# Tag Info

15

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

In the beginning, we had a plot of yields of individual bonds against time to maturity, the crudest form of "yield curve." Years later, people began hand-drawing a smoothed line through these yields as closely as possible. Because bonds have different coupon rates, making their yields hard to compare, people tend to draw the curve through bonds trading ...

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

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 ...

6

The chart you posted does not give a correct visual representaion of convexity . Convexity is not $\frac{\partial^2 P}{\partial y^2}$ but $\frac{1}{P}\frac{\partial^2 P}{\partial y^2}$. So you have to normalize for P. The 4 curves you plot have very different P. When the curves are redrawn normalized so they go through the same point $(y_0,P_0)$ you will ...

6

There is a liquidity premium between on-the-run treasury issues and off-the-run issues with similar characteristics. This is why when building a yield curve, typically on-the-run issues are used to compute this curve as a representation of the risk-free rate. Depends on what you're using the curve for. In practice, it is far more prevalent to use only OFF-...

5

A Consol Bond is a bond that pays an annual coupon of c every year. Therefore its price is $P=\frac{c}{1+r}+\frac{c}{(1+r)^2}+\cdots$. Factoring out the c and using the known formula for a geometric series, namely $u+u^2+u^3+\cdots = \frac{u}{1-u}$ we get $P=c[\frac{1}{1+r}/(1-\frac{1}{1+r})]=\frac{c}{r}$ Clearly this is a discrete compounding, not ...

5

It is useful in risk reports because it tells a trader the interest rate risk of each bond in his portfolio. A trader then only needs to multiply the duration by the expected yield change to calculate the price change. Scenario analysis is then easier. Hedging a bond portfolio with duration measures is common. But as these must rely on the assumption that ...

5

Let's go back to basics. In terms of its yield $y$, the price of a bond maturing in $n$ years is $$P_n(y) = \sum_{i=1}^n\frac{c}{(1+y)^i} + \frac{100}{(1+y)^n}$$ One year later, the yield is now $y^*$ and the bond now matures in $(n-1)$ years, and its price is $$P_{n-1}(y^*) = \sum_{i=1}^{n-1}\frac{c}{(1+y^*)^i} + \frac{100}{(1+y^*)^{n-1}}$$ We can ...

5

Tough to answer specifically because I don't know what bonds you're looking at, but my guess is it has less to do with the spread-building blocks and more to do with the base curve. G spread is based off the interpolated government bond curve, and Z spread is off the Swap curve, if you mouse over on YAS it will show you the base curve. Since right now the ...

5

Your formula is the definition of the running yield, which is a crude approximation. Let $P$ be the price of a zero-coupon bond paying 100 at maturity and $y$ its yield. Then it holds that $$P = 100 \times \exp(- y T),$$ where $T$ is the maturity. If we set $y = i+r$, where $i$ is the inflation and $r$ is the real interest rate (similar to the Fisher ...

5

The shadow rate is what the interest rate would be if money did not behave like an option. The concept was created by Fischer Black and his insight was that money acts like an option. Someone with a dollar can either (1) buy something today or (2) not spend the dollar and have a dollar tomorrow. When the economy is good, an investor can loan money and, in ...

5

Your question is more or less answered in How to calculate bond yield in QuantLib - Python. Once you've built the fixed-rate bond object (as in the post you linked) you can call fixedRateBond.bondYield(targetPrice, day_count, compounding, frequency) Comparing the above to the Excel interface in your link, targetPrice is pr, frequency is the frequency as ...

5

Please refer to the picture below for what each trade is betting on. As an example, in a bull flattening trade, you're betting that rates will decline AND the yield curve will flatten. The flattening aspect can be easily expressed by buying a long-term bond, while simultaneously shorting a shorter-term bond. If you do NOT structure the two legs to be DV01 ...

5

I would start by saying that yes, this is an acceptable precision. However, the reason you are not getting the same result is because, by default, QuantLib has accuracy=1.0e-8 and maxEvaluations=100. You can set these parameters like this: bond.bondYield(bond_price, dayCount, ql.Simple, ql.Quarterly, ql.Date(), 1.0e-16, 100) This will get you much closer....

