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13 votes
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Cochrane on Return Predictability

Let $P_t$ be the price of the overall market index at the end of quarter $t$ Let $D_t$ be the dividend for the overall market in quarter $t$ Let $X_t = \frac{D_t}{P_t}$ be the dividend to price ratio. ...
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10 votes

Cochrane on Return Predictability

Maybe I am a little bit late to the party, but I want to give a shot. As in Campbell and Shiller, start from the identity $R_{t+1}\equiv\frac{P_{t+1}+D_{t+1}}{P_t}$ where $R_{t+1}$ is the gross return ...
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7 votes
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reason behind bond yield diverge for bonds with the same maturity during 2008 crisis

Just to elaborate on the comments above to include some visuals. As you pointed out, the high coupon, seasoned 10.625s traded at a steep discount. The first chart below shows the yield spread against ...
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6 votes

question regarding carry & roll of a bond

Carry and roll-down are two different measures. The carry is the PNL resulting from holding a position. However, even if you don't finance the bond in repo, you can still measure your carry as the ...
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6 votes
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question regarding carry & roll of a bond

The formula you quote (forward minus spot) is the yield carry for a financed position. The problem is that different people use the word carry to mean different things. The most commonly used ...
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6 votes
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Why does the YTM equal the coupon rate at par?

Let $P$ denote the dirty price, $F$ the face value and $i$ the YTM. Using the geometric sum we get \begin{align} P &= \sum_{j=1}^n \frac{C}{{(1+i)}^j} + \frac{F}{(1+i)^n}\\ &= C\frac{1-\...
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  • 569
6 votes
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Data on historical, cross-country nominal yield curves

First, a quick comment on Bloomberg symbols such as USGG10YR. These are actually yields on "generic bonds"; typically these are benchmark, on-the-run ...
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5 votes
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Yield-to-Maturity and its assumption

It's simpler to just think of the yield to maturity as the internal rate of return of the bond given the current price. It's like the discount rate you would apply to the final payout and coupons, ...
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  • 5,311
5 votes

Constructing yield curve directly from yield-to-maturity data

Unless all of your yields are par yields (yield of bonds trading at par), you'll get very unreliable results if you fit your curve using yields alone. This is because yields can be distorted by the ...
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5 votes
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Par Yield, Bond Yield and Zero Rate

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, ...
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5 votes
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Hedging EURUSD with negative rates

For a US investor to hedge the bonds the investor would (1) Buy EURUSD in the Spot market, (2) Buy the German bonds with the EUR proceeds, (3) Short EURUSD in the forward market to provide a ...
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  • 9,117
5 votes

How to compute par yield from zero rate curve?

For simplicity, let us assume continuously compounded zero rates and periodically compounded par yields. If you have to work with continuous rates, you may adapt the formulas accordingly. Using the ...
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  • 5,853
5 votes

Hull's book par yield example

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 ...
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4 votes
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Do all bonds of the same maturity have the same yield to maturity?

In practice, bonds of the same maturity will have yields that vary slightly from each other. Several possible reasons (a) a bond with a higher coupon is effectively shorter maturity than a bond with ...
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  • 14.1k
4 votes

Intuitively, why does liquidity premium contribute to bond yield?

For clarity, I'll use two expressions, "liquidity premium" and "illiquidity premium": "Liquidity premium" arises when investors value the liquidity profile of an instrument so much that they are ...
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4 votes

What's the logic behind 3-10 UST yield inversion predicting recession?

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/...
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  • 2,127
4 votes

Why does the ultra long-end of a yield curve invert?

I would not say that this is universally acknowledged but here is my view: Instead of considering par rates, i.e. 10Y and 20Y, consider forward rates, such as 10y and 10y10y. The useful difference ...
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  • 8,089
4 votes

Why does the ultra long-end of a yield curve invert?

Suppose 40yr bond and 30yr bond have the same yield. It is a mathematical fact as @attack68 has pointed out, that the convexity of the 40yr is greater than the convexity of the 30yr bond. So ...
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4 votes
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Why does the ultra long-end of a yield curve invert?

It's an interesting question. The fundamentally devout macro wannabe-strategist within cries out for a long-term growth/inflation expectation narrative. However, the cynical realist within reminds ...
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4 votes
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How to get the price of a bond if the yield is given or viceversa in QuantLib

To get the bond yield from the price: ...
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  • 5,345
3 votes
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Why should central bank intervention cause inverted yield curve to be less effective as a recession signal?

He's talking about central bank intervention in the longer maturities, not the short end. The Fed bought a lot of long dated Treasuries, which helped flatten the curve. Hence an inverted curve may ...
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  • 14.1k
3 votes

Difference between Excel's Rate Function and Paul Wilmott's Goal Seek Method for finding YTM

I did some tinkering with the numbers... It seems to me that Wilmott is expressing his answer as a continuous time interest rate. Notice that $e^{0.0658}=1.03347\times2$. That is how your answer 3....
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3 votes
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Computing T-Bill Yield across leap year boundary

Due to the leap year 366 days need to be used here to match UST conventions (which is ACT/ACT). In this case it doesn't matter whether your interest period extends to only 1 day after the 29th of ...
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3 votes
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Calculating coupon yield and continous compounding

Hint: Let $$z = \mathrm{e}^{-y} $$ That way you get a quadratic equation in $z$ (note that $z$ is positive) and then you can get back to $y$ using: $$ y = -\ln (z) $$
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  • 5,038
2 votes

Intuition behind interest rate models

Some models do use ln(r_t), like Black–Derman–Toy and the Black–Karasinski models. Mainly to avoid negative interest rates in low rates / high volatility environments through the use of the log-normal ...
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2 votes

Calculating "Market Index Dividend Yield" of the ASX

If you are not able to find a data set, containing the dividend yield information for all the companies listed in ASX20/50/100/200/300, the only way is for you to make it by researching the companies. ...
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2 votes

Are there any opensource C# libraries for calculating bond duration and other FI Analytics?

Have you looked at Quantlib.net? We use it both in the back office and some soft realtime trading system for pricing bonds. There are a few questions on this site that deal with using it for pricing ...
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  • 1,349
2 votes

Weights Blowing up in PCA

A couple quick thoughts. Do the PCA on changes or log-changes in your series. That is often how PCA is conducted in fixed-income settings. You're large move in wights corresponds to outlier moves in ...
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2 votes

Using IRR to calculate future value of cashflow

The IRR cannot be used to move the Present Value to a Future Value, because it doesn't represent the rate for that interval of time. It is a complicated average of rates for 1,2,3 years, not the rate ...
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  • 14.1k
2 votes

What is the yield on an infinitely lived ZCB?

while it is true that $$\lim_{T\to\infty} Z(t, T) = \lim_{T\to\infty} e^{-r(T-t)} = 0$$ this is when $r$ is independent of time to maturity, a flat and constant yield curve. In practice, we use yield ...
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