The level and shape of the YC and the CTD decision? (p61)
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Hi ajsa,
Please see (4) in this thread, that came up last month: http://forum.bionicturtle.com/viewreply/3170/
I (frankly) can never recall exactly why, then i have to re-logic it out, like here.
(or, if there is a nifty intuition, that it has so far escaped me!)
Thanks, David
Please see (4) in this thread, that came up last month: http://forum.bionicturtle.com/viewreply/3170/
I (frankly) can never recall exactly why, then i have to re-logic it out, like here.
(or, if there is a nifty intuition, that it has so far escaped me!)
Thanks, David
Thanks David!
"If yield > 6%, market prices (costs) are higher and the short does not want to exploit this discrepancy (short maturity, high coupon minimizes the discrepancy just as it minimizes the bond’s duration)."
If a CTD "candidate" bond's yield > 6%, why could not the short choose another candidate bond whose yield is lower or even lower than 6%? or why is the "yield" fixed?
Also how the duration minimization is related to lowering bond price so that the discrepancy can be minimized? (sorry I am a little slow)
thanks again!
"If yield > 6%, market prices (costs) are higher and the short does not want to exploit this discrepancy (short maturity, high coupon minimizes the discrepancy just as it minimizes the bond’s duration)."
If a CTD "candidate" bond's yield > 6%, why could not the short choose another candidate bond whose yield is lower or even lower than 6%? or why is the "yield" fixed?
Also how the duration minimization is related to lowering bond price so that the discrepancy can be minimized? (sorry I am a little slow)
thanks again!
Hi ajsa
The 6% is fixed by CBOT in order to produce tables that can create an "apples to apples" comparison among bonds that otherwise have differenct features/prices. (if the short didn't have a choice, no table would be necessary, nor a standardizing 6% assumption)
re if yield > 6%, the "yield" is a market variable: if yields are 8% (at a given maturity, for an approximate risk level including riskless), the other bonds will have also a 8% yield. There won't be any 5% yields, eg. It is good to meditate on this: market rates can be characterized by a spot rate curve; if you add 1% to all spot rates, you will roughly increase the yield (yield to maturity) by 1% also.
duration is a function of when you expect the cash flows. All other things being equal, cash flows received soon are less sensitive to interest rate changes and imply a lower duration. Shorter maturity is directly a sooner return of principal; higher coupons is also sooner cash flow (b/c if not coupons, then wait later until return of par)
David
The 6% is fixed by CBOT in order to produce tables that can create an "apples to apples" comparison among bonds that otherwise have differenct features/prices. (if the short didn't have a choice, no table would be necessary, nor a standardizing 6% assumption)
re if yield > 6%, the "yield" is a market variable: if yields are 8% (at a given maturity, for an approximate risk level including riskless), the other bonds will have also a 8% yield. There won't be any 5% yields, eg. It is good to meditate on this: market rates can be characterized by a spot rate curve; if you add 1% to all spot rates, you will roughly increase the yield (yield to maturity) by 1% also.
duration is a function of when you expect the cash flows. All other things being equal, cash flows received soon are less sensitive to interest rate changes and imply a lower duration. Shorter maturity is directly a sooner return of principal; higher coupons is also sooner cash flow (b/c if not coupons, then wait later until return of par)
David
Hi David,
" if yields are 8% (at a given maturity, for an approximate risk level including riskless), the other bonds will have also a 8% yield. "
Why does the maturity need to be fixed or "given"? If YC is upward sloping, the short can choose short maturity bond, so lower yield, right? so I think all boil down to the YC's shape...
"Shorter maturity is directly a sooner return of principal; higher coupons is also sooner cash flow"
Agree. But I still do not understand why shorter duration bond is in favor for CTD decision if yield > 6%.
Thanks.
" if yields are 8% (at a given maturity, for an approximate risk level including riskless), the other bonds will have also a 8% yield. "
Why does the maturity need to be fixed or "given"? If YC is upward sloping, the short can choose short maturity bond, so lower yield, right? so I think all boil down to the YC's shape...
