rekrap

01-24-2007, 02:18 PM

This might be a good place for question regarding the Babbel text, Litterman text, Tilman text and study notes, such as V-C129-07, the old Maginn MIP text.

View Full Version : Questions about Inv Mgmt text and SNs

rekrap

01-24-2007, 02:18 PM

This might be a good place for question regarding the Babbel text, Litterman text, Tilman text and study notes, such as V-C129-07, the old Maginn MIP text.

AggieAct02

01-29-2007, 10:34 AM

Did anyone get SN 129 in their original packet from the SOA? It is not listed as one that we will get later so I didn't know if it was just missing from my packet.

Thanks

Thanks

seattleIslander

01-29-2007, 01:22 PM

It was missing in mine too. I think they probably just forgot to put a *

uncultured

01-29-2007, 02:29 PM

yeup, missing in mine too.

hershey220

01-29-2007, 02:50 PM

Has anyone heard any rumors of when the second mailing will be? I'm following JAM's order and it's kind of annoying to have to skip sections.

carzymathematician

01-29-2007, 03:34 PM

Has anyone heard any rumors of when the second mailing will be? I'm following JAM's order and it's kind of annoying to have to skip sections.

At least you HAVE the 1st mailing! SOA sent me the ERM SNs instead of the APM!

At least you HAVE the 1st mailing! SOA sent me the ERM SNs instead of the APM!

sx06103

01-29-2007, 04:00 PM

Did anyone get SN 129 in their original packet from the SOA? It is not listed as one that we will get later so I didn't know if it was just missing from my packet.

Thanks

I found SN129 was missing and sent SOA an email. Here is what I got from Beverly Haynes at SOA:

"The study note is coming with the second mailing. Sorry it was not marked. They should be coming out sometime the first week in February."

Thanks

I found SN129 was missing and sent SOA an email. Here is what I got from Beverly Haynes at SOA:

"The study note is coming with the second mailing. Sorry it was not marked. They should be coming out sometime the first week in February."

uncultured

01-30-2007, 01:41 PM

At least you HAVE the 1st mailing! SOA sent me the ERM SNs instead of the APM!

:lol: that's funny.

:lol: that's funny.

onceandforall

02-04-2007, 04:13 PM

In Performance Measurement Using Transfer Pricing by Wallace, does anybody know on page 10, how they come up with the benchmark 1, with a deposit account of 5305 and the transfer pricing rate of 6.06%? Is 6.06% a guess?

rekrap

02-05-2007, 12:12 PM

In Performance Measurement Using Transfer Pricing by Wallace, does anybody know on page 10, how they come up with the benchmark 1, with a deposit account of 5305 and the transfer pricing rate of 6.06%? Is 6.06% a guess?

Not a guess. The 6.06% is the discount rate which sets the total benchmark cash flows equal to the total initial invesment cash flows, $5,000. Just try a quick solve with Excel, take a few minutes with your handheld to verify.

Year Benchmark CD Rate CD amount

1 1,055.00 5.50% 1,000

2 1,118.31 5.75% 1,000

3 1,191.02 6.00% 1,000

4 1,269.64 6.15% 1,000

5 1,354.08 6.25% 1,000

5,988.05 6.06% 5,000

If you set the last cell of the last column (where I have 5,000) in Excel as "=NPV(cell beside it, 1055, 1118.31, etc)" and put in 6% as your guess in the "cell beside it" or where 6.06% is in my example, and use goal seek (solve the rate cell for the last column last row cell to equal 5000), it will solve for you.

Not a guess. The 6.06% is the discount rate which sets the total benchmark cash flows equal to the total initial invesment cash flows, $5,000. Just try a quick solve with Excel, take a few minutes with your handheld to verify.

Year Benchmark CD Rate CD amount

1 1,055.00 5.50% 1,000

2 1,118.31 5.75% 1,000

3 1,191.02 6.00% 1,000

4 1,269.64 6.15% 1,000

5 1,354.08 6.25% 1,000

5,988.05 6.06% 5,000

If you set the last cell of the last column (where I have 5,000) in Excel as "=NPV(cell beside it, 1055, 1118.31, etc)" and put in 6% as your guess in the "cell beside it" or where 6.06% is in my example, and use goal seek (solve the rate cell for the last column last row cell to equal 5000), it will solve for you.

onceandforall

02-05-2007, 02:05 PM

Not a guess. The 6.06% is the discount rate which sets the total benchmark cash flows equal to the total initial invesment cash flows, $5,000. Just try a quick solve with Excel, take a few minutes with your handheld to verify.

Year Benchmark CD Rate CD amount

1 1,055.00 5.50% 1,000

2 1,118.31 5.75% 1,000

3 1,191.02 6.00% 1,000

4 1,269.64 6.15% 1,000

5 1,354.08 6.25% 1,000

5,988.05 6.06% 5,000

If you set the last cell of the last column (where I have 5,000) in Excel as "=NPV(cell beside it, 1055, 1118.31, etc)" and put in 6% as your guess in the "cell beside it" or where 6.06% is in my example, and use goal seek (solve the rate cell for the last column last row cell to equal 5000), it will solve for you.

Thanks for answering my questions! That helps!

Year Benchmark CD Rate CD amount

1 1,055.00 5.50% 1,000

2 1,118.31 5.75% 1,000

3 1,191.02 6.00% 1,000

4 1,269.64 6.15% 1,000

5 1,354.08 6.25% 1,000

5,988.05 6.06% 5,000

If you set the last cell of the last column (where I have 5,000) in Excel as "=NPV(cell beside it, 1055, 1118.31, etc)" and put in 6% as your guess in the "cell beside it" or where 6.06% is in my example, and use goal seek (solve the rate cell for the last column last row cell to equal 5000), it will solve for you.

Thanks for answering my questions! That helps!

rekrap

02-16-2007, 09:23 AM

is funding ratio : A0/L0 ? Thanks.

Yes, the ratio of Assets to Liabilities is the "funding ratio" discussed on page 53 of the Waring SN (V-C127-07).

I love the term "suplus tulips"...

Yes, the ratio of Assets to Liabilities is the "funding ratio" discussed on page 53 of the Waring SN (V-C127-07).

I love the term "suplus tulips"...

AggieAct02

02-16-2007, 02:46 PM

Yeah, I couldn't figure out how those charts looked like a tulip. Is that supposed to be like those ink blot tests to see if you are crazy? I think that I pass!

rekrap

02-16-2007, 03:17 PM

Yeah, I couldn't figure out how those charts looked like a tulip. Is that supposed to be like those ink blot tests to see if you are crazy? I think that I pass!

In color (http://www.q-group.org/archives_folder/fa2004/Waring.pdf) [Waring pdf], they do look a little more floral (rotate 90 degrees, too).

In color (http://www.q-group.org/archives_folder/fa2004/Waring.pdf) [Waring pdf], they do look a little more floral (rotate 90 degrees, too).

campbell

02-16-2007, 03:59 PM

Oooh, that's a great link.

carzymathematician

02-22-2007, 12:45 PM

after EIB enter the swap with BNP, EIB receive fixed payment, then transfer that to investor, or EIB receive floating payment from BNP, and transfer those to the investor? Thanks.

EIB is the official issuer of the bond. The bond payment each year (from EIB to investors[pension plans]) is adjusted based on actual mortality rates. So for example, if mortality rates decrease, the bond pays higher cash flows and vice versa. EIB then enter into a swap with BNP to eliminate their int rate risk (EIB is paying floating + receiving fixed proceeds). BNP then seeks to cover any deviations between expected and actual mortality rates by getting reinsurance from Partner Re. Hope this helps!

EIB is the official issuer of the bond. The bond payment each year (from EIB to investors[pension plans]) is adjusted based on actual mortality rates. So for example, if mortality rates decrease, the bond pays higher cash flows and vice versa. EIB then enter into a swap with BNP to eliminate their int rate risk (EIB is paying floating + receiving fixed proceeds). BNP then seeks to cover any deviations between expected and actual mortality rates by getting reinsurance from Partner Re. Hope this helps!

onceandforall

02-26-2007, 09:06 PM

On Page 440 they talked about the "market directional" investments. Isn't it an indication of negative convexity of MBS? Because of the negative convexity the price appreciation of MBS portfolio is compressed vs. that of the hedge portfolio that's why the duration hedge performs poorly when rates go down. Somehow I don't feel I am on the right track of understanding the directionality.

Also on page 438 footnote 7 where they solve for the 2-bond hedge portfolio, what do those numbers stand for?

Also on page 438 footnote 7 where they solve for the 2-bond hedge portfolio, what do those numbers stand for?

rekrap

02-27-2007, 01:04 PM

I received a case study from SOA last week, and yesterday, I received another one in a separate mail. anybody the same as me? I got two case study :-?

They redistributed the case study with the correct cover page (notice the SN number in the bottom left corner).

Nothing significant. No worries.

They redistributed the case study with the correct cover page (notice the SN number in the bottom left corner).

Nothing significant. No worries.

rekrap

03-02-2007, 10:15 AM

On Page 440 they talked about the "market directional" investments. Isn't it an indication of negative convexity of MBS? Because of the negative convexity the price appreciation of MBS portfolio is compressed vs. that of the hedge portfolio that's why the duration hedge performs poorly when rates go down. Somehow I don't feel I am on the right track of understanding the directionality.

I think you got their point. Because of the negative convexity of MBSs, it becomes clear (using the duration hedge) that duration is not a good measure of interest rate risk. Using the D-hedge implies that MBSs are market-directional (P goes up when rates go up) when, in fact, they aren't.

