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lovenatalya
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Joined: December 10th, 2013, 5:54 pm

### Why Is Bond Time Value Risk Not Considered in Bond Immunization?

lovenatalya
Topic Author
Posts: 287
Joined: December 10th, 2013, 5:54 pm

### Why Is Bond Time Value Risk Not Considered in Bond Immunization?

QuoteOriginally posted by: list1QuoteOriginally posted by: lovenatalyaQuoteOriginally posted by: list1My advice to rename bond's theta in alpha. Such action will add this alpha to well known collection of alphas. And wolves will be full and all sheeps will be come out with their livesAs I have answered martinghoul, I am renaming theta of bond $\frac{\partial P}{\partial t}$ bondtheta and other greeks of bond bondgreeks. Satisfied?Sorry, I can comprehend but not satisfied. Imagine that one taking your logic will decide to rename your nick lovenatalya and call you theta in this site. If he said about such action in advance as you did it might confused you and for others it is not common idea. For others it is violation of the general rules. Of course you can call all others haters but it does not change the situation.You logic is flawed and you did not "take my logic". Your analogy does not hold. My nickname lovenatalya has already been taken to represent an old member of this site. So no other can use that nickname. Also no one can rename the nickname to something else and still intend to represent the same old member. The time derivative of a bond price (analogous to a new member) is not named, according to you. The name "theta (of an option)" is taken for the time derivative of a European option (analogous to an old member). The name "bondtheta" is not used by any financial variable (analogous to member of this site) --- in fact it is not used by anything else on the earth. I am using the new name to name a variable that is not named before. And I am not renaming "theta (of an option)" to "bondtheta" which would have corresponded to your example of renaming "lovenatalya" to "theta".That is why your logic and analogy are wrong.

list1
Posts: 1696
Joined: July 22nd, 2015, 2:12 pm

### Why Is Bond Time Value Risk Not Considered in Bond Immunization?

I probably was not enough clear. For example from this moment I will apply to call you theta and ask you theta please can you find on internet or in a handbook a reference which explains what does it mean the notion bond theta. If you could not find the reference then one can imagine that other experts can call it $\alpha_ {102}$ as far as all $\alpha_ {n}$ , n = 1 , 2, ... 101 are already known and described. And other people will be confused which way to choose and all finance will fell in recession. Do you have such goal?
Last edited by list1 on June 8th, 2016, 10:00 pm, edited 1 time in total.