"Shorter maturity is directly a sooner return of principal; higher coupons is also sooner cash flow"
Agree. But I still do not understand why shorter duration bond is in favor for CTD decision if yield > 6%.
Thanks.
Hi ajsa,
Kudos for pushing the point: as I mentioned, I can never seem to summon the intuition. What I just did is play with the learning XLS at bit (this is the XLS i created that mimics the CF logic, it requires XLS due to the ISEVEN function: http://www.bionicturtle.com/premium/spreadsheet/3.a.10_ctd_tbonds/) to understand this better.
First, in regard to: "Why does the maturity need to be fixed or “given”? If YC is upward sloping, the short can choose short maturity bond, so lower yield, right? so I think all boil down to the YC’s shape…" I totally agree with this, but we are referring to Hull's statement "when bond yield's are in excess of 6%, the CF system tends to favor the delivery of low-coupon long maturity bonds" so Hull's original point here is in reference to a flat (by definition) yield to maturity.
Okay, so as I play with the XLS, here is how it looks to me:
The short position wants to minimze the cost - receipt (or max receipt - cost), and the short is buying the CTD bond at the quoted price and "selling" at the conversion*settlement. I find the useful to think of this simply in terms of wanting to maximize his net revenue:
revenue = settlement * conversion
cost = quoted bond price
the conversion factor system is based on a 6% yield assumption. You can look at the XLS to explore the logic; but basically it is using a 6% yield to price the bond (e..g, I/Y = 6% = YTM). For a given settlement price, this will not change. So, the "baseline" is a CF based on a 6% yield assumption and this "fixes" the revenue
so the goal is now to find the bond with the lowest quote price, all other things being equal. But not really, more specifically, to find the bond where the quoted price is most at variance with the "artificial" price under a 6% yield. When the yield is high, these bonds tend to trade at a discount, and this discount is maximized by long maturity bonds. Okay, so in regard to this factor (I can see it's a little more complicated, but...) I would summarize this in the following way:
At high yields, the CTD bonds will tend to trade at a discount and the short wants to exploit the distortion (i.e., between market price and model price with yield=6%); the discount is highest for a long maturity bond with lower coupons
At low yields, the CTD bond tend to trade at a premium, and since the CTD is paying for the distortion, now it's the opposite, the short wants to mimize the distortion because it's a premium. The premium is lowest for shorter bonds with higher coupons.
In this way, this reveals to me as largely a variation on the "pull to par" idea. If we think about the distortion caused by the artificial 6% pricing, the "discount" is something the short wants to maximize (with longer bonds) but the premium is something he wants to minimze. I hope that helps, I think (tragically!) it's even a bit more complicated...David
Kudos for pushing the point: as I mentioned, I can never seem to summon the intuition. What I just did is play with the learning XLS at bit (this is the XLS i created that mimics the CF logic, it requires XLS due to the ISEVEN function: http://www.bionicturtle.com/premium/spreadsheet/3.a.10_ctd_tbonds/) to understand this better.
First, in regard to: "Why does the maturity need to be fixed or “given”? If YC is upward sloping, the short can choose short maturity bond, so lower yield, right? so I think all boil down to the YC’s shape…" I totally agree with this, but we are referring to Hull's statement "when bond yield's are in excess of 6%, the CF system tends to favor the delivery of low-coupon long maturity bonds" so Hull's original point here is in reference to a flat (by definition) yield to maturity.
