NAME for the MPT or CAPM-based diagram with the hyperbola and tangent line?

Discuss all general (i.e. non-personal) investing questions and issues, investing news, and theory.
User avatar
nisiprius
Advisory Board
Posts: 35706
Joined: Thu Jul 26, 2007 9:33 am
Location: The terrestrial, globular, planetary hunk of matter, flattened at the poles, is my abode.--O. Henry

Re: NAME for the MPT or CAPM-based diagram with the hyperbola and tangent line?

Post by nisiprius » Tue May 08, 2018 7:59 am

bobcat2 wrote:
Mon May 07, 2018 9:13 pm
Why would two bond funds hedge risk, but one bond fund not hedge risk? If the Vanguard Total Bond Market Index Fund does not hedge the risk of the stock funds, what would be an example of two bond funds that would?
With two bond funds you can duration match a liability over time by changing the weighted average duration of the two funds over time. If the two funds are a ST TIPS fund and a LT TIPS fund the duration matching of the funds is equivalent to holding a TIPS ladder. BTW, this is what DFA does with TIPS funds in their TDFs.

BobK
Well, at this point I'm pretty sure we're talking past each other... anyway I've ordered a second-hand copy of Bodie & al Financial Economics, 2nd edition, and I will see what I can get from it. I do not understand how a time-varying allocation to two different assets fits into what I take to be the standard MPT framework. Nor do I understand how a time-varying allocation to two different TIPS funds "protects against a loss" which is what you seemed to be saying, at one point, was necessary for you to call something a "hedge." It protects against a loss in a kind of partial or soft way, but so does a single TIPS fund. It's not as if the two-fund-duration-matched combination were likely to spike in value during a stock market crash.
Annual income twenty pounds, annual expenditure nineteen nineteen and six, result happiness; Annual income twenty pounds, annual expenditure twenty pounds ought and six, result misery.

User avatar
bobcat2
Posts: 5164
Joined: Tue Feb 20, 2007 3:27 pm
Location: just barely Outside the Beltway

Re: NAME for the MPT or CAPM-based diagram with the hyperbola and tangent line?

Post by bobcat2 » Tue May 08, 2018 7:44 pm

nisiprius wrote:
Tue May 08, 2018 7:59 am
Nor do I understand how a time-varying allocation to two different TIPS funds "protects against a loss" which is what you seemed to be saying, at one point, was necessary for you to call something a "hedge." It protects against a loss in a kind of partial or soft way, but so does a single TIPS fund. It's not as if the two-fund-duration-matched combination were likely to spike in value during a stock market crash.
You are immunizing your targeted income stream against interest rate risk by matching the weighted average duration of the bond funds against the duration of the targeted income stream. As the duration of the income stream shortens over time you need to shorten the weighted duration of the bond funds accordingly to keep the TIPS duration matched to the income stream. If you don't keep the durations matched, the TIPS assets cease being risk-free.

BobK
In finance risk is defined as uncertainty that is consequential (nontrivial). | The two main methods of dealing with financial risk are the matching of assets to goals & diversifying.

User avatar
nisiprius
Advisory Board
Posts: 35706
Joined: Thu Jul 26, 2007 9:33 am
Location: The terrestrial, globular, planetary hunk of matter, flattened at the poles, is my abode.--O. Henry

Re: NAME for the MPT or CAPM-based diagram with the hyperbola and tangent line?

Post by nisiprius » Tue May 08, 2018 9:00 pm

bobcat2 wrote:
Tue May 08, 2018 7:44 pm
nisiprius wrote:
Tue May 08, 2018 7:59 am
Nor do I understand how a time-varying allocation to two different TIPS funds "protects against a loss" which is what you seemed to be saying, at one point, was necessary for you to call something a "hedge." It protects against a loss in a kind of partial or soft way, but so does a single TIPS fund. It's not as if the two-fund-duration-matched combination were likely to spike in value during a stock market crash.
You are immunizing your targeted income stream against interest rate risk by matching the weighted average duration of the bond funds against the duration of the targeted income stream. As the duration of the income stream shortens over time you need to shorten the weighted duration of the bond funds accordingly to keep the TIPS duration matched to the income stream. If you don't keep the durations matched, the TIPS assets cease being risk-free.

