Bonds: trading rich vs trading cheap

[sridhar]

David:

Can you shed light on these terms? If a bond is trading rich -- it means what?

For example, let's say we are talking about a 2-year bond...If we say that this bond is trading rich, are we making a comment on the comparison between the 2-year spot-rate and the YTM of the bond?

Specifically, are we saying that:

1. The 2-year spot rate is greater than the YTM?

2. That the bond price is higher than what can be inferred from the YTM?

If either is true:

3. Does this present an arbitrage opp? More to the point, why (or when) do bonds trade rich or trade cheap?

--sridhar

 

[David Harper CFA FRM]

Sridhar,

"Trading rich" is different than, but may be related to, these relationships between spot, YTM and price. (this prior forum thread may be helpful). Here is how I look at Tuckman's use of "trade rich/cheap":

It is analogous to, in our Hedge Fund strategy reading, volatility trading where volatility trading is "buying cheap volatility" and "selling expensive volatility." What is the similarity bwtn this and "rich or cheap bonds?" Both refer to observed market values compared to model values (i.e., values implied by a model or no-arbitrage replication idea).

So in Tuckman, a rich bond is a bond that has a higher price (lower spot rate) than the price (and spot rate) we expect when using the "law of one price" (bootstraping the spot rate curve with other traded bonds) or, for that matter, any bond pricing methodology. You ask, "Does this present an arbitrage opp?" and this is interesting because, if like Tuckman, we construct a spot rate curve based on other traded bonds, then a "cheap or rich bond" finding implies, YES, by definition there is an arbitrage opportunity.

Let me give one more example of trading cheap: many banks currently pushback against fair value accounting because it requires them to, in their view, write down these asset values to temporarily and artificially low values. And some advocates of the bail out plan argue the US gov't could be making the best trade ever b/c they can buy cheap paper and sell it later at a much higher price. The banks would say, these assets having virtually no liquidity, are trading very very cheap (e.g., the market price is 0.20, but our models say it's fundamental value should be 0.50). The current market price is arguably different than their fundamental value.

But, now we get to why I think this is somewhat profound and thematic to the FRM. I've suggested that trade rich/cheap is a simple idea: it's when the observed price varies from the model's predicted price. Throughout finance, we use models to price and get risk; e.g., a multifactor model:

E(return) or Risk = (exposure)(factor)+(exposure)(factor) + ... + residual

Then we observe: the market price or measured risk does not match the model; e.g., CAPM does not predict expected returns. Now why not? I can think of at least two reasons:

1. The model is incomplete, it does not include factors or variables which might contribute to the explanation
2. Luck or complexity beyond the model

So, getting back to your question of "why do Tuckman's bonds trade rich or cheap,"

My general answer is: because actual prices are impacted by things not in our model. This is always the case; the models are always caricatures of complex reality. The large omissions tend to be so-called technical omissions, notably supply/demand.

Tuckman's specific answer is: liquidity. For his sample, he says for example that long-term P-STRIPS trade rich b/c they are highly liquid (high liquid = no liquidity discount or high demand = higher price). Note he "blames" the difference on something not in his model.

But i frame it this way, sorry for the length, b/c ultimately there may not be a great answer to the "why do they trade rich or cheap" question and you can see how this doesn't trouble me at all. Note, for example, that we may not want to infer anything from Tuckman's rich/cheap findings because they are several years old. Trading rich or cheap merely reflects that the models are simplifications in the face of enormous complexity. Trading rich/cheap confirms that model risk is real.

David

 

[sridhar]

Thanks for the explanation...What I learned from your response is this:

1. You can regress the bond price against spot rate and YTM -- but because the bond price may also be affected by other variables not modeled in the regression eqn, the market (or observed) price could be different from the predicted price. Correct?

On a related topic: the expression "the bond is trading rich" -- is this identical to saying that the bond sells at a premium to par (when the coupon > YTM.)

--sridhar

 

[David Harper CFA FRM]

sridhar,

1. We don't need regression for this, i sort of think that complicates it...

2. If the coupon > YTM, then absolutely the bond price > par (or the coupon return would be too generous). But that is still within the bond pricing model.

So, for example, if yield is 6% and 30-year bond pay semiannual coupon, the bond price = $1,139 [i.e., =PV(6%/2,30*2,7%*1000/2,1000) = $1,139].

Okay, so far, that is bond pricing "within the model." Now let's say we go look at the traded price of the bond and it is $1,146. That's "trading rich" b/c market price > model price. The vast majority of our practice in the FRM is "within the model" and does not really test against observed market prices to ascertain rich/cheap.

David