Okay, so as I play with the XLS, here is how it looks to me:
The short position wants to minimze the cost - receipt (or max receipt - cost), and the short is buying the CTD bond at the quoted price and "selling" at the conversion*settlement. I find the useful to think of this simply in terms of wanting to maximize his net revenue:
revenue = settlement * conversion
cost = quoted bond price
the conversion factor system is based on a 6% yield assumption. You can look at the XLS to explore the logic; but basically it is using a 6% yield to price the bond (e..g, I/Y = 6% = YTM). For a given settlement price, this will not change. So, the "baseline" is a CF based on a 6% yield assumption and this "fixes" the revenue
so the goal is now to find the bond with the lowest quote price, all other things being equal. But not really, more specifically, to find the bond where the quoted price is most at variance with the "artificial" price under a 6% yield. When the yield is high, these bonds tend to trade at a discount, and this discount is maximized by long maturity bonds. Okay, so in regard to this factor (I can see it's a little more complicated, but...) I would summarize this in the following way:
At high yields, the CTD bonds will tend to trade at a discount and the short wants to exploit the distortion (i.e., between market price and model price with yield=6%); the discount is highest for a long maturity bond with lower coupons
At low yields, the CTD bond tend to trade at a premium, and since the CTD is paying for the distortion, now it's the opposite, the short wants to mimize the distortion because it's a premium. The premium is lowest for shorter bonds with higher coupons.
In this way, this reveals to me as largely a variation on the "pull to par" idea. If we think about the distortion caused by the artificial 6% pricing, the "discount" is something the short wants to maximize (with longer bonds) but the premium is something he wants to minimze. I hope that helps, I think (tragically!) it's even a bit more complicated...David
if it "pull to par", it seems we are assuming CTD bond's coupon is 6% when comparing CTD candidates? Is it legitimate?
no worries (I enjoy pushing the harder ideas i really do)
the variety of eligible CTD bond will have various coupons. By pull to par, I refer to the price of these bonds regardless of the coupon. If yields are 8%, most coupons will be less than 8% and therefore, the CTD bonds will trade at a discount (< 100). This will be true for any coupon less than 8%. Now if you take that discounted bond, and extend the maturity (the reverse of pull to par), the discount gets greater. The short, since he is buying the price, likes this dynamic. At low yields, for yield < coupon, bonds trade at premium: extend maturity here exacerbates the premium and the short is not liking this (I have omitted a few factors, this is my simplification to explain what i perceive to be the largest factor based on playing with the XLS)...David
the variety of eligible CTD bond will have various coupons. By pull to par, I refer to the price of these bonds regardless of the coupon. If yields are 8%, most coupons will be less than 8% and therefore, the CTD bonds will trade at a discount (< 100). This will be true for any coupon less than 8%. Now if you take that discounted bond, and extend the maturity (the reverse of pull to par), the discount gets greater. The short, since he is buying the price, likes this dynamic. At low yields, for yield < coupon, bonds trade at premium: extend maturity here exacerbates the premium and the short is not liking this (I have omitted a few factors, this is my simplification to explain what i perceive to be the largest factor based on playing with the XLS)...David
not as a rule or anything (that i know of), it just seems that coupons tend to be < 8%.
Look at this list of Treasuries
but i was just making up numbers to get at the intuition (of a concept that may not have an easy, direct intuition!), my point was, given an average coupon of C%, at some point a low (high) yield forces a premium (discount). And, directionally, this would seem to explain the dynamic
David
Look at this list of Treasuries
but i was just making up numbers to get at the intuition (of a concept that may not have an easy, direct intuition!), my point was, given an average coupon of C%, at some point a low (high) yield forces a premium (discount). And, directionally, this would seem to explain the dynamic
David
thank you for the insight David, it would be nice to update the notes PDF on page 61 with your explanation on this post:
"At high yields, the CTD bonds will tend to trade at a discount and the short wants to exploit the distortion (i.e., between market price and model price with yield=6%); the discount is highest for a long maturity bond with lower coupons
At low yields, the CTD bond tend to trade at a premium, and since the CTD is paying for the distortion, now it's the opposite, the short wants to mimize the distortion because it's a premium. The premium is lowest for shorter bonds with higher coupons."
it gave me a lot more intuition.
thank you
Martim
"At high yields, the CTD bonds will tend to trade at a discount and the short wants to exploit the distortion (i.e., between market price and model price with yield=6%); the discount is highest for a long maturity bond with lower coupons
At low yields, the CTD bond tend to trade at a premium, and since the CTD is paying for the distortion, now it's the opposite, the short wants to mimize the distortion because it's a premium. The premium is lowest for shorter bonds with higher coupons."
it gave me a lot more intuition.
thank you
Martim
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