# Tag Info

13

Treasury futures are actually really complicated... There are complete books dedicated to this topic (e.g., The Treasury Bond Basis) and really good sell-side research papers ("Understanding Treasury Bond Futures" by Salomon Brothers) that I highly recommend. You're actually very much on the right track, but I'll try to paint a somewhat complete picture. ...

12

If I were to recommend one, it would be: Bruce Tuckman's Fixed Income Securities. This is by far my absolute favorite. It is extremely well written and discusses complex concepts in very easy-to-understand terms. Tuckman is both an academic and a practitioner (Salmon/Credit Suisse/Lehman/Barclays), so the book takes great care in addressing many real-life ...

9

This is a surprisingly complicated question that encompasses many moving parts. Without knowing exactly what your objectives are, it's a bit difficult to offer concrete advice, so I'll provide some general comments below. Mechanically, you earn the total return when you buy and hold a real bond or a bond ETF. By contrast, bond futures are financed ...

7

Based on the your comments, I believe the issue lies with what you consider to be "carry." The reality is that there's no consensus. So let's take mini steps. We'll start with what rates guys consider as "pure carry." In this most classical and fairly strict definition, carry is the deterministic component of expected returns – you know exactly what it is ...

7

Let's make a simplifying assumption that futures perfectly track their CTDs, then $$D_\text{mod, fut} = \frac{1}{f}\frac{df}{dy} = \frac{1}{F_\text{CTD} / \lambda_\text{CTD}} \cdot \frac{dF_\text{CTD} / dy}{\lambda_\text{CTD}} = \frac{1}{F_\text{CTD}}\frac{dF_\text{CTD}}{dy},$$ where $f$ is the futures price, $F_\text{CTD}$ is the CTD's forward price, and ...

6

There are three sources of carry for bond futures - Carry on the underlying (coupon accrual and yield roll-down) for which you just compute the carry on the cheapest-to-deliver as you suggest. Implied financing rate, for which you need the term repo rate for the CTD. Theta on the various short options inherent in a long futures position (switch option, end-...

6

It is preferable to use constant maturity yields (ideally par yields) for running PCA analyses. Using constant maturity par yields has several advantages: By definition, the yields are of constant maturity, so your results won't be distorted by "rolls." When you use either rolling futures yields or on-the-run bond yields, there could be many breaks in the ...

5

@Arrigo's answers are quite good; I'll try to beef up his points a bit more. Yield curves should be constructed using instruments of similar credit risks. If you're building a US Treasury yield curve, then you should use Treasury bills, notes, and bonds (although lots of people actually exclude Treasury bills because of market segmentation concerns). On the ...

5

There's always a balance between model complexity and interpretability. Of course, it'll be great if we can perfectly capture the comovement of all the bonds in the deliverable basket, but that would require the volatilities of all the bond's yields and the correlations amongst all these bonds as well -- it's not easy to come up with reliable assumptions for ...

5

Just adding to @dm63's answer: A good way to identify CTD is by computing each deliverable's implied repo rate minus its actual repo rate. The deliverable with the highest implied-to-actual repo spread is usually taken as the CTD. (Some investors use the bond with the lowest net basis as CTD. Don't – this can occasionally be unreliable!) To identify CTD ...

5

The future will not maintain its duration as it approached maturity. The position will need to be rolled as it approaches maturity. The future will also be very sensitive to one or a series of deliverable bonds to settle the future at maturity. The cheapest to deliver bond will be the driver of the sensitivity to the set of deliverable bonds. As the ...

4

The Fixed-Income bible is definitely this one: Damiano Brigo, Fabio Mercurio. Interest Rate Models - Theory and Practice It is a 1,007-pager covering a large range of topics including: Basic definitions and no-arbitrage pricing Short rate models Market models Volatility smile for fixed income instruments Exotic payoffs Inflation and credit-linked ...

4

This is an interesting exercise and would be compelled to see the results of your data gathering. The principal purpose of treasury note (cash bond) analysis is for yields and the cross-asset class relative valuation where both provide signals. Alternatively, futures provide a technical analysis picture supplementary to yield dynamics. Personally I would ...

4

First, the exact computation of conversion factor is actually quite tricky. The "6% yield" rule is really an approximation (although a very good one). CME provides a spreadsheet that you can use to compute the exact conversion factor for each bond and each contract (http://www.cmegroup.com/trading/interest-rates/us-treasury-futures-conversion-factor-...

