Investors Playing the Odds

George Rebane

At the risk of boring the bejeezus out of RR’s readership, here’s a bit of quantitative follow-up for all you investors playing the odds on the approaching collapse of socialist Europe.  Well, maybe that’s putting it on a little too strong, but looking at the way sovereign debt is being priced by the bond markets today, you gotta do more than wonder.

My last yawner on this (it got all of 4 reader comments) was ‘Greece and the 100% haircut’ where I showed how to calculate the probability that a borrower (here Greece) would default within a future interval of time, say, in the next year or two years.  The probability would be assessed by the world bond markets.  I gave the formula for computing that probability on your calculator using your own input values.

The piece also had another formula for computing what minimum interest you should demand from a borrower if you thought he’d go belly up with a certain probability within a given time.  Fun stuff if you are an investor playing that great American favorite ‘You Bet Your Ass'.

Anyway, for those who don’t want to mess with their calculator, and still want to keep track of the real shenanigans in Europe (the rest is just BS), I made a plot of default probability as a function of time and the rate difference.  The numerate reader will notice that the probability of default (Q) depends on the interest rate spread (r_B – r_RF) between the current bond rate and the so-called available ‘risk free’ rate – for the faithful, that’s what a 10-year US Treasury pays.  The formula for Q is shown in the figure below, and when you use it remember to convert percents into decimals.


Suppose you hear in the news one morning that some teetering country’s bonds are going for 23% per annum, and US Treasuries are paying 3% - that gives you r_B – r_RF = 23%  - 3% = 20%.  And you want to find out what is the probability that said country will default before two years from now (T = 2).  Then enter the horizontal T-axis at two, go straight up to the 20% curve, and then left to the vertical Q axis to read off about 33%.  The market is saying that there’s a one out of three chance that you’re going to get a haircut if you buy and plan to hold those bonds for two years - that's the real news.  Now is 23% enough of a return for you to take that risk?  If your numbers fall between the values given in the figure, you'll have to remember how to interpolate.  See, you’re having fun already.

Comments

[Bill tozer]

Dr. Rebane, I was never good at math so I took geometry, accounting and stats to avoid the real math subjects like Calculus and Algebra. However, even though I don't understand all the y's and x's, I do know plus, minus, and % key. I know the Eurozone has given up on Greece and has retreated to Italy as its last line of defense. Italy has a GNP growth rate of 0.1% and is selling bonds at 6-7%. What possibly could go wrong with those numbers? Italy has 25% of the entire Eurozone debt and 1/3 of that is due and payable in 2012. Maybe they should move their last line of defense to France, leap frogging over Spain. France announced late last night its 3rd quarter GNP is a respectable 0.4% after a 0% 2nd quarter and the French forecast a flat 4th quarter at best, probably a negative 4th quarter. Problem with France is 50% of all their trade is within the Eurozone, which ain't looking too healthy right now. The French are all up in arms as their bonds rates are inching up and rumors of a credit downgrade got them choking on their sauteed snails. Maybe Germany should just take over the region and install some fine German discipline to the area. Germany could buy Greece and Spain and turn them into tourist attractions or vacation spots for German citizens to escape the harsh winters. Graphs? Graphs are beyond my pay grade.

[Douglas Keachie]

Seems like there are not too many math enthusiasts here. Try this on for size. It's you random Keachie Alice in Wonderland post:

I'll bet if you rewrote the math questions and examples to reflect the realities of growing MJ, math scores would shoot up 100%. "Dispensary owner John wants to sell a blend of three different types of bud, which cost him three different prices. How much of each does he need to weigh out to sell his house blend at $155 an oz? What are the cost advantages to buying and burying a cargo container, and using photovoltaics to illuminate the grow, when considering the almost total immunity from the costs of getting caught? List those costs and figure out the risk factor. it's 800 feet up from the river to an exellent grow site. What is your cost per finished oz of bud for electricty? And so on.

This was inspired by a police blotter story about some kid on the ridge using a joint as a bookmark, in school no less. On the other hand, it would appear that Steve Jobs has managed to clone himself, down in Manhatten Beach, as a 6th grade who develops IPhone apps:

http://www.youtube.com/watch?v=ehDAP1OQ9Zw

[George Rebane]

Exellent DougK - While I think there are enough of us "math enthusiasts" here, you have demonstrated that we may be thinking too much in the box. Perhaps more real life economic scenarios would motivate the now dormant to increase their math skills and enthusiasm for entrepreneurship.