasury bonds as risk free.  This only works up to a point.  But it is certainly true that every country with a developed treasury market can and does have market participants whose primary concern is expressed all in that countries national currency.  In other words, FX risk is a bolt-on concern with bonds, at base.  However purchasing power risk is a core risk for all countries everywhere.  As is the risk that interest rates will change (up or down, a primary risk, or up/down more frequently, a kind of volatility risk which crops up with corporate bonds).

There are risks which exist exclusively in the corporate bond world.  But even though the corporate bond world en mass is huge, the market for specific issuers (and more so for issues) is much smaller.

In a nation there are many people and companies.  Nations are naturally much larger than companies.  So it isn't surprising that liquidity risk is more of a factor for corporates, individually, than for treasuries.  Currently (2015) the world's biggest company is ICBC in China, which is worth 1.8 trillion dollars.  The GDP of the United Kingdom is worth about 2.9 trillion dollars.  It is an open question whether in time any company will become so big and so reliable that the liquidity of its bonds will rival the liquidity of sovereigns.  Part of the reason is that national tax takes in developed countries are much more stable than the revenues of any one particular firm.  Perhaps fairer comparisons are with huge stable companies and medium sized developing countries with nascent treasury markets.

The firm itself is essentially a transient entity, since so many of them go out of business due to competition, poor management, obsolescence.  Very few firms last a long time.  Recent research by Richard Foster at Yale suggests that for S&P 500 companies, the average life has dropped from 67 years in the 1920s to 15 years today.  That is a huge change, but it is also a small number, compared to the expected age of a modern developed country, which is in the hundreds of years.

So liquidity may always be much more of a risk for corporate bonds than sovereigns.  A second major difference is that, to some degree, nation states are masters of their own interest rate destiny, meaning that interest rates can be adjusted to suit the health of the nation.  Since this is beyond the control of corporates, they try to buy some refinancing protection in their bond issues through contract clauses, provisions, which give them a kind of refinancing right - through owning a long call on the debt.  If rates drop, the issuer might prefer to cancel its debt and issue new cheaper debt.  they do this by constructing call clauses.  Call clauses, being call options, are additionally sensitive to expected interest rate volatility, something which is essentially out of their control.

They are also sensitive to default risk, credit spread risk, and ratings agency downgrade risk, all of which address the very real possibility that the firm might become impaired and fail to meet their repayment obligations.

So out of all this, I can see that the primary differences in corporates and sovereigns must be driven by the fact that corporates are more frequently failing, more often (always) smaller and therefore more often becoming illiquid.  Their response to the exogenous nature of interest rates is to attach refinancing options to their prospectus.  Of course, making a new bond issue is an expensive business, so the timing of their call will be not entirely driven just by interest rate moves.  For the refinancing to be worth it, the cost of the new issue must be factored in too.

One last point.  Corporate bonds can have embedded puts in them too - on a finite set of dates, the holder can ask for his money back at par.  So this clearly works in the opposite direction than for calls.

Bond calls are primarily a hedge for the issuer so that they can refinance in a favourable new interest rate environment.  If rates, however go up, the call is not exercised, but the price of the call can continue to fall in the market place.  So the call can't really interfere with the read that market participants make on the credit worthiness of the issue (and therefore issuer).

Bond puts, on the other hand, can be exercised by the holder if interest rates rise dramatically, but also if the credit spread widens.  So the price of the bond doesn't purely reflect the credit worthiness of the issuer, unless you adjust for the stickiness of the price around the fact that there's some put date coming up at which point the holder can offload the bond at par.

Likewise I would imagine the call price is sensitive to the expected interest rate volatility but the put would be sensitive to not only this volatility but also to the credit spread volatility.  If so, then market participants could in theory read off this expected credit spread volatility from an analysis of the respective price of the call and put in an issue.

Bond pricing discounts cash-flows using a rate or set of rates which are a function of the prevailing interest rate environment, but it also assumes reinvestment of cash-flows.  When rates, move, you always gain on one side and lose on the other.  This interesting effect means that there might be some combination of cash flows which 'naturally' is less sensitive to interest rate moves.  The process of finding this out for a portfolio of loans (or cash-flows) is called immunisation.

### How to convert between a bank discount yield and a money market yield

The bond books describe the bank discount yield as $(F-P)/F \times 360/D$ and the money market equivalent yield as $(F-P)/PP \times 360/D$.  Let's combine these two equations.  Why?  in doing so, we will arrive at a relationship between the discount yield $y_d$ and the money market equivalent yield $y_m$.  This means you can do a direct yield to yield translation if required.

It turns out that $y_m = \frac{F}{P}y_d$.  Usually $F > P$ so $y_m > y_d$ so the discount yield will always look artificially lower than the money market convention, so you're up scaling the yield in the move from discount to money market.

Also, plugging this newly found relation back into original pair of equations, you see that $y_m = y_d \times \frac{360}{360 - D \times y_d}$ where $D$ is the number of days in the holding period. Again the numerator is greater than the denominator.