4

I think you have a little misunderstanding about treasury futures. I would get this book: http://www.amazon.com/Treasury-Bond-Basis-Depth-Arbitrageurs/dp/0071456104?ie=UTF8&psc=1&redirect=true&ref_=oh_aui_search_detailpage It is the absolute best guide to this product. A few important things to understand: Every treasury future has ...

4

Suppose the CTD DV01 is 10cents. If the CTD yield falls by 1bp then price goes up by 10cents. The price of the future (if the net basis remains at 0) will increase by: $$DV01.Future= (10 \times (1+repo*day.count.frac)) \div conv.factor$$ The repo is a small adjustment. (See Helins comment about using the forward DV01 instead of repo-adjusted DV01)

4

There are two equations that help me understand this: 1) Gross Basis = Spot CTD Price - Conversion Factor * Futures Price If the Gross basis is positive, this means that it is a positive carry. In other words, buying the underlying CTD and delivering it against selling the futures results in a gain 2) Net Basis = Forward CTD Price - Conversion Factor * ...

4

The first two answers point out some interesting things but I think they are not making the most important point clearly: The bond ETF is the equivalent of holding the entire basket of bonds bought with your cash. You pay a management fee to the ETF sponsor for that privilege. The fees are small, usually around 15bp, but you need to be aware of them The ...

3

Checking calculation with Bloomberg it seems that all 3 Korean bond futures contracts are of type (1). The pdf in the link must be out-dated.

3

The market price of the roll (aka calendar spread) is defined as $$(\text{front contract price} - \text{back contract price}) \times 32,$$ where the ${}\times32$ part converts the price into "32nds," the standard quoting convention for Treasury futures calendar spreads. Estimating the fair value of the roll, in principle, is straightforward. We'd compute ...

3

DV01 is defined as $$\text{DV01} = -\frac{dP}{dy},$$ so technically you could run a regression of futures price changes vs (CTD) yield changes. The resulting DV01 is known as empirical DV01. In the context of trading bond futures, shorter-term horizons such as 3m and 6m are typically used. The chart below shows the actual TY/WN hedge ratio and an ...

3

I don't have a formal answer, more of a hypothesis: If the implied repo rate for the cheapest to deliver is < than the 3 month treasury bill. You are better off with the future. Specially adding the tax burden on ordinary income from holding the Bond ETF vs the hybrid rate of futures. Right now the 3m rate is 2.45% and the implied repo rate for the ...

3

We are going to this operation using borrowed money (via repo). How much capital do you need to do this? How many dollars for how many years? At first thought you need to raise $(P+A_b$) dollars (the dirty price of the bonds) for $d_1/360$ years, but actually you need less because you will receive $I_c$ in cash when there are $d_2$ days left to go and can ...

2

I'll try to give you an answer. I think the term structure is built from those financial products because they are the most liquid for those maturities: theoretically, a liquid instrument has a price coming from a large consensus which you can think of the market. This is an "academical" reason, probably there are other reasons also (I'm still learning). ...

2

Not sure this is a quantitative finance question, since it's more or less a judgment call. There is no futures contract that you can use to make this estimation; instead, it requires an understanding of the Fed, what's going on in the economy, what's priced in by the market, what's the positioning profile of different players, etc. Assuming the Fed hiked, ...

2

Treasury bonds go "special" when many participants want to short them (playing for s higher yield). The person who shorts the bond needs to deliver it to the counterparty, so must borrow that exact bond (versus investing cash) in the repo market. If lots of people want to do that , the repo rate goes down.

2

In repo/securities lending one person lends money (cash) and the other person lends securities. It is easier to understand if you think of the cash lender, who requires compensation for supplying the liquid asset (cash). If the cash lender supplies cash and receives ordinary ("general") collateral he receives one interest rate (usually clse to the FF rate), ...

2

If you think about carry as a cushion against a change in the forward yield then carry (in basis points) for the underlying bond equals with (coupon income of the bond - repo rate) / forward DV01 of the bond. (Carry could be also calculated as the forward yield - spot yield) That is how much the forward yield can rise before you start loosing money on the ...

2

To answer the first question, many people like to use scenario analysis. Check what is the CTD if rates move up or down 50bp for example. That will give you a sense of the likelihood. Sometimes the CTD switches on a curve move, so you should also check flatteners and steepeners. For the second question, I think you should calculate the net basis of ...

2

The change in the gross basis would simply be due to carry. You know the spot price of the bond. If you lock in term repo to the forward date, you will know your forward price. The difference between forward and spot price is your carry. Convert the carry to a daily value and this reflects the daily drop in gross basis. Put differently, if we assume last ...

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