BobK
But it doesn't "protect against a loss."

And I'm not sure that they are risk-free if they are bond funds, because you cannot actually match the individual bonds in the funds against income requirements.

If, let's say, you simply let a TIPS ladder unwind, i.e. stop rolling over the bonds as they mature, you get a series of payments as each bond matures that are inflation-protected and in my opinion risk-free (including inflation risk).

As a side effect of this process, the duration shortens.

(Incidentally, this is something close to what the defunct PIMCO Real Income 2019 and 2029 funds actually did).

But I don't think the converse applies. A TIPS ladder is risk-free and has decreasing duration. A long and short-term TIPS fund, with the allocation systematically shifting away from the longer-term TIPS fund and toward the short-term fund also has decreasing duration, but I don't think it's equivalent and I don't think it's risk-free.

Selling the long-term fund incrementally is not the same as letting each bond remove itself from a ladder by maturing. Whenever you sell the fund you are selling a small portion of each of the bonds in the fund, not just the bonds that are at or close to maturity. Some of them will be far from maturity, and you will be constantly exposing yourself to market and interest rate risk.

It may well be superior to 100% Total Bond, but it is a matter of degree. It is not as if Total Bond were risky and a shifting-allocation-combination of VIPSX and VTIPX were risk free. Total Bond is more risky, the duration-adjusted TIPS pair is less risky.
Annual income twenty pounds, annual expenditure nineteen nineteen and six, result happiness; Annual income twenty pounds, annual expenditure twenty pounds ought and six, result misery.

User avatar
bobcat2
Posts: 5164
Joined: Tue Feb 20, 2007 3:27 pm
Location: just barely Outside the Beltway

Re: NAME for the MPT or CAPM-based diagram with the hyperbola and tangent line?

Post by bobcat2 » Tue May 08, 2018 10:50 pm

nisiprius wrote:
Tue May 08, 2018 9:00 pm
But I don't think the converse applies. A TIPS ladder is risk-free and has decreasing duration. A long and short-term TIPS fund, with the allocation systematically shifting away from the longer-term TIPS fund and toward the short-term fund also has decreasing duration, but I don't think it's equivalent and I don't think it's risk-free.

Selling the long-term fund incrementally is not the same as letting each bond remove itself from a ladder by maturing. Whenever you sell the fund you are selling a small portion of each of the bonds in the fund, not just the bonds that are at or close to maturity. Some of them will be far from maturity, and you will be constantly exposing yourself to market and interest rate risk.

It may well be superior to 100% Total Bond, but it is a matter of degree. It is not as if Total Bond were risky and a shifting-allocation-combination of VIPSX and VTIPX were risk free. Total Bond is more risky, the duration-adjusted TIPS pair is less risky.
You are selling from the ST TIPS fund and then adjusting the ratio between the two TIPS funds. It's basically the same thing as a TIPS ladder. In reality, neither the funds nor the ladder will be perfect hedges, but the amount of imperfection in either case will be small.

BTW this is what DFA does in it's retirement target date funds (TDFs). Here is Robert Merton briefly describing the duration matching in DFA TDFs using two TIPS funds.
Level 2 type income, like a fixed-time annuity, provides a periodic payout of inflation-protected income, for a fixed time horizon. As a likely default the horizon may be set at the life expectancy of the participant as of the time of retirement. The assets assigned to level 2 income are invested in an inflation-indexed fixed-income portfolio that is duration-matched to the targeted stream of payments, in the same process and in the same funds that are used for the ‘risk-free’ asset replication of the conservative income goal in the Managed DC plan in the accumulation period. Thus, payouts are made based on a 96 per cent estimated probability of being able to make those payments, creating, in effect, a reserve to cover imperfect hedging. Hedging of level 2 income payments should be more accurate than that of the conservative income goal in Managed DC during the accumulation period because the duration of the level 2 income will be materially shorter than during the accumulation period and all the assets used to support level 2 incomes will be investable funds rather than also including future contributions.
LINK - https://www.nestpensions.org.uk/schemew ... cs,PDF.pdf

For example, DFA's 2015 retirement year target date fund is 14% LT TIPS fund, 61% ST TIPS fund, and 25% equity funds.