Martinghoul
Posts: 3256
Joined: July 18th, 2006, 5:49 am

### Why Is Bond Time Value Risk Not Considered in Bond Immunization?

QuoteOriginally posted by: lovenatalyaQuoteOriginally posted by: MartinghoulQuoteOriginally posted by: lovenatalyaQuoteOriginally posted by: MartinghoulQuoteOriginally posted by: lovenatalyaQuoteOriginally posted by: Martinghoullovenatalya, your questions make it reasonably you're still ignoring what everyone's been telling you all along... Let me try it again.1) There is no theta for a bond. Period. You defining a particular partial as "theta" doesn't magically change the language and the underlying framework used by practitioners. Given that your original post was a question, it's rather strange to see that you keep denying this and insisting on your interpretation.2) No, it's not useful.3) No, the Greeks are not useful for a bond portfolio, since there's a native, arguably more appropriate framework available.We can leave the other questions for another time...I know people are repeating their mantra "there is no theta". They give no detailed reasoning and explanation of what they actually mean. Rather than I ignoring other people's statements, on the contrary, people are ignoring my questions all along. Aside from amike, almost all evade my direct questions.Let us deal with the first question first. Could you please answer my following questions one by one directly for once?1) I do not understand what you mean by "there is no theta". I have defined what I meant by theta (I don't want to repeat the millionth time the exact mathematical definition). Do you want a different definition for it? If so, what is it? Otherwise, you acknowledge my definition, is that correct? If so, by "no theta" do you mean the theta is zero?I know you have defined something that you want to call "theta". I am urging you to stop doing that, first and foremost. I would like you to call the quantity that you've defined something other than "theta", since, IMHO, using the term "theta" constitutes a frivolous abuse of terminology, to which everyone here, including myself, objects.That is fine. I will call the "theta of bond" bondtheta and correspondingly the other partial derivatives or greeks of bond bondgreeks. Satisfied? With this substitution, would you care to answer the questions and give the reasoning?Sure thing...1. Q: Could you please answer my following questions one by one directly for once? A: Yes.2. Q: Do you want a different definition for it? A: No.3. Q: If so, what is it? A: Not so.4. Q: Otherwise, you acknowledge my definition, is that correct? A: Yes, it's correct that I acknowledge the fact that you have defined something that you really really like.5. Q: If so, by "no theta" do you mean the theta is zero? A: No, I mean "N/A". If that's not allowed, feel free to use zero.Do you want me to give you a broad sense of what you're doing here in this thread?Thank you for finally answering some of my questions. I am satisfied with your answer 1-3. 4. Your answer does not make sense logically. The question is whether you acknowledge the definition (bondtheta being partial time derivative of bond price). By answering "yes" you indicate you acknowledge the definition: bondtheta is partial time derivative of bond price. Yet you add you "acknowledge that fact I have defined something I really really like". First it is irrelevant to the definition bondtheta being partial time derivative of bond price. Second by what do you judge whether I like something or not much less "really really"?5. Could you please define what you mean by "N/A"? Here is my guess: by "N/A" do you mean $\frac{\partial P}{\partial t}$ does not exist? If this is true, then you are wrong, $\frac{\partial P}{\partial t}$ DOES EXIST and is NOT zero."Do you want me to give you a broad sense of what you're doing here in this thread?"Sure.Before I try to explain to you what this whole discussion resembles, IMHO, let me address the above...4. I don't see anything illogical in my answer. You asked whether I acknowledge your definition and I stated that I do. As to my judgement regarding you "really really liking it", it's relatively clear, since you keep talking about it.5. Yes, I could certainly define it. I am surprised you're not familiar with the concept. In our daily lives we occasionally have to fill out questionnaires of varying silliness. Occasionally, you would get questions where the most appropriate response is "N/A", since the question makes little sense. In our case, I didn't mean that the partial that you've defined doesn't exist. It means that I am profoundly uninterested in it. If I were to spend any effort on trying to determine whether it's zero or not, it would be a monumental waste, hence I choose "N/A" as a response.So here's the way I see the whole discussion. Imagine there's a room full of people engaged in multiple conversations. They're all speaking the same language, say, English and are able to communicate and debate reasonably successfully. Then you walk into the room and ask people why, instead of English, they don't speak what you perceive as a better language, say, Latin. Those people already in the room try to suggest to you that Latin wouldn't be helpful, that they are already able to converse adequately and efficiently in English and that there's just no point to your attempts. In response, you start loudly speaking Latin, while aggressively trying to prove to everyone that they're all idiots and that Latin is superior to English in every respect. Eventually, your behavior becomes silly, efforts to convince you to join the conversation fall on deaf ears and people just lose interest.P.S.: Pls note that, when I refer to "people" above, I am not including "list", since he's a person who doesn't speak the same language as the other people in the room most of time.

savr
Posts: 48
Joined: January 21st, 2013, 3:28 pm

### Why Is Bond Time Value Risk Not Considered in Bond Immunization?

Chipping in to repeat the answer found, I think, a few pages below.1) A bond is a tradable instrument. It is linear (identical) in itself, hence has no gamma, hence has no theta.2) It would be confusing terminology to consider the bond as a derivative based on some rate: rates themselves are not tradable instruments, so even if bond price is a function P(t,r) of time and rate, dP/dt and d²P/dr² are not "thetas" and "gammas" in the usual trading-room parlance, because they are not derivatives with respect to tradable instruments. Even if, in some attempt to fall on your feet, you consider r as a function of bond price p, then still " d/dt_{1} [P(t_{1},P^{-1}(t,p))] (at t_{1}=t) " (what I understand you are calling theta) is not equal to d/dt [P(t,P^{-1}(t,p)] (which would be 0).-------Note that 2 also clarifies the strange situation where you would consider a stock spot price as a function of time and an option on that stock. (the option here playing the role of the rate above).------Of course bonds can be repo-ed but that doesn't change the conclusion.
Last edited by savr on June 8th, 2016, 10:00 pm, edited 1 time in total.

