New answers tagged fixed-income
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From recollection don't you only map the fixed cashflows?
If the 6m rate is 1% and your swap is at 0.5% then on a notional of 100 you map:
6m curve @6m: +1
OIS curve @6m: -0.5
If the 6m6m forward rate is 1.25% then on an 1Y irs struct at 2% your flows would be:
6m curve @6m: +1
OIS curve @6m: +1
6m curve @1y: +1.25
OIS curve @1y: +0.75
On a flat curve, ...
0
Either or both assets have are "risk-free" (in the sense of zero volatility, or guaranteed short-term returns). One could then build a portfolio using it/these, ignoring risky assets.
If the assets are perfectly correlated, or perfectly negatively correlated, AND you have confidence in their volatilities, then one could construct a zero vol ...
2
Risk-free assets refer to assets with a definite rate of return and no risk of default. From the perspective of mathematical statistics, risk-free assets refer to assets with zero variance or standard deviation of investment returns. Of course, the covariance and correlation coefficient between the rate of return of risk-free assets and the rate of return ...
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I'd say coupon - repo is strictly cash flow and coupon + pull to par + rolldown - repo is the "carry", most often referenced in fixed income especially in liquid rates. We could replace coupon and pull to par with yield to maturity. You can see carry referenced as % total return or in bps which is "carry" in dollars divided by duration.
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Interest rate duration and credit duration are defined as the derivative of MV of a bond with respect to IR and credit. The first order derivative can be easily approximated using centered difference (which I would call a method rather than a model). The centered difference formula is the one you mentioned: it has the good property that the error goes to ...
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I disagree with your definition of carry. Carry is the difference between the cash an investment throws off less the cost to finance it. I would argue a zero coupon bond has zero or negative carry (depending if you finance it or not). The yield to maturity is capturing the price appreciation you’d expect as you roll closer to maturity. It’s a bit of a grey ...
3
From the US Treasury FAQ:
"CMT rates are read from fixed, constant maturity points on the curve and may not match the exact yield on any one specific security ...
For example, the 20-year daily yield curve rate (i.e., the 20-year CMT) represents the yield for a new theoretical 20-year bond as of that date."
Due to aging of the 10 year and 20 year ...
1
how does one actually go about hedging?
Your OAS model determines your hedging instruments, hedge ratios, and hedging (model) risk. If your OAS model calibrates to the LIBOR swap curve and swaption vols (which is common), then you can generate hedge ratios by computing key rate durations of the underlying swap and swaption instruments.
For example:
Hedging ...
1
"Essentially a positive OAS implies that once hedged against the forward LIBOR rates, a security will have positive returns": I don't believe this statement is correct. Essentially, the OAS is a statement about expected excess returns (after hedging out duration and volatility risk as described in the comments above) and says little to nothing ...
1
The kinds of corporate actions that would affect equities in the index context are splits, reverese splits, stock dividends, etc. E.g., you start out with 1 share, and the next day you have 2 shares worth half the old price, but the same net claim on the corporation.
But these corporate actions don't affect bonds. You have an obligation promising to repay ...
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Is this all that there is to this product, no early termination, no embedded caps, floors, minimums, maxiumums, or any other optionality? If the curve inverts so much that 10Y>30Y at time t, will the client pay you instead?
As currently described, the cash flow at t simply has sensitivities to two yields that no one knows now: 10Y+t and 30Y+t.
To hedge ...
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I’m going to go on a limb and suggest that it was Stigum’s Money Market back in the late 70’s that formalised many of these conventions. This was the major reference at the time the bond and money markets exploded in size and volume. Along with academic / practitioner stalwarts like Frank Fabozzi, these conventions just became entrenched (and also why there ...
1
I've recently been learning about TIPS and their role as an inflation protection instrument. If you buy a TIP even when it has a negative real yield-to-maturity, is it still possible to have a profitable position?
Absolutely. Let's consider two scenarios:
1. You are not holding the bond to maturity:
In this case, recall that Canadian-style linkers, such as ...
1
TIPS is two instruments in one - a bond whose principal is linked to the Consumer Price Index for All Urban Consumers CPIAUCNS published by the BLS, and a put option with strike set to par value. The par value protection offered by the Treasury is not free and is paid by the bond investor. Also, not all investors may agree with BLS methodology for measuring ...
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Recently issued TIPS have negative real yields, meaning that they are issued at a price P>100. The payment at maturity will be 100*cpi(maturity)/cpi(issue date). The latter expression may or may not be greater than P. So if your definition of ‘profitable’ is in terms of nominal dollars, it is unclear.
I ignored the fact that newly issued TIPS have a ...
-1
"where does the idea of a bonds carry = forward yield - spot yield tie into all of this?"
I'd refer to that as rolldown rather than carry.
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Bond price quoting conventions differ in different countries... In the vast majority of markets, they are quoted as percentage of par. But there are a few exceptions.
If you're looking at Brazil LTN's (BLTN on Bloomberg) or NTN-F's, for example, 1,000 is the par price, so 950 quote means 95% of par.
If you're looking at Mexican cete's (MCET on Bloomberg), ...
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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 ...
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