BobK
In finance risk is defined as uncertainty that is consequential (nontrivial). | The two main methods of dealing with financial risk are the matching of assets to goals & diversifying.

User avatar
nisiprius
Advisory Board
Posts: 35706
Joined: Thu Jul 26, 2007 9:33 am
Location: The terrestrial, globular, planetary hunk of matter, flattened at the poles, is my abode.--O. Henry

Re: NAME for the MPT or CAPM-based diagram with the hyperbola and tangent line?

Post by nisiprius » Wed May 09, 2018 8:20 am

Bob, for the record--I doubt that either of us thinks it amounts to anything--since about 2012 the bond component in Vanguard's target date funds has included a glide toward shorter duration at the same time as it replaces some nominal with inflation-protected bonds.

Target Retirement 2025, duration 6.65 years; bonds are 68% Total [US] Bond, 32% Total International Bond.

Target Retirement Income, duration 5.73 years; bond allocation is 53% Total Bond, 23% Total International Bond, 24% Short-term TIPs.
Annual income twenty pounds, annual expenditure nineteen nineteen and six, result happiness; Annual income twenty pounds, annual expenditure twenty pounds ought and six, result misery.

User avatar
bobcat2
Posts: 5164
Joined: Tue Feb 20, 2007 3:27 pm
Location: just barely Outside the Beltway

Re: NAME for the MPT or CAPM-based diagram with the hyperbola and tangent line?

Post by bobcat2 » Wed May 09, 2018 9:13 am

nisiprius wrote:
Wed May 09, 2018 8:20 am
Bob, for the record--I doubt that either of us thinks it amounts to anything--since about 2012 the bond component in Vanguard's target date funds has included a glide toward shorter duration at the same time as it replaces some nominal with inflation-protected bonds.
I couldn't disagree more strongly. The Merton approach is basically the way I have structured my portfolio and I believe it makes a huge difference. My portfolio is performing much like a pension and my investing has become close to worry-free.

The DFA approach is designed to provide safe retirement income. The Vanguard approach is apparently designed to lessen portfolio volatility in retirement. So if your goal is to provide safe retirement income, then DFA is the superior approach. If instead your goal is to stabilize your level of wealth in retirement, then Vanguard is better. Vanguard's glide path to shorten duration reduces portfolio volatility, it does little in the way of providing safe retirement income.

Here is Wade Pfau discussing the difference between the DFA retirement income target date funds and traditional target date funds such as those from Vanguard. I came to my views on this difference before I read Pfau's article, but my views and his on this issue are in near total agreement.

Meeting Retirement Goals with Dimensional’s Target-Date Retirement Income Funds
Link - https://www.advisorperspectives.com/art ... come-funds
The essential point to understanding how target-date retirement income funds (DFA TDFs) differ dramatically from traditional target date funds is to realize that controlling account balance volatility and spending volatility are two entirely different matters. It is easy to overlook this point in our world where something like the 4% rule tends to be the default retirement strategy. The 4% rule indicates that an inflation-adjusted income equal to 4% of the retirement-date wealth level will be sustainable from a portfolio of stocks and bonds. Its success is justified because it worked historically or can be expected to work on average, rather than because any effort is made to link how current interest rates or capital market expectations relate to a sustainable spending rate.

Target-date funds focus on controlling portfolio volatility as the target (retirement) date approaches. This focus may be due either to the belief that capital preservation becomes the primary concern of the retiree near their target date, or due to a naïve belief (because something like the 4% rule is in the back of one’s mind) that reduced portfolio volatility is equivalent to sustainable and non-fluctuating spending power.