Also on page 438 footnote 7 where they solve for the 2-bond hedge portfolio, what do those numbers stand for?

The number of 2-year and 10-year notes you need to hedge the MBS price changes are H(2) and H(10). The first of the simultaneous equations is how the prices change for a level interest rate change (H2 goes up 62 cents, H10 up $1.69 and the MBS $1.22), while the second is how the prices change for a twist (H2 only changes 1 cent, H10 55 cents and the MBS only 25 cents).

How those numbers are determined not shown, because it presumably took some calculating/computing, since they had to consider both up/down or flattening/steepening for each equation, respectively.

I think you got their point. Because of the negative convexity of MBSs, it becomes clear (using the duration hedge) that duration is not a good measure of interest rate risk. Using the D-hedge implies that MBSs are market-directional (P goes up when rates go up) when, in fact, they aren't.

Also on page 438 footnote 7 where they solve for the 2-bond hedge portfolio, what do those numbers stand for?

The number of 2-year and 10-year notes you need to hedge the MBS price changes are H(2) and H(10). The first of the simultaneous equations is how the prices change for a level interest rate change (H2 goes up 62 cents, H10 up $1.69 and the MBS $1.22), while the second is how the prices change for a twist (H2 only changes 1 cent, H10 55 cents and the MBS only 25 cents).

How those numbers are determined not shown, because it presumably took some calculating/computing, since they had to consider both up/down or flattening/steepening for each equation, respectively.

rekrap

03-02-2007, 10:29 AM

in Oxford Guide to Financial Modeling: chapt5

Arbitrage Free Models:

the one by using binmornial tree,

for T=1, we have a std1, which will make rH=rL*exp(2*std1), and in t2, we will have a different std2, which make rH=rL*exp(2*std2)?

this calibration is adjusting std with different maturity, std1 for T=1, is using bond with maturity =1, std2 for T=2, is using maturity=2, which they use the yield curve? Thanks.

In the basic Ho-Lee model, the volatility remains constant over all periods.

In the extended Ho-Lee model, volatility is period specific. You can see either forward volatilities (one-year volatilities at time T) or spot volatilities (from which you can determine the forward volatilities).

In the BDT model, which I think you are referencing, you use forward volatilites, just like Ho-Lee. And yes, you solve/calibrate for the unknown mu parameter using each period's forward volatility.

Arbitrage Free Models:

the one by using binmornial tree,

for T=1, we have a std1, which will make rH=rL*exp(2*std1), and in t2, we will have a different std2, which make rH=rL*exp(2*std2)?

this calibration is adjusting std with different maturity, std1 for T=1, is using bond with maturity =1, std2 for T=2, is using maturity=2, which they use the yield curve? Thanks.

In the basic Ho-Lee model, the volatility remains constant over all periods.

In the extended Ho-Lee model, volatility is period specific. You can see either forward volatilities (one-year volatilities at time T) or spot volatilities (from which you can determine the forward volatilities).

In the BDT model, which I think you are referencing, you use forward volatilites, just like Ho-Lee. And yes, you solve/calibrate for the unknown mu parameter using each period's forward volatility.

rekrap

03-06-2007, 01:45 PM

Recall page 4 (section 3. Assign Probabilities to n Representative Scenarios) of the Study Note:

...if R1,..., Rn compromise the reprepsentative scenario set, and T1,... ,TN compromise the total scenario set, then each Rj, j=1,...n, represents certain scenarios in T1,... ,TN.

In other words, a representative scenario has to "represent" the other scenarios "around it" (i.e., all those similar in distance from the other 99 representative scenarios), and there may be several Rn that represent more than 100 scenarios (if there are 10,000 total, say), so that there will be others that represent less than 100, and thus the probability weights will not be equal.

The rest of that section discusses methods for assigning probabilities.

...if R1,..., Rn compromise the reprepsentative scenario set, and T1,... ,TN compromise the total scenario set, then each Rj, j=1,...n, represents certain scenarios in T1,... ,TN.

In other words, a representative scenario has to "represent" the other scenarios "around it" (i.e., all those similar in distance from the other 99 representative scenarios), and there may be several Rn that represent more than 100 scenarios (if there are 10,000 total, say), so that there will be others that represent less than 100, and thus the probability weights will not be equal.

The rest of that section discusses methods for assigning probabilities.

campbell

03-06-2007, 01:47 PM

I'm sorry, hw, but often I have trouble understanding what you're writing. I don't want to freak you out, but I hope you can write more comprehensible English (or perhaps French) than what's going on here. It need not be perfect, but the grader will need to have an idea of what you're saying.

Okay, so this is how the algorithm described works. (I have actually implemented this, and intend to do so again in the future)

Let's suppose you have 10,000 scenarios. And you're going to pare it down to 100 "representative" scenarios out of that original 10,000.

1. So pick one scenario at random. Call it P1 (for pivot #1).

2. Now calculate the "distance" of all the =other= scenarios using either distance D1 or D2 (see page 72 of the manual for those defns)

3. The scenario farthest from P1 will be the second pivot P2.

4. Now you've got 9,998 scenarios remaining, and you're going to calculate the distance of each of these to P2 (you've already calculated the distance to P1).

5. Now you're assigning the 9,998 scenarios to P1 and P2. Those "closer" to P1 have P1 as their representative, and those closer to P2 have P2 as their representative. There will not be the same number of scenarios in each pivot group, most likely.

6. Find the scenario farthest away from its pivot representative. This will be the third pivot P3.

7. Update the pivot groups, by calculating the distance to P3 from the other 9,997 non-pivot scenarios.

8. Keep doing this sort of process until you've got 100 pivots. At the end, you're going to have scenarios grouped with their closest pivot, which will "represent" them. Each pivot represents itself, of course. It's entirely possible that the pivot represents only itself (indeed, this is what's going to happen with extreme scenarios, usually). Each pivot is going to get the weight of the number of original scenarios represented by that pivot divided by the total number of original scenarios.

So if there's 10,000 original scenarios, and it's pared down to 10 scenarios, suppose the breakdown is like this:

P1: 1000

P2: 4000

P3: 500

P4: 500

P5: 1

P6: 49

P7: 150

P8: 800

P9: 2500

P10: 500

Then you're going to weight the results from the scenarios like this:

P1: 0.1

P2: 0.4

P3: 0.05

P4: 0.05

P5: 0.0001

and so on.

The whole point of this exercise is to generate a whole bunch of economic scenarios that have equal likelihood in whatever model you're using, and then pick special scenarios out of that original set that you're going to actually run your asset/liability models on for the purposes of something like CTE. The situation is that scenarios generally take a long time to run for complex models, and if you're doing something like CTE90, 90% of the scenario results are going to get thrown out anyway. If you could figure out which were the tail scenarios - the 10% you care about - and just do those without running those other, then you could save a lot of time in modeling.

Okay, so this is how the algorithm described works. (I have actually implemented this, and intend to do so again in the future)

Let's suppose you have 10,000 scenarios. And you're going to pare it down to 100 "representative" scenarios out of that original 10,000.

1. So pick one scenario at random. Call it P1 (for pivot #1).

2. Now calculate the "distance" of all the =other= scenarios using either distance D1 or D2 (see page 72 of the manual for those defns)

3. The scenario farthest from P1 will be the second pivot P2.

4. Now you've got 9,998 scenarios remaining, and you're going to calculate the distance of each of these to P2 (you've already calculated the distance to P1).

5. Now you're assigning the 9,998 scenarios to P1 and P2. Those "closer" to P1 have P1 as their representative, and those closer to P2 have P2 as their representative. There will not be the same number of scenarios in each pivot group, most likely.

6. Find the scenario farthest away from its pivot representative. This will be the third pivot P3.

7. Update the pivot groups, by calculating the distance to P3 from the other 9,997 non-pivot scenarios.

8. Keep doing this sort of process until you've got 100 pivots. At the end, you're going to have scenarios grouped with their closest pivot, which will "represent" them. Each pivot represents itself, of course. It's entirely possible that the pivot represents only itself (indeed, this is what's going to happen with extreme scenarios, usually). Each pivot is going to get the weight of the number of original scenarios represented by that pivot divided by the total number of original scenarios.

So if there's 10,000 original scenarios, and it's pared down to 10 scenarios, suppose the breakdown is like this:

P1: 1000

P2: 4000

P3: 500

P4: 500

P5: 1

P6: 49

P7: 150

P8: 800

P9: 2500

P10: 500

Then you're going to weight the results from the scenarios like this:

P1: 0.1

P2: 0.4

P3: 0.05

P4: 0.05

P5: 0.0001

and so on.

The whole point of this exercise is to generate a whole bunch of economic scenarios that have equal likelihood in whatever model you're using, and then pick special scenarios out of that original set that you're going to actually run your asset/liability models on for the purposes of something like CTE. The situation is that scenarios generally take a long time to run for complex models, and if you're doing something like CTE90, 90% of the scenario results are going to get thrown out anyway. If you could figure out which were the tail scenarios - the 10% you care about - and just do those without running those other, then you could save a lot of time in modeling.

carzymathematician

03-24-2007, 07:51 AM

Can someone pls explain Black's Arbitrage? (SN111)

hershey220

03-26-2007, 03:28 PM

Black is just saying that you should invest in bonds rather than stocks in your pension plan to take advantage of the tax arbitrage opportunity. The SN goes through both Black and Tepper's arguments. They are both pretty similar except Tepper requires the shareholder to switch some bonds into equity, while Black has the corporation do this for them by buying back their own stock. Page 53 and 54 nicely outline how to calculate the savings to the shareholder.

carzymathematician

03-26-2007, 03:58 PM

Black is just saying that you should invest in bonds rather than stocks in your pension plan to take advantage of the tax arbitrage opportunity. The SN goes through both Black and Tepper's arguments. They are both pretty similar except Tepper requires the shareholder to switch some bonds into equity, while Black has the corporation do this for them by buying back their own stock. Page 53 and 54 nicely outline how to calculate the savings to the shareholder.

