# Tag Info

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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 ...

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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. ...

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Of course making money is always the key issue. That (not completely facetious) comment aside: On the practical side, in many firms IT is struggling with being clear, transparent, and intuitive in their handling of multiple curves and their associated risks. Stumbling over your own systems is an annoying way to lose money. These risks can be surprisingly ...

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I am not an investment banker, but usually the procedure is something like this: (0) The IB knows the yield of existing bonds with the same maturity and credit rating, so it is not too difficult for them to estimate the yield of the new bonds. They usually announce this as a spread above a benchmark (Ex: "We estimate the new bonds will yield 25 to 50 bps ...

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Day-count conventions. You can't live with them, you can't live without them. The reason the prices differ is that the pricing engine can't calculate correctly the time over which the first coupon is discounted, and thus it gets slightly different discount factors to apply to the coupon amounts. Please sit down, it'll take some explaining. Ultimately, both ...

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Pull-to-par says that the bond's price will gradually converge toward par (100% of face value) when yield is unchanged. This process is also known as accretion for a bond trading at a discount (since its price gradually goes higher toward par) and amortization for a bond trading at a premium (since its price gradually declines toward par). Pull-to-par says ...

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Pull-to-par just says that a bond's (clean) price will converge towards its face value as the bonds approaches maturity. There is nothing really interesting about pull-to-par - a bond's (clean) price has to converge to its face value, because a bond with just a few days to maturity is essentially a short-term cash deposit. Look at it this way - the price of ...

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Here are some general directions: Alternative Risk Premia The ARP, or "smart beta," space has gained a lot of tractions over the past few years. These are rule-based strategies that provide systematic exposures to risk factors that have historically generated positive excess returns. Some of the best-known factors are, of course, trend, value, carry, etc. ...

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It is helpful to think of the yield $r_b$ of a risky bond (say a corporate) in your country as the yield of the risk-free government bond $r_f$ plus a "spread" $r_s$ ($r_b = r_f + r_s$). This extra spread is the extra yield that the market needs to be paid to purchase the corporate bond instead of buying an equivalent amount of risk-less bonds. In other ...

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It's a topic of intense interest to me, so it'll likely be a bit more than you asked for =) Decomposing the yield curve Simply put, a default-free interest rate can be decomposed as follows: $$\text{default-risk bond yield} = \text{rate expectations} + \text{bond risk premium} + \text{convexity bias}$$ I provided some comments in this post and will ...