To understand why a stable account balance does not necessarily translate into sustainable income, we must take a step back to view the spending objective for retirement. Because target-date funds, by design, must be generalized to provide a reasonably close approximation to the typical investor needs, DFA views the spending objective for the target-date income fund is to provide support for 25 years of inflation-adjusted spending commencing at the target date. This could reflect ages 65 to 90, for instance. Twenty-five years extends beyond the life expectancy for 65 year olds, but there is still risk of outliving this time frame. However, lengthening time frames require spending less to extend assets out for longer, and DFA views 25 years as a reasonable compromise between supporting longevity and supporting higher income for the typical investor.

The next step is to recognize which variables create the largest impact on the amount of wealth needed to support 25 years of inflation-adjusted spending. General market volatility may be important for those seeking a higher income through the inclusion of growth assets with a risk premium, but it is important to assess the importance of interest rates and inflation. This is why traditional target-date funds fail to support a retirement spending objective. They rarely make sufficient effort to coordinate the investments to provide proper hedging for interest rate and inflation variability.
BobK
In finance risk is defined as uncertainty that is consequential (nontrivial). | The two main methods of dealing with financial risk are the matching of assets to goals & diversifying.

User avatar
nisiprius
Advisory Board
Posts: 35706
Joined: Thu Jul 26, 2007 9:33 am
Location: The terrestrial, globular, planetary hunk of matter, flattened at the poles, is my abode.--O. Henry

Re: NAME for the MPT or CAPM-based diagram with the hyperbola and tangent line?

Post by nisiprius » Wed May 09, 2018 9:47 am

I think we are talking past each other again. My point was simply that DFA isn't the only company using a pair of bond funds and relatively adjusting them according to the participant's age. I don't think Vanguard's approach amounts to anything because the change is so small and the final TIPS allocation so small. I expected you to agree with me on my judgement of Vanguard's approach.
Annual income twenty pounds, annual expenditure nineteen nineteen and six, result happiness; Annual income twenty pounds, annual expenditure twenty pounds ought and six, result misery.

User avatar
nisiprius
Advisory Board
Posts: 35706
Joined: Thu Jul 26, 2007 9:33 am
Location: The terrestrial, globular, planetary hunk of matter, flattened at the poles, is my abode.--O. Henry

Re: NAME for the MPT or CAPM-based diagram with the hyperbola and tangent line?

Post by nisiprius » Wed May 09, 2018 10:26 am

Bob, last try to see if I can catch your drift. Remember, my intended topic is "understanding what efficient frontier diagrams with tangent lines mean," not "designing practical real-world product combinations to support retirement."

I think this is what you are saying.

1) Real-world retirement planning should not be done on the basis of systematic purchases-then-withdrawals, from a portfolio of traditional mutual funds based on securities (stocks, bonds, near-cash)

2) The asset combination should be divided conceptually into a risky part and a low-risk part.

3) As a practical, real-world matter, the low-risk part should not be a simple investment into low-risk things like Treasury bills, bank accounts, money market mutual funds, or short-term bond market funds.

4) The low-risk part is better structured as a sophisticated, planned group of actively hedged holdings, plus insurance-company annuity products. Overall, this group that may be founded on underlying risky assets, but is risk-free within the context of the individual retiree's total picture by virtue of defeasing, liability matching, contractual guarantees, etc.

5) These products actually do not make sense to plot on an efficient frontier diagram, because their nature is not adequately captured by their return, standard deviation, and annual or monthly correlation with other assets. They are active bits of machinery that adjust themselves year to year to the retiree's individual circumstances and to the performance of other assets in the portfolio.

6) Therefore, the way to treat these surrogate risk-free assets is to accept them as risk free from the point of view of the retiree, plot them on the Y axis as if they were an ideal risk-free asset with the same return as the surrogate, and use that to determine the optimum allocation among the remaining assets. That is, use MPT for the riskier assets, but don't try to incorporate the actively-managed, hedged, defeased, insurance-like components into the MPT framework.
Annual income twenty pounds, annual expenditure nineteen nineteen and six, result happiness; Annual income twenty pounds, annual expenditure twenty pounds ought and six, result misery.