Tx Hershey! I was able to follow the formulas for Tepper but just couldn't seem to grasp how Black was coming up with his formulas. I'll try going back through the suggested pages. Tx a ton!

Tx Hershey! I was able to follow the formulas for Tepper but just couldn't seem to grasp how Black was coming up with his formulas. I'll try going back through the suggested pages. Tx a ton!

rekrap

03-29-2007, 09:26 AM

it is related to real estate portfolio management.

when it comes to measure that portfolio manager's individual property selection, the solution said it is 0. but if apply the formula Sum(Wib*Rip)-sum(Wib*Rib), it is not zero.

Wib is the weight of each sector in benchmark, here is the index.

Rip is the corresponding portolio return, Rib is the corresponding benchmark (index) return.

Thanks :popcorn:

Without even looking at the question, if you are talking about the 2004 8V exam, the provided solutions are not perfect solutions, they are model solutions (which presumably earned a 10). There can, and will, be errors and extraneous information in those solutions.

If the candidate made the appropriate conclusion given their answer of 0, regardless of whether it was actually supposed to be 0, they may still get close to full credit for that portion of the solution.

when it comes to measure that portfolio manager's individual property selection, the solution said it is 0. but if apply the formula Sum(Wib*Rip)-sum(Wib*Rib), it is not zero.

Wib is the weight of each sector in benchmark, here is the index.

Rip is the corresponding portolio return, Rib is the corresponding benchmark (index) return.

Thanks :popcorn:

Without even looking at the question, if you are talking about the 2004 8V exam, the provided solutions are not perfect solutions, they are model solutions (which presumably earned a 10). There can, and will, be errors and extraneous information in those solutions.

If the candidate made the appropriate conclusion given their answer of 0, regardless of whether it was actually supposed to be 0, they may still get close to full credit for that portion of the solution.

campbell

03-29-2007, 09:44 AM

FWIW, you will not get points taken off for correct but irrelevant info. You can also put in incorrect info and not have points taken off... because the way papers are graded are to add up points for those bits which you do get correct.

That said, putting down two contradictory statements that cover all bases will net you no points.

That said, putting down two contradictory statements that cover all bases will net you no points.

rekrap

03-29-2007, 09:58 AM

That said, putting down two contradictory statements that cover all bases will net you no points.

I do not agree with you at all. I could not agree more.

I do not agree with you at all. I could not agree more.

rekrap

03-29-2007, 01:56 PM

:-? if "That said, putting down two contradictory statements that cover all bases will net you no points.". then that means they take point off for the wrong statement, is it? But you said they will not....FWIW, you will not get points taken off for correct but irrelevant info. You can also put in incorrect info and not have points taken off... because the way papers are graded are to add up points for those bits which you do get correct.

That said, putting down two contradictory statements that cover all bases will net you no points.

To clarify:

You start with 0 points earned for a question. The graders give you points for correct work. If you make an appropriate statement based on your work, you get points. If you later contradict that statement, though, you do not get the points (effectively "taking the points back").

That said, putting down two contradictory statements that cover all bases will net you no points.

To clarify:

You start with 0 points earned for a question. The graders give you points for correct work. If you make an appropriate statement based on your work, you get points. If you later contradict that statement, though, you do not get the points (effectively "taking the points back").

campbell

03-29-2007, 02:04 PM

I used to teach math, and I graded the tests using the "adding up points" method.

Let me show you how this is different from "subtracting points" method:

In a "subtracting points" method, every time you screw up, I take off a certain number of points for the particular type of mistake. (Say, give me a negative probability, and I take off 10 points). Generally there's a certain number of points per problem, and graders don't go into the negative points territory, so once you've made enough mistakes you get zero points on the problem.

In the "adding points" scenario, I add on a certain number of points for each bit you get right (say I give 5 points for showing the proper formula, and 2 points for putting the proper numbers in, 1 point for each item in a prescribed list, etc.). As long as you don't directly contradict one of your items, each additional correct item will increase your score, until you top out at whatever the max points designated for that problem is (you can get a perfect score on a problem and still be missing bits -- that's why the solution sets are rarely complete. They're made up from real solutions submitted.)

To a certain extent, "subtracting points" and "adding points" are equivalent... until you hit the floor or ceiling. That's what makes them different.

------

And now to get really silly, consider incorrect items in your write-up as specific antiparticles, and the correct items specific particles. If there are two pairs that are exact opposites of each other, they annihilate. Otherwise, the antiparticles don't interfere with the particles.

Let me show you how this is different from "subtracting points" method:

In a "subtracting points" method, every time you screw up, I take off a certain number of points for the particular type of mistake. (Say, give me a negative probability, and I take off 10 points). Generally there's a certain number of points per problem, and graders don't go into the negative points territory, so once you've made enough mistakes you get zero points on the problem.

In the "adding points" scenario, I add on a certain number of points for each bit you get right (say I give 5 points for showing the proper formula, and 2 points for putting the proper numbers in, 1 point for each item in a prescribed list, etc.). As long as you don't directly contradict one of your items, each additional correct item will increase your score, until you top out at whatever the max points designated for that problem is (you can get a perfect score on a problem and still be missing bits -- that's why the solution sets are rarely complete. They're made up from real solutions submitted.)

To a certain extent, "subtracting points" and "adding points" are equivalent... until you hit the floor or ceiling. That's what makes them different.

------

And now to get really silly, consider incorrect items in your write-up as specific antiparticles, and the correct items specific particles. If there are two pairs that are exact opposites of each other, they annihilate. Otherwise, the antiparticles don't interfere with the particles.

Jy88

03-29-2007, 11:43 PM

Anyone understand the exhibit 4 in the study notes V-C107-07 chapter 21?

I don't understand how accretion, rolldwon, shift, twist, butterfly component works? Anyone can shed some light?

The example says the Alabama Power 6.85% of 2002 was priced for settlement on 1/1/96 at 101.72, for a yield to maturity of 6.525%. Repricing at this yield for settlement on 2/1/96 obtain a price of 101.7, which give a price return of -1bp. How do you get -1bp? And 101.712+2.854 = 104.566. Where does 2.854 come from?

It follows on the say the OAS 21.6bp. Where is that from? and so on. At the end it says the OAS of 22.2bp which is intepreted as a -1bp return due to change in spread?? Why??

Thank you so so much. I am totally confused.

I don't understand how accretion, rolldwon, shift, twist, butterfly component works? Anyone can shed some light?

The example says the Alabama Power 6.85% of 2002 was priced for settlement on 1/1/96 at 101.72, for a yield to maturity of 6.525%. Repricing at this yield for settlement on 2/1/96 obtain a price of 101.7, which give a price return of -1bp. How do you get -1bp? And 101.712+2.854 = 104.566. Where does 2.854 come from?

It follows on the say the OAS 21.6bp. Where is that from? and so on. At the end it says the OAS of 22.2bp which is intepreted as a -1bp return due to change in spread?? Why??

Thank you so so much. I am totally confused.

rsgoldfarb

04-02-2007, 08:46 PM

Sorry for the confusion.

Since the question focused only on how to use the DVBP information to determine the proper hedge ratio, I wasn't as clear as I should have been about the assumptions. The question said that the term structure was flat with a 6.5% yield, but I didn't clearly specify that I was assuming that was the annual effective yield, not the bond equivalent yield. So the swap pays 6% interest semi-annually (3% every 6 months) but the discounting should be done as 1.065^-t rather than 1.0325^-2t. Doing this will allow you to match the DVBP information given in the question (and in the previous one that also uses the same term structure assumption). It isn't clear how you are getting the result you are getting, but perhaps you should double check your duration calculations and your initial price calculation.

By the way, regarding the performance attribution question from the 2004 exam, the zero answer is correct using the formula. The text in the answer says how it is done - using the weights for the index rather than the weights in the actual portfolio. Perhaps the exhibit confused you since I carried over the "total" portfolio and index returns that were given in the question and showed those along with the weighted average returns using the index weights.

Richard Goldfarb

Since the question focused only on how to use the DVBP information to determine the proper hedge ratio, I wasn't as clear as I should have been about the assumptions. The question said that the term structure was flat with a 6.5% yield, but I didn't clearly specify that I was assuming that was the annual effective yield, not the bond equivalent yield. So the swap pays 6% interest semi-annually (3% every 6 months) but the discounting should be done as 1.065^-t rather than 1.0325^-2t. Doing this will allow you to match the DVBP information given in the question (and in the previous one that also uses the same term structure assumption). It isn't clear how you are getting the result you are getting, but perhaps you should double check your duration calculations and your initial price calculation.

By the way, regarding the performance attribution question from the 2004 exam, the zero answer is correct using the formula. The text in the answer says how it is done - using the weights for the index rather than the weights in the actual portfolio. Perhaps the exhibit confused you since I carried over the "total" portfolio and index returns that were given in the question and showed those along with the weighted average returns using the index weights.