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Method 1: PCA directionality hedged Here is one way to do it using PCA and hedging the directionality implied by the first principal component. Since you have quoted 3 effective instruments; 2s5s10s, 2s10s and 5Y you will observe that you can derive these instruments from the underlying 2Y, 5Y, and 10Y. That is; $$\begin{bmatrix} 5Y \\\ 2s10s \\\ 2s5s10s ... 10 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 ... 9 The Hull-White model can represents the risk free rate as a stochastic process, that is, in terms of expected return and volatility. The zero curve only gives you expected returns and you have to find a source to calibrate volatility, as FQuant told you. Common volatility sources used for this calibration are historical series of the zero curve or ... 9 I'm familiar with the library, but not with the way it is exported to R. Anyway: gearings are optional multipliers of the LIBOR fixing (some bonds might pay, for instance, 0.8 times the LIBOR) and spreads are the added spreads. In your case, the gearing is 1 and the spread is 0.0140 (that is, 140 bps; rates and spread must be expressed in decimal form). ... 9 Treasury bond futures are surprisingly complicated - this is an attempt at a short explanation, it will obviously gloss over some details, but hopefully gives you a flavour of how they are priced. The most important fact is that the underlying is not a single bond, but a basket of bonds. For example, the US Treasury Bond Futures contract spec says that you ... 9 Don't get discouraged – this is how we all felt when we got started. This is particularly true in fixed income, where a lot of jargons are thrown around. Ask your colleagues. You can potentially figure everything out by reading books, but it's much better to just consult your colleagues – it's one thing to have an academic understanding of how things work, ... 9 It's complicated. Assuming there is no CTD switches, then yes, the theoretical modified duration should be unchanged and the DV01 will be lower. For simplicity, imagine that there is only one bond eligible for delivery into the contract. We'll also ignore all the other complications (e.g., variation margins), then the theoretical futures price is simply the ... 8 Do you have any strict definition of YTM of FRN? I googled and asked many times but I failed to find good and clear explanation. The problem with FRNs is that we do not know what are the future coupons except for only one. If we solved this problem, we could treat FRN just like standard bond. In the text below I will first consider spread to be zero. In ... 8 I assume that you are working in a single curve theory. While this theory used to do well, it is not adapted to today's market and — as Brian B pointed it out — you cannot get a useful information from swap rates alone. The swap rate S(t) at t for a given tenor T and period P is the fixed rate such that a swap starting at t and ending at t+T ... 8 The Strata project is the new pure Java market risk quant library from OpenGamma. For more information, see the documentation and GitHub. It is Apache v2 licensed. Strata takes the experience of the OG-Platform codebase referenced in the question and turns it into a library - no need for databases, servers or similar. Ease of use is a big focus and there ... 8 This is called on the run/off the run arbitrage, a type of convergence trade. The basic idea is that as the liquidity premium disappears for the on-the-run issue, the price will fall and converge to the price of previous issues. Here are a couple papers - http://people.stern.nyu.edu/lpederse/courses/LAP/papers/SearchBargaining/VayanosWeill.pdf http://... 8 There are many reasons why a yield curve can be inverted. A default-free yield curve reflects a combination of - market expectation of future short-term interest rates; bond risk premium: usually positive, longer duration bonds are more volatile and riskier, so investors demand a compensation in the form of higher yields; convexity. Let's consider a case ... 8 It looks like it's referring to Wu and Xia (2016) shadow rates. Some more media coverage is here. The core idea of a shadow rate goes back at least to Fischer Black. Black (1995) Fischer Black's idea was that the nominal short rate r_t is an option. One can either: Invest and earn the real shadow rate s_t, which is based on the investment opportunity ... 8 No. The dirty price is the market's estimate of fair value for the bond. The clean price is just a quoting convention (so that the price doesn't jump when you pass over a coupon date). The market doesn't try to estimate the clean price and then get the all-in (dirty) price wrong. The market estimates the all-in price, and then applies the accrued interest ... 8 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 The one-factor Hull-White model is given by$$dr(t) = (\theta(t) - \alpha\; r(t))\,dt + \sigma(t)\, dW(t)\,\!.$$The zero curves are only sufficient for the calibration of the parameter \theta(t), which is given in terms of them by$$\theta\mathrm{(t)=}\frac{\partial f(0,t)}{\partial T}+\alpha f(0,t)+\frac{\sigma^2}{2\alpha}(1-e^{-2\alpha t}),$$... 7 You can use DV01 * (change in yields) to calculate the approximated P&L, but you really shouldn't do it. The exact PnL calculation depends on the instruments you're trading. If it's exchange-traded (e.g., futures, futures options), then its price is readily available from the exchange, and the daily change in price should be used for marking to market. ... 7 Short answer It's complicated. A satisfactory solution is not known. Long answer A satisfactory solution is not known and research is ongoing. That doesn't mean there is nothing interesting to say about it. The phrasing in the question is not entirely correct: First off all, there's is no risk free arbitrage between bonds and stocks. Both are risky and ... 7 There's a lot of intracacies involved and you've got several options. Let's go through an example, using the current front-month 5-year contract FVU6 (FV expiring in September 2016). CTD Yield: The cheapest-to-deliver ("CTD") into FVU6 is the 1.625s of 11/30/2020 and its yield to maturity as of last close is 1.075%. You can simply use this as a proxy as the ... 7 To calculate rolldown that accounts for the coupon effect requires a fitted curve. Assuming such a curve is available, then the following procedure is usually followed: First, calculate the z-spread of the bond in question relative to the fitted curve:$$ P = \sum_{i=1}^n c_i \cdot d(t_i) \cdot e^{-s t_i},  where $P$ is the current quoted dirty price (...

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