US T Bills - an unremittingly fair price

US Tbills are key participants in the manufacture of the risk free yield curve.  That is to say, whatever the yield to maturity of a T-bill priced at $P$ just now, at the tenor $t$, that yield to maturity is also the discount rate to value the future cash flow which constitutes the payment of face value $F$ at time horizon $t$.

So when we come to model the present value of the (singular) cash flow of $F$ at $t$, we realise that the present value of this is simply the current market price of the instrument, $P$.

There may be quibbles.  The yield curve in practice isn't usually a treasury yield curve, but a money markets, futures, swap based yield curve.  Or perhaps one which is blended or fitted.

Certificates of Deposit : credit spread?

In a previous post, I mentioned that one possible explanation for why two identically termed CDs available from two companies might have different yields.  I'm not so sure any more.  In the US anyway, there is the FDIC system, which covers short dated CDs up to a quarter of a million dollars per person per bank.  It ought in principle to be possible for one person to pay an intermediary to spread around any arbitrary sum across N banks such that no one bank gets more than a quarter of a million dollars of his money.  In other words, it ought to be possible to put much larger sums in CDs, if you so desire, and receive the US government's full backing.  Maybe the net effect of this possibility is to drop off the credit risk associated with you having lent an institution some of your cash.  If your CD was with Lehman Brothers in 2009 versus Wells Fargo, then if it wasn't for deposit insurance then you'd expect to get a higher yield for leaving your cash with Lehman.  This yield differential $y_{L}$ versus $y_{WF}$ is a kind of credit spread.  The credit spread is the little bit extra you expect to get for leaving your cash with an institution which could go bust.  But perhaps FDIC pushes both of these rates down towards a common $y$, since the deposit insurance takes virtually all of the (domestic currency valued) risk out of the saving.  This therefore must be a constraint from above on CDs.  You can offer no more than $y_h$ since any higher is effectively ignoring the FDIC factor.  

And the constraint from below must be bounded by inflation: since if the CD supplier offers a nominal rate which is lower than expected inflation $y_{l}$, then capital is being constantly eroded.  It does not make sense for an economic agent to lend his money and get back less in real terms than he lent.  This window $y_l \leq y \leq y_h$ is probably quite narrow, meaning the product is more or less going to keep your cash safe from inflation, probably.    The 'probably' comes from many factors, not least of which is the fact that no-one can predict future inflation, even over a short time period, with any certainty, so there'll be a prediction error in the offered near-inflation rate.

CD providers like to throw in extra terms and conditions on the purchase of a CD, all if which can affect the valuation.  This makes it harder for customers to do side-by-side comparisons.  This is a familiar trick.  The CD I have been describing in the last couple of postings has been as simplistic a schematic CD as you could imagine.

All of this is a bit too vague.  I'd like to continue thinking about the rate implied in CDs, but before diving into some detail on CD rates, I'd like to pull back and ask a general question: what goes into a rate in the first place?  What factors make up a rate?  What risk are you taking in lending your cash to someone else for a while?

Certificates of Deposit : market price = fair value

If the simple CD is tradeable, when what is its price?  Well, that's two questions:  what is its fair price at any moment during its life, and second, what is its market price.  Well, remember, it is a two step process - first you get the future value of that single cash flow you'll get on expiry (par plus whatever interest you earned) for some given principal amount $P$.  There's nothing really in that which could vary over time.  The value at expiry is the same regardless of how close to expiry you are.

What might change is the yield you'd use to discount this singular known future value.  Why? Well, imagine you bought a 1 year CD for principal $P$ and a nominal yield $y$, which was the going rate when you entered the market.  The market being that set of institutions from that country who are also offering 1 year CDs on principals the size of $P$.  Now where does this number come from?  Well, as you'd imagine, it is sensitive to short term interest rates.  So Imagine you just bought this new CD and got a rate of $y$ when that very moment the domestic central bank raised the short term policy rate by a whole percentage point.  Well, the CD market would adjust and offer the marginal next customer a higher rate of return $y^\prime$.  So when you come to present value the same fixed future value $P(1+y)$ you get $P \times \frac{1+y}{1+y^\prime}$ since the fraction is less than 1, which results in some amount less than $P$.  That is, the fair value of your security, this instrument which was going to give you $P(1+y)$ in a year, is now worth less than $P$.  Another way of saying this is that the value of the CD is sensitive to fluctuations in interest rates in the economy.  It has interest rate risk.  That new value, call it $P^\prime$, is the new fair value of the CD.

The only moving part here is $y^\prime$, the single prevailing rate you discount your future payment.  This, in a sense, is also the market price.  Now this is unlike more complex securities in a number of ways.  Often other securities have more moving parts, but you'll always just have a single market price.  But for now, enjoy the simplicity of the relationship.  Regardless of how the market actually quotes this rate, whether they tell you it as the current value $P^\prime$, whether it is quoted as $y^\prime$ itself, whether it is $100-y^\prime$ or any other transformation, the bottom line is, that market quote can be transformed into $y^\prime$.  Now imagine I had two CDs, each with different nominal yields $y_1$ and $y_2$, on identical principals $P$ and expiry 1 (year).   Clearly they'll be worth different amounts in any given prevailing market environment $y^\prime$ and time to expiry $t$.

Just for now, let's pretend the market quotes the market yield as the current cash value of an invested principal $P=1$.  That is, pretend the market price of a CD is expressed as $P^\prime = \frac{1+y}{1+y^\prime}$.  This market price is then synonymous with the fair value of the instrument, which is also $P^\prime$.  That identity relationship doesn't often happen with other financial instruments.  With other instruments, there's a gap between the market price and the fair value.

In the next post I'd like to introduce you to the second of the great risks in finance, already present in this simplified product.