Paul
Posts: 10787
Joined: July 20th, 2001, 3:28 pm

### Why Is Bond Time Value Risk Not Considered in Bond Immunization?

I think you are all coming at this from different angles. You are all right in your own ways. (Maybe even list!)P

daveangel
Posts: 17031
Joined: October 20th, 2003, 4:05 pm

### Why Is Bond Time Value Risk Not Considered in Bond Immunization?

QuoteOriginally posted by: PaulI think you are all coming at this from different angles. You are all right in your own ways. (Maybe even list!)P
knowledge comes, wisdom lingers

list1
Posts: 1696
Joined: July 22nd, 2015, 2:12 pm

### Why Is Bond Time Value Risk Not Considered in Bond Immunization?

QuoteOriginally posted by: PaulI think you are all coming at this from different angles. You are all right in your own ways. PIt would sound more precisely with a little adjustment such as : " I think you are all coming at this from different angles. You are all right in your own wrong ways. (Maybe even list with his adjustment)"
Last edited by list1 on June 9th, 2016, 10:00 pm, edited 1 time in total.

lovenatalya
Topic Author
Posts: 287
Joined: December 10th, 2013, 5:54 pm

### Why Is Bond Time Value Risk Not Considered in Bond Immunization?

QuoteOriginally posted by: savrChipping in to repeat the answer found, I think, a few pages below.1) A bond is a tradable instrument. It is linear (identical) in itself, hence has no gamma, hence has no theta.2) It would be confusing terminology to consider the bond as a derivative based on some rate: rates themselves are not tradable instruments, so even if bond price is a function P(t,r) of time and rate, dP/dt and d²P/dr² are not "thetas" and "gammas" in the usual trading-room parlance, because they are not derivatives with respect to tradable instruments. Even if, in some attempt to fall on your feet, you consider r as a function of bond price p, then still " d/dt_{1} [P(t_{1},P^{-1}(t,p))] (at t_{1}=t) " (what I understand you are calling theta) is not equal to d/dt [P(t,P^{-1}(t,p)] (which would be 0).-------Note that 2 also clarifies the strange situation where you would consider a stock spot price as a function of time and an option on that stock. (the option here playing the role of the rate above).------Of course bonds can be repo-ed but that doesn't change the conclusion.1) This reasoning does not stand. I presume by "no theta" you mean theta being zero. a. Are you saying: any tradable instrument that is linear (identical) in itself has no gamma? If so, any tradable instrument is linear (identical) in itself, then its gamma should be zero. This is obviously wrong. Consider a European call dynamically hedging against its underlying stock.b. Are you saying (your second "hence") when the gamma is zero, theta is zero? If so, consider a portfolio of a stock and cash. Its gamma is zero but its theta is the cash multiplied by the short rate and NOT zero. This proposition is obviously wrong.2) $r$ being an untradable instrument is not a concern. A (zero coupon) bond can be hedged with another with different maturity. $P(r,t,T)$ is a function of 3 variables. The short rate $r(P,t,T)$ is simply its inverse function or $P(r(p,t,T),t,T)\equiv p$. However $T$ may take on infinitely many values. $P(r(p,t,T_2),t,T_1)\not\equiv p$ for $T_1\neq T_2$. That is how a bond is hedged, that is by another bond of a different maturity. That is in fact how the bond PDE is derived. You made the mistake of assuming there was only one bond or one $T$. All the greeks (theta included) of a bond thus is a variable relative to another particular instrument. They transform to each other algebraically simply via the implicit function theorem. So they form an equivalent class with respect to the particular short rate process. They actually form a Lie group --- not that the structure is of concern here. The theta will certainly not be (identically) zero in infinitely many cases. Just consider two bonds of different maturities under a constant short rate.But this is not strange at all and is not unique to bonds. For a given stock, you may have vanilla options, exotic options. You can dynamically hedge an exotic with the stock, or with a vanilla or other exotic's (in principle). The greeks will be different in value depending on which hedging instrument you pick. But they are all equivalent. This is precisely like the coordinate transformation in physics. The velocity of a single particle is different relative to different coordinates. But it is absurd to claim there is no velocity, no matter "no velocity" means velocity does not exist or zero.You presumed "d/dt_{1} [P(t_{1},P^{-1}(t,p))] (at t_{1}=t)" to be my theta. That is certainly not correct. I do not know how you would have derived that to be my theta given a specific hedging insrument. My theta of bond with maturity $T_1$ would have been $\frac{\partial}{\partial t}P(r(p,t,T_2),t,T_1)$ relative to bond with price $p$ and maturity $T_2\neq T_1$.-------------As the logic of your 2) fails, it fails to clarify the presumed stock paradox. In fact there is nothing strange about stocks.
Last edited by lovenatalya on June 10th, 2016, 10:00 pm, edited 1 time in total.