User avatar
bobcat2
Posts: 5164
Joined: Tue Feb 20, 2007 3:27 pm
Location: just barely Outside the Beltway

Re: NAME for the MPT or CAPM-based diagram with the hyperbola and tangent line?

Post by bobcat2 » Wed May 09, 2018 11:10 am

nisiprius wrote:
Wed May 09, 2018 10:26 am
Bob,
I think this is what you are saying.

1) Real-world retirement planning should not be done on the basis of systematic purchases-then-withdrawals, from a portfolio of traditional mutual funds based on securities (stocks, bonds, near-cash)

2) The asset combination should be divided conceptually into a risky part and a low-risk part.

3) As a practical, real-world matter, the low-risk part should not be a simple investment into low-risk things like Treasury bills, bank accounts, money market mutual funds, or short-term bond market funds.

4) The low-risk part is better structured as a sophisticated, planned group of actively hedged holdings, plus insurance-company annuity products. Overall, this group that may be founded on underlying risky assets, but is risk-free within the context of the individual retiree's total picture by virtue of defeasing, liability matching, contractual guarantees, etc.

5) These products actually do not make sense to plot on an efficient frontier diagram, because their nature is not adequately captured by their return, standard deviation, and annual or monthly correlation with other assets. They are active bits of machinery that adjust themselves year to year to the retiree's individual circumstances and to the performance of other assets in the portfolio.

6) Therefore, the way to treat these surrogate risk-free assets is to accept them as risk free from the point of view of the retiree, plot them on the Y axis as if they were an ideal risk-free asset with the same return as the surrogate, and use that to determine the optimum allocation among the remaining assets. That is, use MPT for the riskier assets, but don't try to incorporate the actively-managed, hedged, defeased, insurance-like components into the MPT framework.
In other words, don't put them on the efficient frontier. Yes that seems like a reasonable summary. But an important point is that this is simply an extension of Tobin's basic framework of the separation property. Merton and others have made Tobin's work more realistic by moving from a static to a dynamic framework and adding hedging assets to the model. As Tobin remarked many years ago - Mine are the first words on this subject, not the last. Tobin's insight from 60 years ago can be used today as a practical guide to portfolio construction. It's Tobin's extension of MPT that makes the Markowitz MPT model a useful guide for today's individual investor.

To put it another way, Markowitz's MPT is a practical framework if you are an institutional investor such as an investment bank, college endowment fund, or the Catholic Church. MPT is not a practical foundation for the individual investor. For the individual investor you need to start with the separation property. Institutional investors have investment horizons measured in centuries, or in the case of the Church, millennia. Individuals have investment horizons of a few decades. Institutional investors are often both accumulating assets and disbursing assets. Individual investors accumulate assets for a few decades and then decumulate assets for a few decades. These are quite different processes and, as Markowitz himself has noted, the MPT framework was always intended for institutional investors - not individual investors.

BobK
In finance risk is defined as uncertainty that is consequential (nontrivial). | The two main methods of dealing with financial risk are the matching of assets to goals & diversifying.

User avatar
Epsilon Delta
Posts: 7335
Joined: Thu Apr 28, 2011 7:00 pm

Re: NAME for the MPT or CAPM-based diagram with the hyperbola and tangent line?

Post by Epsilon Delta » Wed May 09, 2018 12:51 pm

bertilak wrote:
Mon May 07, 2018 9:56 am
In answer to the question in my previous post...
bobcat2 wrote:
Mon May 07, 2018 8:54 am
Yes that is one purpose of the separation property, but there can be more than two risky assets. What that means is that everyone who picks the same surrogate for the risk-free asset and holds the same risky assets, and has the same expectations for the returns, variances, and covariances of the risky assets should hold the risky assets in the same proportions. Both the retired low risk taking widow and the young willing to take lots of risk company executive should hold the two risky assets in the same proportions. (Note that while the returns and variances of the risky assets have to be estimated, the return of the risk-free surrogate is known and its variance is zero.)