Richard Goldfarb

rekrap

04-04-2007, 01:52 AM

If he borrows at 5%, then it will cost him 10,000*$7.29 (cost of options at 5%), but if he buys the actual options on the market at $7 (implied 3.64%), then he is saving 10,000*(7.29-7) = $2,900

bagheera

04-12-2007, 11:06 PM

In this note, something to this effect is stated. SPDA does not exhibit negative convexity because the responsiveness of the crediting strategy offsets the tendency to lapse. I have a very basic question regarding this. The option to lapse is basically a put option, and the option for an issuer to redeem an issue is a call option. We talk of negative convexity in connection with call options-- as the rates decline the price appreciation is limited and that causes negative convexity. But for SPDA, I think that as market rates decline the "price" will increase in the normal fashion (there is no question of responsiveness here), but for a *rise* in rates, if the crediting strategy is not responsive, then the *fall* in "price" would be limited as policyholders lapse i.e the yield curve would show "extra positive convexity". But extra positive convexity is not talked about anywhere and I don't see how negative convexity fits into the discussion. Any thoughts?

rekrap

04-13-2007, 07:46 AM

In this note, something to this effect is stated. SPDA does not exhibit negative convexity because the responsiveness of the crediting strategy offsets the tendency to lapse. ... But extra positive convexity is not talked about anywhere and I don't see how negative convexity fits into the discussion. Any thoughts?

I think the issue is that since they are using a lapse function that is similar to a mortgage prepayment function, one would expect the SPDA to exhibit negative convexity (like MBSs do), but the crediting rate strategy mitigates that behavior, and so the SPDA does not have negative convexity.

Also, a security, such as MBSs can exhibit negative convexity in low rate environments and positive convexity in higher rate environments, which is what is implied for the SPDA (following your logic). However, the SPDA doesn't switch to negative convexity when rates are low, because of the aforementioned point.

I think the issue is that since they are using a lapse function that is similar to a mortgage prepayment function, one would expect the SPDA to exhibit negative convexity (like MBSs do), but the crediting rate strategy mitigates that behavior, and so the SPDA does not have negative convexity.

Also, a security, such as MBSs can exhibit negative convexity in low rate environments and positive convexity in higher rate environments, which is what is implied for the SPDA (following your logic). However, the SPDA doesn't switch to negative convexity when rates are low, because of the aforementioned point.

bagheera

04-13-2007, 08:34 AM

I think the issue is that since they are using a lapse function that is similar to a mortgage prepayment function, one would expect the SPDA to exhibit negative convexity (like MBSs do), but the crediting rate strategy mitigates that behavior, and so the SPDA does not have negative convexity.

Also, a security, such as MBSs can exhibit negative convexity in low rate environments and positive convexity in higher rate environments, which is what is implied for the SPDA (following your logic). However, the SPDA doesn't switch to negative convexity when rates are low, because of the aforementioned point.

Assume for a moment that the SPDA crediting rate strategy is *not* responsive. Let us then see what will happen in a low interest rate environment. Policy holders are getting a higher credited rate than is being offered in the market, so they will not lapse. Instead the "price" of SPDA will keep increasing as rates fall. Again, there is no negative convexity.

My point is irrespective of whether crediting rate strategy is responsive or not, there is never any negative convexity. But there is indeed extra positive convexity if crediting rate strategy is *not* responsive when market rates rise since policy holders start surrendering their policies.

Also, a security, such as MBSs can exhibit negative convexity in low rate environments and positive convexity in higher rate environments, which is what is implied for the SPDA (following your logic). However, the SPDA doesn't switch to negative convexity when rates are low, because of the aforementioned point.

Assume for a moment that the SPDA crediting rate strategy is *not* responsive. Let us then see what will happen in a low interest rate environment. Policy holders are getting a higher credited rate than is being offered in the market, so they will not lapse. Instead the "price" of SPDA will keep increasing as rates fall. Again, there is no negative convexity.

My point is irrespective of whether crediting rate strategy is responsive or not, there is never any negative convexity. But there is indeed extra positive convexity if crediting rate strategy is *not* responsive when market rates rise since policy holders start surrendering their policies.

bagheera

04-13-2007, 11:10 AM

It is stated in the notes that if the prepayment rate lies between the two collars of a PAC, both the upper and the lower collar drift upwards. I think the lower collar should drift downwards because the higher actual prepayment rate *relative* to the lower collar has created greater "resistance" to future, possibly very low, prepayment rates resulting in a lower extension risk. This effect ought to be reflected in a downward drift of the lower collar. Can anyone shed light on this issue?

rekrap

04-13-2007, 11:27 AM

Assume for a moment that the SPDA crediting rate strategy is *not* responsive. Let us then see what will happen in a low interest rate environment. Policy holders are getting a higher credited rate than is being offered in the market, so they will not lapse. Instead the "price" of SPDA will keep increasing as rates fall. Again, there is no negative convexity.

My point is irrespective of whether crediting rate strategy is responsive or not, there is never any negative convexity. But there is indeed extra positive convexity if crediting rate strategy is *not* responsive when market rates rise since policy holders start surrendering their policies.

Right, in real life, the SPDA does not exhibit negative convexity. However, in the SPDA model, the lapse function will create negative convexity (because it is the same as MBSs, which should have negative convexity), but fortunately there is a responsive crediting rate strategy in place to keep that from happening in the model. Ho even ends that section saying, "this result has to be dependent on the specification of the lapse function."

My point is irrespective of whether crediting rate strategy is responsive or not, there is never any negative convexity. But there is indeed extra positive convexity if crediting rate strategy is *not* responsive when market rates rise since policy holders start surrendering their policies.

Right, in real life, the SPDA does not exhibit negative convexity. However, in the SPDA model, the lapse function will create negative convexity (because it is the same as MBSs, which should have negative convexity), but fortunately there is a responsive crediting rate strategy in place to keep that from happening in the model. Ho even ends that section saying, "this result has to be dependent on the specification of the lapse function."

bagheera

04-13-2007, 11:47 AM

Right, in real life, the SPDA does not exhibit negative convexity. However, in the SPDA model, the lapse function will create negative convexity (because it is the same as MBSs, which should have negative convexity), but fortunately there is a responsive crediting rate strategy in place to keep that from happening in the model. Ho even ends that section saying, "this result has to be dependent on the specification of the lapse function."

In that case, is it even appropriate to use the MBS prepayment model for SPDA lapses? Prepayments represent the "exercise of a call", lapses represent the "exercise of a put".

In that case, is it even appropriate to use the MBS prepayment model for SPDA lapses? Prepayments represent the "exercise of a call", lapses represent the "exercise of a put".

rekrap

04-13-2007, 11:56 AM

It is stated in the notes that if the prepayment rate lies between the two collars of a PAC, both the upper and the lower collar drift upwards. I think the lower collar should drift downwards because the higher actual prepayment rate *relative* to the lower collar has created greater "resistance" to future, possibly very low, prepayment rates resulting in a lower extension risk. This effect ought to be reflected in a downward drift of the lower collar. Can anyone shed light on this issue?

This is a difficult topic apparently:

http://www.actuarialoutpost.com/actuarial_discussion_forum/showthread.php?t=45529

Bands can't drop... only rise. http://www.actuarialoutpost.com/actuarial_discussion_forum/showthread.php?t=8948

Response with a link (that is broken): http://www.actuarialoutpost.com/actuarial_discussion_forum/showthread.php?t=24127

but either of these here could be the intended link:

http://www.actuarialoutpost.com/actuarial_discussion_forum/showthread.php?t=22241 or

http://www.actuarialoutpost.com/actuarial_discussion_forum/showthread.php?t=9215

Nick (of Actex fame) even answers: http://www.actuarialoutpost.com/actuarial_discussion_forum/showthread.php?t=15178

This is a difficult topic apparently:

http://www.actuarialoutpost.com/actuarial_discussion_forum/showthread.php?t=45529

Bands can't drop... only rise. http://www.actuarialoutpost.com/actuarial_discussion_forum/showthread.php?t=8948

Response with a link (that is broken): http://www.actuarialoutpost.com/actuarial_discussion_forum/showthread.php?t=24127

but either of these here could be the intended link:

http://www.actuarialoutpost.com/actuarial_discussion_forum/showthread.php?t=22241 or

http://www.actuarialoutpost.com/actuarial_discussion_forum/showthread.php?t=9215

Nick (of Actex fame) even answers: http://www.actuarialoutpost.com/actuarial_discussion_forum/showthread.php?t=15178

bagheera

04-13-2007, 04:46 PM

This is a difficult topic apparently:

http://www.actuarialoutpost.com/actuarial_discussion_forum/showthread.php?t=45529

Bands can't drop... only rise. http://www.actuarialoutpost.com/actuarial_discussion_forum/showthread.php?t=8948

Response with a link (that is broken): http://www.actuarialoutpost.com/actuarial_discussion_forum/showthread.php?t=24127

but either of these here could be the intended link:

http://www.actuarialoutpost.com/actuarial_discussion_forum/showthread.php?t=22241 or

http://www.actuarialoutpost.com/actuarial_discussion_forum/showthread.php?t=9215

Nick (of Actex fame) even answers: http://www.actuarialoutpost.com/actuarial_discussion_forum/showthread.php?t=15178

Thank you very much, rekrap. I see that there is a plethora of opinions, hypotheses and explanations. This topic has been much talked about.. Although I did not get a direct answer to my question, I gathered a lot of useful information. The explanation of the mechanics of PAC at http://www.actuarialoutpost.com/actuarial_discussion_forum/showthread.php?t=22241 is particularly helpful.

I thought about this some more and concluded that one observation certainly conforms to intuition: Prepayments above the top collar cause it to drift downwards and prepayments below the top collar cause it to drift upwards.

Disclaimer: Whatever I write after this point is my theory, and people are welcome to point out holes in it.