lovenatalya
Topic Author
Posts: 287
Joined: December 10th, 2013, 5:54 pm

### Why Is Bond Time Value Risk Not Considered in Bond Immunization?

QuoteOriginally posted by: PaulI think you are all coming at this from different angles. You are all right in your own ways. (Maybe even list!)PYou are most likely to be correct. However, I have no way to judge whether what they are saying is correct until they have made their claim precise and coherent. It surprisingly has not happened after such a long thread. Until then their claim borders on being not even wrong. I have been all ears wanting to hear exactly what they have to say. But so far, not a single person except amike and most recently savr is willing (or --- I now start to suspect --- capable?) to put down precisely what they are saying. Instead of precisely making their case, most of them have been evasive and equivocating, as is on full display in Martinghoul's last post equivocating and refusing to even answer trivial questions (not logically paradoxical ones, mind you) --- comparing to others at least he did make an attempt to respond, I will give him that. It is true only list1 has at least been honest. Prior to savr, only amike has made a comparatively valiant attempt to precisely make his point, even though he failed and came back to square one where we started. The most recent attempt by savr unfortunately does not stand either.
Last edited by lovenatalya on June 10th, 2016, 10:00 pm, edited 1 time in total.

Paul
Posts: 10787
Joined: July 20th, 2001, 3:28 pm

### Why Is Bond Time Value Risk Not Considered in Bond Immunization?

QuoteOriginally posted by: daveangel QuoteOriginally posted by: PaulI think you are all coming at this from different angles. You are all right in your own ways. (Maybe even list!)PHow long have you been waiting for that!!!P

Paul
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Joined: July 20th, 2001, 3:28 pm

### Why Is Bond Time Value Risk Not Considered in Bond Immunization?

lovenatalya, meet list. list, meet lovenatalya. You two have a lot in common, I'm sure you'll have lots to talk about.P

list1
Posts: 1696
Joined: July 22nd, 2015, 2:12 pm

### Why Is Bond Time Value Risk Not Considered in Bond Immunization?

QuoteOriginally posted by: Paullovenatalya, meet list. list, meet lovenatalya. You two have a lot in common, I'm sure you'll have lots to talk about.PTheta of the bond is not a subject to discuss. Everything are already said about the subject. If it were not convincing use the term theta and future will dotting subjects at its right places.. Subject was discussion was initially interesting but later was switched and became tiresome boring.
Last edited by list1 on June 10th, 2016, 10:00 pm, edited 1 time in total.

daveangel
Posts: 17031
Joined: October 20th, 2003, 4:05 pm

### Why Is Bond Time Value Risk Not Considered in Bond Immunization?

QuoteOriginally posted by: PaulQuoteOriginally posted by: daveangel QuoteOriginally posted by: PaulI think you are all coming at this from different angles. You are all right in your own ways. (Maybe even list!)PHow long have you been waiting for that!!!PI was premature in thinking that you had killed the joke ! It seems to be a shaggy dog story. Now we have portfolios that hold cash having theta apparently.
Last edited by daveangel on June 10th, 2016, 10:00 pm, edited 1 time in total.
knowledge comes, wisdom lingers

bearish
Posts: 5621
Joined: February 3rd, 2011, 2:19 pm

### Why Is Bond Time Value Risk Not Considered in Bond Immunization?

QuoteOriginally posted by: Paullovenatalya, meet list. list, meet lovenatalya. You two have a lot in common, I'm sure you'll have lots to talk about.PWait, I thought I made that introduction. Or maybe, on second thought, I just made some reference to a rabbit hole...