So what it also says is that both the widow and the exec only account for risk in the overall portfolio by how they divide the portfolio between the risk-free asset and the combination of risky assets. The widow has a high proportion of her overall portfolio in the risk-free asset, but the exec has a low proportion in the risk-free asset.
Thanks! I see my understanding was right, if incomplete. I intentionally left out discussion of more than two risky assets to focus on the main idea. I believe it all applies to "n" risky assets, the diagram would then be n-dimensional, but the math to establish the shape and tangent point could be extended even if that was beyond my math skills!
It's worth mentioning two things, these don't disagree with the above but may add context.

While the separation theorem says you can construct any efficient portfolio as some combination of two portfolios it doesn't uniquely specify which two portfolios. In fact any two portfolios on the tangent line will do. For reasons outside of the math it makes sense to pick the zero risk asset and the tangent portfolio*, but you don't have to.

If there is no riskless asset there is still a separation theorem. You can take any two portfolios on the efficient frontier and every other efficient portfolio is some combination of these two. Again people usually pick the lowest risk portfolio (the apex of the hyperbola) as one of the two but you don't have to.

The separation theorem is one of the reasons two risky assets are often shown. You can crunch the numbers on a thousand risky assets to get the hyperbola. Now you can pick any two points on the hyperbola and use those two risky assets instead of the original thousand and you get the same results.

* From other arguments the tangent portfolio should also be the total market portfolio.

User avatar
nisiprius
Advisory Board
Posts: 35706
Joined: Thu Jul 26, 2007 9:33 am
Location: The terrestrial, globular, planetary hunk of matter, flattened at the poles, is my abode.--O. Henry

Re: NAME for the MPT or CAPM-based diagram with the hyperbola and tangent line?

Post by nisiprius » Wed May 09, 2018 1:28 pm

Epsilon Delta wrote:
Wed May 09, 2018 12:51 pm
...It's worth mentioning two things, these don't disagree with the above but may add context.

While the separation theorem says you can construct any efficient portfolio as some combination of two portfolios it doesn't uniquely specify which two portfolios. In fact any two portfolios on the tangent line will do. For reasons outside of the math it makes sense to pick the zero risk asset and the tangent portfolio*, but you don't have to.

If there is no riskless asset there is still a separation theorem. You can take any two portfolios on the efficient frontier and every other efficient portfolio is some combination of these two. Again people usually pick the lowest risk portfolio (the apex of the hyperbola) as one of the two but you don't have to.

The separation theorem is one of the reasons two risky assets are often shown. You can crunch the numbers on a thousand risky assets to get the hyperbola. Now you can pick any two points on the hyperbola and use those two risky assets instead of the original thousand and you get the same results.

* From other arguments the tangent portfolio should also be the total market portfolio.
Thanks, that's helpful.
Annual income twenty pounds, annual expenditure nineteen nineteen and six, result happiness; Annual income twenty pounds, annual expenditure twenty pounds ought and six, result misery.

User avatar
bobcat2
Posts: 5164
Joined: Tue Feb 20, 2007 3:27 pm
Location: just barely Outside the Beltway

Re: NAME for the MPT or CAPM-based diagram with the hyperbola and tangent line?

Post by bobcat2 » Wed May 16, 2018 3:04 pm

Here's Zvi Bodie earlier this month talking about retirement planning. While he doesn't explicitly mention the separation property, it is definitely the framework he is using in planning for retirement. For the surrogate for the risk-free asset he discusses duration matching with ST & LT TIPS funds.

Link to interview - https://assettvus.getmediamanager.com/v ... 88768b4714

In Bodie's presentation slides at the above retirement conference, Zvi discusses how one adds Merton's dynamic continuous time model and hedging to Tobin's separation property to produce best practice retirement plans.

BobK
In finance risk is defined as uncertainty that is consequential (nontrivial). | The two main methods of dealing with financial risk are the matching of assets to goals & diversifying.

