13
votes
Accepted
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.
...
- 6,924
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 ...
- 1,886
7
votes
Accepted
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-\...
- 609
7
votes
Accepted
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, ...
- 6,204
7
votes
Accepted
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 ...
- 11.4k
7
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 ...
- 6,425
7
votes
Accepted
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 ...
- 11.4k
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 ...
- 71
6
votes
Accepted
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 ...
- 11.4k
6
votes
Does the rolling of bond payments from non-business days to the next or previous business day affect the calculation of accrued interest and YTM?
It all depends on the individual bond/loan. Read the bond prospectus.
Fixed $C\%$ per year, coupon frequency $n$, usually means exactly $C/n$ regular coupons. The daycounting convention is used if the ...
- 11.9k
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 ...
- 11.4k
5
votes
Accepted
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, ...
- 5,391
5
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 ...
- 9,215
5
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 ...
- 16.5k
5
votes
Accepted
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 ...
- 9,332
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 ...
- 16.5k
5
votes
Pricing a bond denominated in USD but issued in Europe
If this German company already has other similar debts denominated in USD, and you are able to observe the yields at which they trade, then you can just interpolate their yields to the maturity of ...
- 11.9k
4
votes
Accepted
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 ...
- 16.5k
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 ...
- 11.4k
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/...
- 2,187
4
votes
Accepted
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 ...
- 5,041
4
votes
Accepted
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 ...
- 1,841
4
votes
Accepted
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:
...
- 5,685
4
votes
Accepted
Strange Market Data YTM for a Zero Coupon Bond
This bond has a slightly different calculation logic to your average zero coupon bond. Denote $t$ the trade date, $t_0$ the issue date, $T$ the maturity date and $P$ the traded price.
You'll first ...
- 1,841
4
votes
Accepted
Computing treasury note/bond prices from yield
The answer to this is the calculation mode of the bond. The street convention is to use your formula as you have stated, which uses a compounded interest formula for the first period. But the Federal ...
- 9,215
3
votes
Accepted
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 ...
- 16.5k
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....
- 9,332
3
votes
Accepted
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:
$$ y = -\ln (z) $$
- 5,008
3
votes
Pricing a bond denominated in USD but issued in Europe
You should use the US Treasury yields but this is probably not the only thing you should take into account in pricing that bond.
I don't know if the bond you are trying to price would strictly qualify ...
- 1,026
3
votes
Computing treasury note/bond prices from yield
There is a typo in your invoice price formula.
It should be $\dfrac{F}{(1+y)^{-a}}$, not $\dfrac{F}{(1+y)^{a}}$.
It may explain some of the differences when you consider an accrued different from zero....
- 31
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