Another claim, not very obvious, is that when the prepayment rate is below the bottom collar, the latter drifts upwards. I think the reason for this is the following. Let the first few, say k, prepayments be below the bottom collar. This results in the PAC schedule getting affected since the first, say n (n>k), principal payments of the PAC are equal to the n principal payments corresponding to the prepayment rate of the lower collar (I deduced this from the excellent example given by bc in the thread above). Now even if the k+1 st prepayment is exactly at the bottom collar and remains there, the PAC schedule continues to remain in a state of delay. This clearly indicates that after k prepayments the effective bottom collar has drifted upwards. For if this were not the case then the PAC would have been repaid on the original schedule inspite of the initial "setbacks" once the k+1 st prepayment got to the original bottom collar.

The only case that remains to be handled is the effect on the lower collar of the prepayment rate being higher than it. The lower collar cannot drift downwards because once the prepayment rate falls, even slightly, below the (initial) lower collar at the k+1 st (k+1<n) step, the PAC schedule gets disrupted i.e there is a deficit in the principal payment of the k+1 st period, and remains that way if prepayment rates remain at their new level.

I am not sure whether the lower collar would drift upwards either; there is no reason to since the PAC schedule has been met so far and since, in principle, the upward drift of the lower collar only indicates that prepayments need to accelerate for the PAC schedule to be met. Revolutionary, dubious conclusion: Lower collar should not be affected when the prepayment rate is above the lower collar.

http://www.actuarialoutpost.com/actuarial_discussion_forum/showthread.php?t=45529

Bands can't drop... only rise. http://www.actuarialoutpost.com/actuarial_discussion_forum/showthread.php?t=8948

Response with a link (that is broken): http://www.actuarialoutpost.com/actuarial_discussion_forum/showthread.php?t=24127

but either of these here could be the intended link:

http://www.actuarialoutpost.com/actuarial_discussion_forum/showthread.php?t=22241 or

http://www.actuarialoutpost.com/actuarial_discussion_forum/showthread.php?t=9215

Nick (of Actex fame) even answers: http://www.actuarialoutpost.com/actuarial_discussion_forum/showthread.php?t=15178

Thank you very much, rekrap. I see that there is a plethora of opinions, hypotheses and explanations. This topic has been much talked about.. Although I did not get a direct answer to my question, I gathered a lot of useful information. The explanation of the mechanics of PAC at http://www.actuarialoutpost.com/actuarial_discussion_forum/showthread.php?t=22241 is particularly helpful.

I thought about this some more and concluded that one observation certainly conforms to intuition: Prepayments above the top collar cause it to drift downwards and prepayments below the top collar cause it to drift upwards.

Disclaimer: Whatever I write after this point is my theory, and people are welcome to point out holes in it.

Another claim, not very obvious, is that when the prepayment rate is below the bottom collar, the latter drifts upwards. I think the reason for this is the following. Let the first few, say k, prepayments be below the bottom collar. This results in the PAC schedule getting affected since the first, say n (n>k), principal payments of the PAC are equal to the n principal payments corresponding to the prepayment rate of the lower collar (I deduced this from the excellent example given by bc in the thread above). Now even if the k+1 st prepayment is exactly at the bottom collar and remains there, the PAC schedule continues to remain in a state of delay. This clearly indicates that after k prepayments the effective bottom collar has drifted upwards. For if this were not the case then the PAC would have been repaid on the original schedule inspite of the initial "setbacks" once the k+1 st prepayment got to the original bottom collar.

The only case that remains to be handled is the effect on the lower collar of the prepayment rate being higher than it. The lower collar cannot drift downwards because once the prepayment rate falls, even slightly, below the (initial) lower collar at the k+1 st (k+1<n) step, the PAC schedule gets disrupted i.e there is a deficit in the principal payment of the k+1 st period, and remains that way if prepayment rates remain at their new level.

I am not sure whether the lower collar would drift upwards either; there is no reason to since the PAC schedule has been met so far and since, in principle, the upward drift of the lower collar only indicates that prepayments need to accelerate for the PAC schedule to be met. Revolutionary, dubious conclusion: Lower collar should not be affected when the prepayment rate is above the lower collar.

bagheera

04-17-2007, 02:21 PM

On page 201 in the chapter "Implied volatility surface:Calibrating the models"

it's written in the third last paragraph "Therefore we need to calibrate the implied volatility surface to the observed market prices. Calibrating the HJM model to the prices of benchmark derivatives can be difficult because the HJM models are recombining".

As far as I know, the HJM model gives an interest rate model given a volatility surface. So one should just get the volatility surface from Black's model and feed it to HJM. How should it matter whether the surface is obtained from market prices or is an arbitrarily specified surface? Why is it difficult for HJM to give an interest rate model given a market volatility surface? And if there is a reason, why is it not applicable to an arbitrarily specified volatility surface? What is meant by calibrating the HJM model to the implied volatility surface? Do we "calibrate" HJM in the conventional sense? I mean the "operational" diagram is

Volatility surface ---> HJM --> Interest rate model

Where does the step of calibration happen?

it's written in the third last paragraph "Therefore we need to calibrate the implied volatility surface to the observed market prices. Calibrating the HJM model to the prices of benchmark derivatives can be difficult because the HJM models are recombining".

As far as I know, the HJM model gives an interest rate model given a volatility surface. So one should just get the volatility surface from Black's model and feed it to HJM. How should it matter whether the surface is obtained from market prices or is an arbitrarily specified surface? Why is it difficult for HJM to give an interest rate model given a market volatility surface? And if there is a reason, why is it not applicable to an arbitrarily specified volatility surface? What is meant by calibrating the HJM model to the implied volatility surface? Do we "calibrate" HJM in the conventional sense? I mean the "operational" diagram is

Volatility surface ---> HJM --> Interest rate model

Where does the step of calibration happen?

bagheera

04-19-2007, 02:32 AM

C129-07, MIP: chp 12: evaluating portfolio performance

quality control charts:

if the cumulative value-added annuliazed percentages are outside the confidence bands, then we reject the "manager has no investment skills". isn't it? Thanks.

Yes.

quality control charts:

if the cumulative value-added annuliazed percentages are outside the confidence bands, then we reject the "manager has no investment skills". isn't it? Thanks.

Yes.

bagheera

04-19-2007, 02:50 PM

In the whole component approach to valuing liabilities, with respect to dividing the liability between the different components, it is stated that credit for offsetting fee can be taken only in excess of DAC recoverability requirements at 95 percentile. Can anyone elaborate on what this means? What do the DAC focussed approach and the fee income bifurcation approach intuitively do?

rekrap

04-19-2007, 10:32 PM

Actex pp-26, for SN C110-07

d) for a long cash flow that occurs at time 5.2, in calculating the following key rate duration, determine the size of the shock to be applied to the 5.2 year spot rate:

i) 3 year KRD

ii) 5-year KRD

iii) 7-year KRD

what is exactly this question asking about?

in order to shift spot rate for 5.2 , up 0.25%, need to shift 3 year KRD 0, 5-year KRD 22.5pbs, and 7 year KRD 2.5 pbs? Thanks :crazy:

Ok. You want to know how the 3 different KRD are affected by a shift in the 5.2-yr rate. Since 5.2 falls between the 5 and 7 KRDs, those are the only two that will be affected.

So, that's why i) 3yr KRD = 0.

Now, 5.2 is closer to 5 than to 7, so most of that 25 bps change will affect the 5yr KRD, and the rest will affect the 7yr KRD. Simple linear interpolation (5.2-5)/(7-5) = .1, so 10% (or 2.5bps) of the shift goes to the 7yr KRD (the one farther away), and the rest (22.5bps) affects the 5yr KRD.

:study:

d) for a long cash flow that occurs at time 5.2, in calculating the following key rate duration, determine the size of the shock to be applied to the 5.2 year spot rate:

i) 3 year KRD

ii) 5-year KRD

iii) 7-year KRD

what is exactly this question asking about?

in order to shift spot rate for 5.2 , up 0.25%, need to shift 3 year KRD 0, 5-year KRD 22.5pbs, and 7 year KRD 2.5 pbs? Thanks :crazy:

Ok. You want to know how the 3 different KRD are affected by a shift in the 5.2-yr rate. Since 5.2 falls between the 5 and 7 KRDs, those are the only two that will be affected.

So, that's why i) 3yr KRD = 0.

Now, 5.2 is closer to 5 than to 7, so most of that 25 bps change will affect the 5yr KRD, and the rest will affect the 7yr KRD. Simple linear interpolation (5.2-5)/(7-5) = .1, so 10% (or 2.5bps) of the shift goes to the 7yr KRD (the one farther away), and the rest (22.5bps) affects the 5yr KRD.

:study:

bagheera

04-20-2007, 01:12 AM

Ok. You want to know how the 3 different KRD are affected by a shift in the 5.2-yr rate. Since 5.2 falls between the 5 and 7 KRDs, those are the only two that will be affected.

So, that's why i) 3yr KRD = 0.

Now, 5.2 is closer to 5 than to 7, so most of that 25 bps change will affect the 5yr KRD, and the rest will affect the 7yr KRD. Simple linear interpolation (5.2-5)/(7-5) = .1, so 10% (or 2.5bps) of the shift goes to the 7yr KRD (the one farther away), and the rest (22.5bps) affects the 5yr KRD.

:study:

I think what the question may be asking is what the impact is on the 5.2 year rate of calculating the 3 year, 5 year and 7 year key rate durations *one* at a time.

In calculating the 3 year key rate, there is no impact.

