Anatomy of a convert - the zen homunculus perspective

Before we can understand a convertible bond, we need to understand straight bonds, and for that we need to be confident about fairly comparing cash flows which we make or receive at different points in time.  Many contracts contain such payments, as I alluded to in an earlier posting. Quite often what you do is to find the value now of the receipt or payment at a later date of any number of cash flows.  This process is often referred to as finding the present value of a future payment.  But it doesn't have to be right now - you could just as well decide to use any arbitrary point in time and fine the historical value, or even the future value of a cash flow.  Another term used to describe this process is as discounting the future cash flow.  This is usually because rates used are usually positive, hence the present value is less than the cash flow value at the future date.  But again, this terminology isn't strictly universally correct.  If rates are negative, then the now value will be more than the then value, so describing it as discounting would be a confusing usage.

What we're really doing when we line up cash flows at different times is taking account of the opportunity cost of cash over that time window, from the now to the then.  The referenced Wikipedia article suggests (at least, it did while I was writing this post) that the concept was invented in 1914, which seems unlikely and no double has its origins in the Western world at least as far back as Aquinas but my guess is the idea originated in India or some early Islamic centre of learning.  Anyway, the opportunity cost of a good factors in what you could have done with the money if you hadn't purchased that good.  It is a cost which is often overlooked in everyday thinking, but is essential to economic and financial thinking.

Of course, what I could do with the money is not going to be the same as what you could do with the money. Come to think of it, what I could do with the money now is probably not even the same as what I could do with the money 5 years ago, or perhaps in 5 years' time.

This isn't a point that's often mentioned in discussions on the opportunity cost, so I'll elaborate.  Imagine three fantasy lenders: the Midas lender, one who has a very high opportunity cost, since all his previous projects result in extraordinarily high profits;  the loser lender, all of whose previous projects lose everything; and  the  homunculus with zero appetite for risk.who in their prior utilisation of capital looks for the safest place to put that capital.

In finance, we almost everywhere like to pretend we're the homunculus, even if we think we're the Midas and even if we're actually the loser.  Usually for any given monetary region, the government bonds of that region are considered safest.  (As I write this post, Greece's sovereign debt is close to default, and it must always be borne in mind that the risk free rate may itself contain risks).  A better term for the so-called risk free rate of return might be the least risky investment, and it is usually the respective government bonds for each of the major currencies.  Even this is questionable given recent economic history - I guess your first thought for the least risky investment might be - money in a bank?  cash?  The bank is considered safe only insofar as the government backed deposit insurance partially protects you from the risk of bankruptcy.  Likewise cash is backed by the full faith and credit of the government which controls that currency jurisdiction - since 1971 anyway.  Still, let's pretend Greece wasn't in the Euro to begin with and if faced a sovereign debt crisis.  I can well imagine the credit spread widening so much that  the capital loss on the Greek government's debt that it performed worse than any drachma weakness.  If that is even a logical possibility, then doesn't it become a contingent question which is the true 'risk free rate'? 

In theory we ought to use the most appropriate opportunity cost factor for us personally, when estimating the worth to us of some cash flow.  But we don't tend to do that - we tend to share inter subjectively the zero risked homunculus- we ask ourselves 'what would he do with the money instead'.  Perhaps the only reason is the difficulty in coming to a decent judgement about our own true opportunity cost.   And we always decide that sovereign debt is the risk-avoiding homunculus's investment of choice.

Interestingly there is one place in finance I know of where this subjectivity wins out over the homunculus with  his head in the sand: inside companies.

Certain corporate projects will get green lighted if they are perceived by the management as likely to exceed the hurdle of the opportunity cost (to the company) of having the money placed in some other projects. (or investments)  You're in effect comparing your current project to a weighted average of all the other projects you have started up.  This is usually referred to as the weighted average cost of capital.  Here the weighted average cost of capital is risky and hence higher than the risk-free rate.  But the various sources of funding have heterogeneous expected returns, which is the main point I'm drawing your attention to right now.

There's another sense in which the so-called risk free rate is not risk free - the government debt in question is always of the non-inflation-adjusted variety.  I.e. the debt which feeds into each and every yield curve has inflation risk baked right in there.  In recent times, governments have developed inflation-protected versions of debt instruments (partly as a way of discovering the market's view on inflation), so why not use these securities?

Given we don't, then this risk free rate can be negative in real terms.  It can also be, believe it or not, negative in nominal terms too.  It happened with U.S. dollars for the first time in October 2010.  So if the risk free rate doesn't even have to be positive, why not go the whole hog and claim that cash under a mattress is the most risk free (providing you have a safe house in a nice neighbourhood).

Anyway, practical lesson number 1: if you ever want to build a yield curve engine, make sure negative rates aren't going to throw it a curve-ball.

Finally, the scope of 'risk feee' seems to be related to a homunculus who isn't properly globalised.  It displays a localist bias.  Why only focus on the set of USD denominated, or GBP denominated, or JPY denominated assets when thinking of risk free.  Shouldn't you be thinking of an FX-adjusted GDP-weighted basket of currencies?  Shouldn't the homunculus be a Euro-homunculus?

To really get to the botton of the yield curve, we must start at the beginning, and that means learning to deal with interest rates.  That'll be the subject of my next post.