5

It's actually written on the treasury page Negative Yields and Nominal Constant Maturity Treasury Series Rates (CMTs): At times, financial market conditions, in conjunction with extraordinary low levels of interest rates, may result in negative yields for some Treasury securities trading in the secondary market. Negative yields for Treasury ...

5

c is the coupon of the bond, so it is paid semiannually. You can see this from the LHS of the first equation, which is the sum of present values of the coupons and principal. The 6.87 and the 6.75 are related by $$(1+6.87/200)^2 = e^{0.0675}$$

4

I think what you wrote is correct. I'll rephrase everything according to my way to give you another point of view. The price of a coupon bond at time $t = 0$ is the sum of the discounted cashflows given by the coupons and the face value: $$P_0 = F \cdot D(0, T_n) + \sum_{i=1}^{n} 11.04\% \cdot 0.5 \cdot F \cdot D(0, T_i)$$ where $F$ is the face value, $... 4 First, the exact computation of conversion factor is actually quite tricky. The "6% yield" rule is really an approximation (although a very good one). CME provides a spreadsheet that you can use to compute the exact conversion factor for each bond and each contract (http://www.cmegroup.com/trading/interest-rates/us-treasury-futures-conversion-factor-... 4 While you may be able to arrive at some answer to this question empirically with a bit of research, theoretically I don't know if there is a formulaic/mathematical way to extract expectations of future rates from floaters. The reason is that, theoretically, a floating rate note's price is determined only from the interest rate corresponding to the next ... 4 Let's start with a single bond. The total return from time$t_0$to time$t_1$can be easily calculated as follows: $$R = \frac{\text{ending price} + \text{ending accrued interest} + \text{coupon payments between t_0 and t_1}}{\text{starting price} + \text{starting accrued interest}} - 1.$$ (This is no different from how you'd calculate the total ... 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 @AlexC has already provided the correct answer, but I thought I'd provide a bit more details. The breakeven inflation (still the mostly widely used practitioner terminology) is defined as follows: $$\text{breakeven inflation} = \text{nominal yield} - \text{TIPS yield}.$$ It is called the breakeven inflation ("BEI") because if ex-post realized inflation is ... 4 The Federal Funds rate is an overnight rate. It may move differently from longer term rates such as the yield on 10yr notes. Possible reasons why 10yr yields might move down when the Fed raises the Fed funds rate : (A) the market thinks that the economy will go into recession so the Fed will have to lower rates down the road. (B) the Fed had been ... 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 I do not know Python but this is what I would do in Excel (I am assuming you are familiar with Excel and can then translate the steps into Python: Pick a time series of Bond Yields which has$n$yields. Generate a series of Bond Yield changes from that time series resulting in$n-1$yield changes in a column. Assign each of these yield changes an integer ... 4 When the market enters a risk-off period the investors proceed to a rotation between more risk assets (commodities, equities etc...) to the less risky ones. At this point there is just a lot of supply/demand imbalance on the bonds which drives the yield of the 10y down When investors proceed to "flight to quality" they want to protect themselves against ... 4 Let's assume we have yearly cash flows, and let's focus on just two years - year 1 and year 2. Let$R_1$and$R_2$represent the zero rates of year 1 and year 2. So if you want to borrow for one year, you pay$R_1$percent, and if you want to borrow for 2 years, you pay$R_2$percent per year. So in an upward sloping scenario, these will look like this: Now,... 4 According to Monika Piazzesi: The word “affine term structure model” is often used in different ways. I will use the word to describe any arbitrage-free model in which [zero coupon] bond yields are affine (constant plus-linear) functions of some state vector x. Affine models are thus a special class of term structure models, which write the yield y(τ) of ... 4 The value of the bond would be the first case, because you have to discount each cashflow with the relevant spot rate for that payment date. Although, because rates are normally expressed in annual terms, you would have to adjust for the days:$(1+R)^{n}$or$(1 + R \times n)\$ What you might be confused with, is the yield of the bond, which would be the ...

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