In calculating the 5 year rate, you move the 5 year rate by 25 basis points without changing the neighboring key rates and find the shifts in intermediate rates (rates with "maturities" between those of key rates) by interpolation. So this shift comes out to 22.5 basis points.

Similarly, in calculating the 7 year key rate, you move the 7 year rate by 25 basis points keeping the other key rates unchanged. By linear interpolation again, the shift in the 5.2 year rate is 2.5 basis points.

So, that's why i) 3yr KRD = 0.

Now, 5.2 is closer to 5 than to 7, so most of that 25 bps change will affect the 5yr KRD, and the rest will affect the 7yr KRD. Simple linear interpolation (5.2-5)/(7-5) = .1, so 10% (or 2.5bps) of the shift goes to the 7yr KRD (the one farther away), and the rest (22.5bps) affects the 5yr KRD.

:study:

I think what the question may be asking is what the impact is on the 5.2 year rate of calculating the 3 year, 5 year and 7 year key rate durations *one* at a time.

In calculating the 3 year key rate, there is no impact.

In calculating the 5 year rate, you move the 5 year rate by 25 basis points without changing the neighboring key rates and find the shifts in intermediate rates (rates with "maturities" between those of key rates) by interpolation. So this shift comes out to 22.5 basis points.

Similarly, in calculating the 7 year key rate, you move the 7 year rate by 25 basis points keeping the other key rates unchanged. By linear interpolation again, the shift in the 5.2 year rate is 2.5 basis points.

rekrap

04-20-2007, 09:43 AM

I think what the question may be asking is what the impact is on the 5.2 year rate of calculating the 3 year, 5 year and 7 year key rate durations *one* at a time.

In calculating the 3 year key rate, there is no impact.

In calculating the 5 year rate, you move the 5 year rate by 25 basis points without changing the neighboring key rates and find the shifts in intermediate rates (rates with "maturities" between those of key rates) by interpolation. So this shift comes out to 22.5 basis points.

Similarly, in calculating the 7 year key rate, you move the 7 year rate by 25 basis points keeping the other key rates unchanged. By linear interpolation again, the shift in the 5.2 year rate is 2.5 basis points.

:iatp:

In calculating the 3 year key rate, there is no impact.

In calculating the 5 year rate, you move the 5 year rate by 25 basis points without changing the neighboring key rates and find the shifts in intermediate rates (rates with "maturities" between those of key rates) by interpolation. So this shift comes out to 22.5 basis points.

Similarly, in calculating the 7 year key rate, you move the 7 year rate by 25 basis points keeping the other key rates unchanged. By linear interpolation again, the shift in the 5.2 year rate is 2.5 basis points.

:iatp:

bagheera

04-21-2007, 03:01 PM

Thanks very much. I got the point.

originally I felt confusing because if checked the example in the study manual, the way to calculate impact on the KRD is shift certain KRD, and any point in between KRD is linearpolated. But this one is shift 5.2 rate first, then use the interpolation to shift the KRD. :toast:

ok..glad you got it.

originally I felt confusing because if checked the example in the study manual, the way to calculate impact on the KRD is shift certain KRD, and any point in between KRD is linearpolated. But this one is shift 5.2 rate first, then use the interpolation to shift the KRD. :toast:

ok..glad you got it.

rekrap

04-21-2007, 09:52 PM

in MIM, ch29, managign a portfolio of hedge fund, it has a general summary of hedge fund strategies into: 1. relative value , 2, event driven, 3, equity long/short, 4. tactical trading (Actex memorization list: LI-70)

in ALMFI: ch6, it classify hedge fund strategies into: 1. market directional strategies, 2. market neutrual strategies, 3 idiosyncratic exposure strategies:

(Actex memorization list: LI-1)

I've tried to reconcile it and merge them into one, but looks like the classification are not always the same, anybody have the same problem?

if in the exam , ask question about classification of hedge fund,.... :aypi:

On the exam either pick one, and say "According to..." or put both and hope for the best. They aren't necessarily contradictory, so you shouldn't "lose" any points.

in ALMFI: ch6, it classify hedge fund strategies into: 1. market directional strategies, 2. market neutrual strategies, 3 idiosyncratic exposure strategies:

(Actex memorization list: LI-1)

I've tried to reconcile it and merge them into one, but looks like the classification are not always the same, anybody have the same problem?

if in the exam , ask question about classification of hedge fund,.... :aypi:

On the exam either pick one, and say "According to..." or put both and hope for the best. They aren't necessarily contradictory, so you shouldn't "lose" any points.

rsgoldfarb

04-25-2007, 06:51 PM

The website contains an "Updates" file that corrects this spreadsheet error.

Jy88

04-28-2007, 04:15 AM

Can someone explain the difference between those two?

We are looking at the gain of switching from equity to bonds on both cases:

Tepper arbitrage:

Net gain = A * (1-corporate tax)*(Personal bond - Personal tax on equities) * return on bond.

Black Arbitrage:

Net gain = Annaul benefit minus by Anual savings?

My point is can we reason those formula out?

Tepper Arbitrage:

The NPV = (1-tc)*(personal bond - personal tax equities) / (1-personal bond)

Black Arbitrage:

NPV = (1-personal tax on equities) * (1-corporate tax) * return on bond * coroporate tax / (1- personal bond) * return on bond.

Can see that for Black arbitrage the gain from personal tax on equities are incorporated. Why?

Thanks for that.

We are looking at the gain of switching from equity to bonds on both cases:

Tepper arbitrage:

Net gain = A * (1-corporate tax)*(Personal bond - Personal tax on equities) * return on bond.

Black Arbitrage:

Net gain = Annaul benefit minus by Anual savings?

My point is can we reason those formula out?

Tepper Arbitrage:

The NPV = (1-tc)*(personal bond - personal tax equities) / (1-personal bond)

Black Arbitrage:

NPV = (1-personal tax on equities) * (1-corporate tax) * return on bond * coroporate tax / (1- personal bond) * return on bond.

Can see that for Black arbitrage the gain from personal tax on equities are incorporated. Why?

Thanks for that.

rekrap

04-28-2007, 07:12 AM

Can someone explain the difference between those two?

We are looking at the gain of switching from equity to bonds on both cases:

Tepper arbitrage:

Net gain = A * (1-corporate tax)*(Personal bond - Personal tax on equities) * return on bond.

Black Arbitrage:

Net gain = Annaul benefit minus by Anual savings?

My point is can we reason those formula out?

Tepper Arbitrage:

The NPV = (1-tc)*(personal bond - personal tax equities) / (1-personal bond)

Black Arbitrage:

NPV = (1-personal tax on equities) * (1-corporate tax) * return on bond * coroporate tax / (1- personal bond) * return on bond.

Can see that for Black arbitrage the gain from personal tax on equities are incorporated. Why?

Thanks for that.

A response to an earlier query in this thread, summarized the two nicely:

Black is just saying that you should invest in bonds rather than stocks in your pension plan to take advantage of the tax arbitrage opportunity. The SN goes through both Black and Tepper's arguments. They are both pretty similar except Tepper requires the shareholder to switch some bonds into equity, while Black has the corporation do this for them by buying back their own stock. Page 53 and 54 nicely outline how to calculate the savings to the shareholder.

So for Tepper's arbitrage:

The corporation shifts from equity to bonds: (1-tps)(1-tc)(rb-re) => (1-tps)(1-tc)rb - (1-tps)(1-tc)re

The shareholder must do the opposite (re-rb), and have different taxes: (1-tps)(1-tc)re - (1-tpb)(1-tc)rb

Net effect (add together/cancel):

{(1-tps)(1-tc)rb - (1-tps)(1-tc)re} + {(1-tps)(1-tc)re - (1-tpb)(1-tc)rb}

= (1-tps)(1-tc)rb - (1-tpb)(1-tc)rb

= (tpb-tps)(1-tc)rb

And likewise for Black...

We are looking at the gain of switching from equity to bonds on both cases:

Tepper arbitrage:

Net gain = A * (1-corporate tax)*(Personal bond - Personal tax on equities) * return on bond.

Black Arbitrage:

Net gain = Annaul benefit minus by Anual savings?

My point is can we reason those formula out?

Tepper Arbitrage:

The NPV = (1-tc)*(personal bond - personal tax equities) / (1-personal bond)

Black Arbitrage:

NPV = (1-personal tax on equities) * (1-corporate tax) * return on bond * coroporate tax / (1- personal bond) * return on bond.

Can see that for Black arbitrage the gain from personal tax on equities are incorporated. Why?

Thanks for that.

A response to an earlier query in this thread, summarized the two nicely:

Black is just saying that you should invest in bonds rather than stocks in your pension plan to take advantage of the tax arbitrage opportunity. The SN goes through both Black and Tepper's arguments. They are both pretty similar except Tepper requires the shareholder to switch some bonds into equity, while Black has the corporation do this for them by buying back their own stock. Page 53 and 54 nicely outline how to calculate the savings to the shareholder.

So for Tepper's arbitrage:

The corporation shifts from equity to bonds: (1-tps)(1-tc)(rb-re) => (1-tps)(1-tc)rb - (1-tps)(1-tc)re

The shareholder must do the opposite (re-rb), and have different taxes: (1-tps)(1-tc)re - (1-tpb)(1-tc)rb

Net effect (add together/cancel):

{(1-tps)(1-tc)rb - (1-tps)(1-tc)re} + {(1-tps)(1-tc)re - (1-tpb)(1-tc)rb}

= (1-tps)(1-tc)rb - (1-tpb)(1-tc)rb

= (tpb-tps)(1-tc)rb

And likewise for Black...

bagheera

04-28-2007, 06:16 PM

In Black's arbitrage, it is apparently the case that the gain is actually experienced when the pension assets are shifted from equities to bonds. The switching from equity financing to debt financing is done by the corporation merely to "highlight the gains". What exactly does this mean in the context of what I write below?