User avatar
alec
Posts: 2905
Joined: Fri Mar 02, 2007 2:15 pm

Re: NAME for the MPT or CAPM-based diagram with the hyperbola and tangent line?

Post by alec » Wed May 16, 2018 6:51 pm

bobcat2 wrote:
Wed May 16, 2018 3:04 pm
Here's Zvi Bodie earlier this month talking about retirement planning. While he doesn't explicitly mention the separation property, it is definitely the framework he is using in planning for retirement. For the surrogate for the risk-free asset he discusses duration matching with ST & LT TIPS funds.

Link to interview - https://assettvus.getmediamanager.com/v ... 88768b4714

In Bodie's presentation slides at the above retirement conference, Zvi discusses how one adds Merton's dynamic continuous time model and hedging to Tobin's separation property to produce best practice retirement plans.

BobK
Was his presentation recorded?
"It is difficult to get a man to understand something, when his salary depends upon his not understanding it!" - Upton Sinclair

User avatar
LadyGeek
Site Admin
Posts: 45036
Joined: Sat Dec 20, 2008 5:34 pm
Location: Philadelphia
Contact:

Re: NAME for the MPT or CAPM-based diagram with the hyperbola and tangent line?

Post by LadyGeek » Wed May 16, 2018 9:43 pm

camontgo wrote:
Fri May 04, 2018 10:03 am
...As you noted (and I failed to point out in my blog post referenced earlier)...the efficient frontier with SD is a hyperbola....so as you approach zero standard deviation for one of the assets you can visualize the plane slicing the cone moving closer to the peak (http://www.algebralab.org/lessons/lesso ... erbola.xml).
Sorry for the delay, but I wanted to mention that your algebra tutorial has a lot of broken images.

Here's one with a working example: Hyperbola Drag point "P" and see how the distance between "P to F" and "P to G" remains constant.

When you're done with that, proceed to: Conic Sections

Also see: Parabola
Oicuryy wrote:
Sun Apr 29, 2018 12:26 pm
dbr wrote:
Sun Apr 29, 2018 10:03 am
I doubt any of the curves involved on these charts are either hyperbolas or ellipses. Is there some reason the curves should be described by those exact mathematical figures?
This guy calls it a parabola and gives an equation for it.
http://www.calculatinginvestor.com/2011 ... rontier-1/

Ron
I should mention that camontgo is the blogger for The Calculating Investor.

His referenced blog post is in the wiki: Using open source software for portfolio analysis (Efficient frontier (mean-variance optimization))
Wiki To some, the glass is half full. To others, the glass is half empty. To an engineer, it's twice the size it needs to be.

User avatar
bobcat2
Posts: 5164
Joined: Tue Feb 20, 2007 3:27 pm
Location: just barely Outside the Beltway

Re: NAME for the MPT or CAPM-based diagram with the hyperbola and tangent line?

Post by bobcat2 » Wed May 16, 2018 10:14 pm

alec wrote:
Wed May 16, 2018 6:51 pm
bobcat2 wrote:
Wed May 16, 2018 3:04 pm
Here's Zvi Bodie earlier this month talking about retirement planning. While he doesn't explicitly mention the separation property, it is definitely the framework he is using in planning for retirement. For the surrogate for the risk-free asset he discusses duration matching with ST & LT TIPS funds.

Link to interview - https://assettvus.getmediamanager.com/v ... 88768b4714

In Bodie's presentation slides at the above retirement conference, Zvi discusses how one adds Merton's dynamic continuous time model and hedging to Tobin's separation property to produce best practice retirement plans.
Was his presentation recorded?
As far as I can tell Bodie's presentation, Optimal Lifecycle Saving and Investing, at the 2018 Investments and Wealth Institute annual conference was not recorded - at least not for the general public. Here's a link to the events schedule, which is the only information I can find on the internet about the conference.
https://investmentsandwealth.org/confer ... e/schedule

BobK
In finance risk is defined as uncertainty that is consequential (nontrivial). | The two main methods of dealing with financial risk are the matching of assets to goals & diversifying.

Post Reply