In Black's argument, the corporation issues 1-t_c of debt and pays (1-t_c)*r_b interest on it. Therefore it accrues tax savings of (1-t_c)*r_b*t_c which are then passed onto the shareholders. They end up with (1-t_c)*r_b*t_c*(1-t_ps) annually after paying equity taxes. If this is valued as a perpetuity, the present value after dividing by r_b*(1-t_rb) comes out to (1-t_c)*t_c*(1-t_ps)/(1-t_rb). This is shown to be the gain in Black's argument. Here I see that the emphasis is actually on the recapitalization by the corporation rather than the shifting of assets in the pension plan. What's more, the shifting in the pension plan figures nowhere in calculating the gain.

Can anybody explain this apparent discrepancy? Thanks!

In Black's argument, the corporation issues 1-t_c of debt and pays (1-t_c)*r_b interest on it. Therefore it accrues tax savings of (1-t_c)*r_b*t_c which are then passed onto the shareholders. They end up with (1-t_c)*r_b*t_c*(1-t_ps) annually after paying equity taxes. If this is valued as a perpetuity, the present value after dividing by r_b*(1-t_rb) comes out to (1-t_c)*t_c*(1-t_ps)/(1-t_rb). This is shown to be the gain in Black's argument. Here I see that the emphasis is actually on the recapitalization by the corporation rather than the shifting of assets in the pension plan. What's more, the shifting in the pension plan figures nowhere in calculating the gain.

Can anybody explain this apparent discrepancy? Thanks!

zjmgyx

04-29-2007, 01:53 AM

Actually, I think the coporation is purchasing shares that the pension plan sold. It is similar to a changing assets between pension plan and the parent corporation.

Am I right?

Am I right?

bagheera

04-29-2007, 02:22 AM

Is that the case..? But the corporation issues only 1-t_c of debt and the shares sold are worth $1. In any case, what about the "loss" of (1-t_ps)(1-t_c)(r_b-r_e) caused by the shifting of $1 of pension assets to bonds that figures in the Tepper argument but not in Black's argument?

Jy88

04-29-2007, 02:28 AM

Would like to ask if, the corporation shifts from equity to bonds; why would there be a personal equity tax on the net return?

Thanks again.

A response to an earlier query in this thread, summarized the two nicely:

So for Tepper's arbitrage:

The corporation shifts from equity to bonds: (1-tps)(1-tc)(rb-re) => (1-tps)(1-tc)rb - (1-tps)(1-tc)re

The shareholder must do the opposite (re-rb), and have different taxes: (1-tps)(1-tc)re - (1-tpb)(1-tc)rb

Net effect (add together/cancel):

{(1-tps)(1-tc)rb - (1-tps)(1-tc)re} + {(1-tps)(1-tc)re - (1-tpb)(1-tc)rb}

= (1-tps)(1-tc)rb - (1-tpb)(1-tc)rb

= (tpb-tps)(1-tc)rb

And likewise for Black...

Thanks again.

A response to an earlier query in this thread, summarized the two nicely:

So for Tepper's arbitrage:

The corporation shifts from equity to bonds: (1-tps)(1-tc)(rb-re) => (1-tps)(1-tc)rb - (1-tps)(1-tc)re

The shareholder must do the opposite (re-rb), and have different taxes: (1-tps)(1-tc)re - (1-tpb)(1-tc)rb

Net effect (add together/cancel):

{(1-tps)(1-tc)rb - (1-tps)(1-tc)re} + {(1-tps)(1-tc)re - (1-tpb)(1-tc)rb}

= (1-tps)(1-tc)rb - (1-tpb)(1-tc)rb

= (tpb-tps)(1-tc)rb

And likewise for Black...

rekrap

04-29-2007, 07:38 AM

Would like to ask if, the corporation shifts from equity to bonds; why would there be a personal equity tax on the net return?

Thanks again.

When the company shifts to bonds, the shareholder has to pick up the equity in his/her own portfolio.

Hence the tax on their new equity holding...

Thanks again.

When the company shifts to bonds, the shareholder has to pick up the equity in his/her own portfolio.

Hence the tax on their new equity holding...

rekrap

04-30-2007, 09:40 PM

is it, after company issue debt=(1-tc)*shifted amount , use them to repurchase the share, then in addition , the company will increase their equity holding buy (1-tc) * shifted amount?

In Black's, yes. Company does all the "work".

In Black's, yes. Company does all the "work".

rekrap

05-01-2007, 09:31 AM

Black's version:

my question is like when the equity holding got increased.

or besides issue debt to purchase shares, they do other thing to increase their equity holding?

The point is to switch from equity to bonds, so the net equity holding will decrease from $1 shares (sold) to $(1-tc) shares (repurchased with debt issuance).

my question is like when the equity holding got increased.

or besides issue debt to purchase shares, they do other thing to increase their equity holding?

The point is to switch from equity to bonds, so the net equity holding will decrease from $1 shares (sold) to $(1-tc) shares (repurchased with debt issuance).

Jy88

05-01-2007, 10:27 AM

I would like to ask in this reading on the market value adjusted annuity, there is something called 'birfucation' anyone know what is this about?

Also, on the EIA i.e. the equity indexed annuities, anyone knows how this work?

My understanding on this EIA, the fund have two component, one is the fixed guaranteed accumulation rate and a final maturity benefit with a portion of return depending on the equity index. Correct?

From this, we can see that it would be like a fixed income investment and a call option on the equity index. This is the part which I am not sure; am I right to say that given the payoff for call option is max(S-K,0). Now, in this case, we have S= equity return on the index and K= maturity benefit.

If the equity return decreases, call option would be exercise and the final amount in the fund would be the (S-K)+fixed income. Similarly, if the equity return decreases to less than the maturity benefit, the final amount in the fund would be just the fixed income investment. Is this correct?

Also, does that mean that the max loss we get from EIA would be guaranteed at the accumulation fixed rate?

In terms of the accounting for EIA, it mention something called annual ratchet. It says that in an annual ratchet, the derivative is really a series of derivatives; they are all included and treated as a single derivative. Anyone know what is annual ratchet?

Thanks a lot for this.

Also, on the EIA i.e. the equity indexed annuities, anyone knows how this work?

My understanding on this EIA, the fund have two component, one is the fixed guaranteed accumulation rate and a final maturity benefit with a portion of return depending on the equity index. Correct?

From this, we can see that it would be like a fixed income investment and a call option on the equity index. This is the part which I am not sure; am I right to say that given the payoff for call option is max(S-K,0). Now, in this case, we have S= equity return on the index and K= maturity benefit.

If the equity return decreases, call option would be exercise and the final amount in the fund would be the (S-K)+fixed income. Similarly, if the equity return decreases to less than the maturity benefit, the final amount in the fund would be just the fixed income investment. Is this correct?

Also, does that mean that the max loss we get from EIA would be guaranteed at the accumulation fixed rate?

In terms of the accounting for EIA, it mention something called annual ratchet. It says that in an annual ratchet, the derivative is really a series of derivatives; they are all included and treated as a single derivative. Anyone know what is annual ratchet?

Thanks a lot for this.

rekrap

05-01-2007, 11:37 AM

I would like to ask in this reading on the market value adjusted annuity, there is something called 'birfucation' anyone know what is this about?

Bifurcation is splitting into two, like limbs on a the branch of a tree.

In terms of the accounting for EIA, it mention something called annual ratchet. It says that in an annual ratchet, the derivative is really a series of derivatives; they are all included and treated as a single derivative. Anyone know what is annual ratchet?

An annual ratchet is where the guarantee is reset annually, usually trending ("ratcheting") upward.

Bifurcation is splitting into two, like limbs on a the branch of a tree.

In terms of the accounting for EIA, it mention something called annual ratchet. It says that in an annual ratchet, the derivative is really a series of derivatives; they are all included and treated as a single derivative. Anyone know what is annual ratchet?

An annual ratchet is where the guarantee is reset annually, usually trending ("ratcheting") upward.

Jy88

05-01-2007, 11:49 AM

Thanks rekrap.

How bout the EIA? Do you think my understanding is correct?

How bout the EIA? Do you think my understanding is correct?

rekrap

05-01-2007, 02:45 PM

Thanks rekrap.

How bout the EIA? Do you think my understanding is correct?

To be honest, my eyes glaze over the middle portion of your post everytime I try to read it...

How bout the EIA? Do you think my understanding is correct?

To be honest, my eyes glaze over the middle portion of your post everytime I try to read it...

campbell

05-01-2007, 03:52 PM

Yes, EIA's have a guaranteed portion and a "participating" portion.

That said, that chapter of Investment Guarantees is not on the APM syllabus (though it was on the 8V) -- which reading are you referring to?

Seriously, ignore all parts of the texts that are not on the official course of reading. You need not waste your time on that stuff.

That said, that chapter of Investment Guarantees is not on the APM syllabus (though it was on the 8V) -- which reading are you referring to?

Seriously, ignore all parts of the texts that are not on the official course of reading. You need not waste your time on that stuff.

rekrap

05-01-2007, 05:42 PM

V124-07:

The great bull market, the new economy, the age wave, and future stock returns:

what is the conclusion? the study notes is confusing, the stock return will increase in the long run or not? Thanks.

Yes.

for utility function, dose the concave shape imply a non-constant risk aversion? or not? Thanks.

Yes.

The great bull market, the new economy, the age wave, and future stock returns:

what is the conclusion? the study notes is confusing, the stock return will increase in the long run or not? Thanks.

Yes.

for utility function, dose the concave shape imply a non-constant risk aversion? or not? Thanks.

Yes.

Jy88

05-01-2007, 11:54 PM

ehhehe..rekrap....that's quite honest..:-p

Campbell, I thought that is in the syllabus isn't it Hardy Chapter 1? You mean if not in the study notes we can ignore it?

Thanks thanks.

Campbell, I thought that is in the syllabus isn't it Hardy Chapter 1? You mean if not in the study notes we can ignore it?

Thanks thanks.

campbell

05-02-2007, 03:55 PM

ehhehe..rekrap....that's quite honest..:-p

Campbell, I thought that is in the syllabus isn't it Hardy Chapter 1? You mean if not in the study notes we can ignore it?

Thanks thanks.

Ah right, Chapter 1 is still on the syllabus. I didn't think that all the product features weren't described until the later chapter. So basically, only worry about the level of detail given in chapter 1. Checking the text, it is a really bare amount of info on EIAs and others. So don't worry about the ratchet vs point-to-point vs high water mark. Those details aren't in chapter 1.

The only way EIAs should come up would be as part of a list of insurance products with equity-linked guarantees. And such a list would likely only be for 1 or 2 points anyway.

Campbell, I thought that is in the syllabus isn't it Hardy Chapter 1? You mean if not in the study notes we can ignore it?

Thanks thanks.

Ah right, Chapter 1 is still on the syllabus. I didn't think that all the product features weren't described until the later chapter. So basically, only worry about the level of detail given in chapter 1. Checking the text, it is a really bare amount of info on EIAs and others. So don't worry about the ratchet vs point-to-point vs high water mark. Those details aren't in chapter 1.

The only way EIAs should come up would be as part of a list of insurance products with equity-linked guarantees. And such a list would likely only be for 1 or 2 points anyway.

Jy88

05-02-2007, 08:59 PM

Ok. Thanks Campbell :-p

bagheera

05-03-2007, 02:53 AM

In the annual cost of ownership formula, why is the term corresponding to mortgage payments not included? The term for tax benefits due to mortgage payments is present though.

rekrap

05-03-2007, 07:27 AM

In the annual cost of ownership formula, why is the term corresponding to mortgage payments not included? The term for tax benefits due to mortgage payments is present though.

It's capturing every cost but the obvious principal payments on the property. All the things that are not directly comparable to renting costs. For example, the tax portion is just the deductibility of mortgage interest (plus property tax), which you don't have with rent payments.

It's capturing every cost but the obvious principal payments on the property. All the things that are not directly comparable to renting costs. For example, the tax portion is just the deductibility of mortgage interest (plus property tax), which you don't have with rent payments.

bagheera

05-03-2007, 08:44 AM

It's capturing every cost but the obvious principal payments on the property. All the things that are not directly comparable to renting costs. For example, the tax portion is just the deductibility of mortgage interest (plus property tax), which you don't have with rent payments.

Thanks rekrap..Somehow I think it should capture the mortgage interest cost as well. That will considerably reduce the price to rent multiple, and may influence our inference of whether a bubble exists or not. But I guess it's ok. Maybe it is accounted for elsewhere or neutralizes something else..

Thanks rekrap..Somehow I think it should capture the mortgage interest cost as well. That will considerably reduce the price to rent multiple, and may influence our inference of whether a bubble exists or not. But I guess it's ok. Maybe it is accounted for elsewhere or neutralizes something else..

rekrap

05-03-2007, 09:06 AM

Thanks rekrap..Somehow I think it should capture the mortgage interest cost as well. That will considerably reduce the price to rent multiple, and may influence our inference of whether a bubble exists or not. But I guess it's ok. Maybe it is accounted for elsewhere or neutralizes something else..

That whole article [pdf (http://www.newyorkfed.org/research/staff_reports/sr218.pdf)] is worthless. Don't overthink it... just know the formula (which has that last catch-all "risk premium" term) and the conclusion:

We hope the following insights emerge from our analysis: First, house price dynamics are a local phenomenon, and national-level data obscure important economic differences among cities. Moreover, one cannot draw conclusions about house prices by comparing cities: price-to-income and price-to-rent ratios that would be considered “high” for one city may be typical for another. Second, when considering local house prices, the economically relevant basis for comparison is the annual cost of ownership. Without accounting for changes in real, long-term interest rates, expected inflation, expected house price appreciation and taxes, one cannot accurately assess whether houses are reasonably priced. Third, changes in underlying fundamentals can affect cities differently. In particular, in cities where housing supply is relatively inelastic, prices will be higher relative to rents, and house prices will typically be more sensitive to changes in interest rates.

That whole article [pdf (http://www.newyorkfed.org/research/staff_reports/sr218.pdf)] is worthless. Don't overthink it... just know the formula (which has that last catch-all "risk premium" term) and the conclusion:

We hope the following insights emerge from our analysis: First, house price dynamics are a local phenomenon, and national-level data obscure important economic differences among cities. Moreover, one cannot draw conclusions about house prices by comparing cities: price-to-income and price-to-rent ratios that would be considered “high” for one city may be typical for another. Second, when considering local house prices, the economically relevant basis for comparison is the annual cost of ownership. Without accounting for changes in real, long-term interest rates, expected inflation, expected house price appreciation and taxes, one cannot accurately assess whether houses are reasonably priced. Third, changes in underlying fundamentals can affect cities differently. In particular, in cities where housing supply is relatively inelastic, prices will be higher relative to rents, and house prices will typically be more sensitive to changes in interest rates.

bagheera

05-03-2007, 11:22 AM

That whole article [pdf (http://www.newyorkfed.org/research/staff_reports/sr218.pdf)] is worthless. Don't overthink it... just know the formula (which has that last catch-all "risk premium" term) and the conclusion:

Alright..Thank you!

Alright..Thank you!

bagheera

05-08-2007, 02:00 AM

Is the convexity of futures negative or positive? Why is it what it is?

This is with reference to Babbel Chapter 19 where it is said that futures hedge better due to negative convexity.

This is with reference to Babbel Chapter 19 where it is said that futures hedge better due to negative convexity.

Jy88

05-08-2007, 03:56 AM

Can anyone explain why if a treasury note with$10,000 face value is quoted with price of 98-245, the price in dollars would be $9,876.95?

Thanks.

Thanks.

rekrap

05-08-2007, 07:22 AM

Can anyone explain why if a treasury note with$10,000 face value is quoted with price of 98-245, the price in dollars would be $9,876.95?

Thanks.

Prices are quoted in 32nds. So $98 and 24.5/32 = .765625, for a total price of $9,876.56. I'm not sure why we don't match there....

Thanks.

Prices are quoted in 32nds. So $98 and 24.5/32 = .765625, for a total price of $9,876.56. I'm not sure why we don't match there....

Jy88

05-08-2007, 10:34 AM

Just wondering for Ho-Lee, BDT, Brennan-Schwartz; are they all risk-neutral?

Thanks.

Thanks.

rekrap

05-08-2007, 10:49 AM

Just wondering for Ho-Lee, BDT, Brennan-Schwartz; are they all risk-neutral?

Thanks.

Don't group the Equilibrium model Brennan-Schwartz with the Arbitrage-free Ho-Lee and BDT models.

The Equilibrium models (CIR and Vasicek and BS) do not use risk-neutral valuation. The Arbitrage-free models (HL, BDT, etc) are risk-neutral by design (as discussed on page 137 [Ch 5] of SN 125).

Thanks.

Don't group the Equilibrium model Brennan-Schwartz with the Arbitrage-free Ho-Lee and BDT models.

The Equilibrium models (CIR and Vasicek and BS) do not use risk-neutral valuation. The Arbitrage-free models (HL, BDT, etc) are risk-neutral by design (as discussed on page 137 [Ch 5] of SN 125).

Jy88

05-08-2007, 11:32 AM

Thanks rekrap.

They mention Babbel ch13 that for CIR, HW and Vacicek, we can transform them to represent risk neutral models. However, guess you are right, equilibrium models are not risk neutral.

They mention Babbel ch13 that for CIR, HW and Vacicek, we can transform them to represent risk neutral models. However, guess you are right, equilibrium models are not risk neutral.

rekrap

05-08-2007, 11:37 AM

Thanks rekrap.

They mention Babbel ch13 that for CIR, HW and Vacicek, we can transform them to represent risk neutral models. However, guess you are right, equilibrium models are not risk neutral.

Do you remember the 4 faces of interest rate models?

Two groups: 1. Equilibrium and Arb-Free, 2. Risk-neutral and real-world.

Equilibrium can be both... but it is real-world by design, and you have to adjust to get risk-neutral. Same, but vice versa, for Arb-free, but keep in mind that it is impossible to reliable determine the real-world term premia for Arb-free models, and so they are impractical.

They mention Babbel ch13 that for CIR, HW and Vacicek, we can transform them to represent risk neutral models. However, guess you are right, equilibrium models are not risk neutral.

Do you remember the 4 faces of interest rate models?

Two groups: 1. Equilibrium and Arb-Free, 2. Risk-neutral and real-world.

Equilibrium can be both... but it is real-world by design, and you have to adjust to get risk-neutral. Same, but vice versa, for Arb-free, but keep in mind that it is impossible to reliable determine the real-world term premia for Arb-free models, and so they are impractical.

vBulletin® v3.7.6, Copyright ©2000-2018, Jelsoft Enterprises Ltd.