Why looking at inflation and average lifespan is insufficient for retirement planning

Methuselah, as per the Hebrew Bible, has lived longer than any other person in history to a ripe old age of 969 years. It is believed that over the centuries, his longevity gene has been passed on to his descendants, although it only expresses itself in some individuals. When this gene finds its expression, that person has the potential to live up to 969 years as Methuselah himself. The chosen ones have lived their long lives by not attracting much attention in various continents.

Astoundingly there is one such person in the San Francisco Bay Area and that too he happens to be your colleague, an IT professional. Coincidentally he too is named Methuselah by his parents, as if the gene’s intention and purpose hinted their way into the imagination of his parents. His recent visit to his doctor’s visit for an unrelated condition revealed this longevity gene in him. He is currently 50 years old and was planning on retiring next year, but he is now too stressed out to even think about it after this discovery.

He has discussed his problem with several Finance professionals.One Financial Analyst,who couldn’t get his head around the situation, told him that he shouldn’t retire unless he has a billion dollars. Another one said that since his remaining life expectancy may be 919 years, some 30 times an ordinary mortal, he needs 30X what an average person needs.

Can we help him out? You too are a 50 year male with an estimated lifespan of 30 more years. Can you figure out how much larger than yours does Methuselah’s nest egg need to be? Let’s assume that both you and he are equally good investors, i.e. your investments are expected to have a same (Return on Investment) ROI. Let’s plug in some numbers into the neat calculator at the following link and see what values we get.



Inputs (3 scenarios):

Current Age:              50

Retirement Age:        51

Tax Rate:                     25%

Yearly Expenses:        $100,000

(Inflation, ROI):          (2%, 10%), (2%,6%), (3.5%, 5%)



Incr. Funds Reqd. Infl: 2%, ROI:10% Infl:2%, ROI:6% Infl:3.5%, ROI:5%
51-80 (You) $1,524,000 $2,328,000 $3,225,000
81-100 $137,000 $575,000 $1,494,000
101-969 $39,000 $497,000 $4,481,000
51-969 (Methusaleh) $1,700,000 $3,400,000 $9,200,000


  • IftheROI is high 8% over inflation(which S&P 500 has done over the last three decades) then he needs only $170K more. Wow!!!
  • If theROI is reasonable 4% over inflationhe wouldneed over a million more.
  • However, if the ROI is only 1.5% over inflation, which we suspect will be the case for most investors going forward, he would needabout $6 million more.

Note: When we say x% over inflation produces such and such result, we are speaking loosely in approximate terms. You would get one result if you assume 2% inflation and 6% ROI than when you use 3.5% inflation and 7.5% ROI, even though both are cases with 4% over inflation, but in relative terms they would be close enough.

When ROI is high how long you live becomes a non-issue, but when ROI is low long life can be expensive. Even a percent or two of excess performance can alter the funds required to retire dramatically. Expecting excess returns over long term is unrealistic however.

Looking at the graph below, we can get a better sense of this phenomena.

retirement graph.JPG


This precise scenario of low returns and longer lifespans will be the curse that most Americans will likely face going forward for next few decades. To grasp the magnitude of a problem, we need to measure it. We have so far only investigated the impact of a couple parameters, namely Lifespan and ROI on the size of the nest egg. In order to obtain a better approximation, we need to introduce few more parameters/variables.


Fine tuning the Inputs:

Typically one uses a retirement calculator of some kind to figure this out. The answer one receives is only as good as the inputs provided. This article attempts to give some guidance in regard to these inputs.

In shortmoney is expected to grow at an assumed Rate of Return while getting depleted by rates of taxation and inflation during one’s life. One hopes thatthe money outlasts them.

Typical inputs may look as shown under the column “Simple”, referring to the simple model. Placed next to the typical inputs (that is values for the parameters or variables as we have referred to them)are the suggested inputs where we feel a change is warranted. At the bottom of the table are the results shown as Funds Required.

As yearly expenses vary from person to person and place to place a round figure of $100,000 is used to make it easy to estimate their Funds-Required by altering the expenses accordingly. If you expect your expenses to be $50,000 all you need to do is reduce the “Ongoing Needs” number shown below by 50%. However we do not recommend altering (Long Term Care) LTC fund and Unexpected Expenses based on your estimated yearly expenses as they would not decrease proportionately.


Parameters Simple Suggested
Current Age 50 Same
Retirement Age 51 Same
Lifespan 80 100
Rate of Return 6% 5%
Tax Rate 25% Same
Inflation Rate 2% 3.5%
Social Security $4000 Same
    COLA adjustment 2% Same
Income Needed $100000 Same


For someone with $4,000 Social Security Monthly benefits and $100,000 yearly expenses the funds required would be as shown below. For a change of $1,000 per month in SS benefits the amount changes by about $200,000.

Results Simple Suggested
Ongoing Needs $1,953,000 $3,844,000
Long Term Care $0 $300,000
Unexpected $0 $300,000
Tot. Funds Reqd. $1,953,000 $4,444,000


In case you are wondering if the funds required include the value of the home, it doesn’t. However when you proverbially kick the bucket, your house belongs to your estate, so from that respect as you wouldn’t be using up all the funds, Funds-Required is being somewhat overestimated though not by the full value of your home. It would be reasonable to reduce the Funds-Required by about a third of the value of your home to bring it closer to the actual value. If your home is worth $1.5 million, you may reduce Funds-Required by $500K bringing the amount to a wee bit below $4 million. 

Appendix A: Detailed discussion of the suggested inputs:

Life span Assumption (80 vs. 100):

The calculation of how long you need the money to last is based on your lifespan. Lifespans continue to increase, according to SOA report. In the past half-century, life expectancy for newborn American males improved by an average of almost two years each decade, from 66.6 years in 1960 to 75.7 years by  2010. For females, the average increase was about 1.5 years per decade, from 73.1 years in 1960 to 80.8 years by 2010.


More insidious than ignoring growing lifespans is the mistake of using the average lifespan as the input number. Would you drive a car that has a 50% chance of breaking down while driving to work? Wouldn’t you want it to get you to work with a 99% certainty?

You can find the 95 and 99 percentile figures here:


For a male of average health who is 50 years old, the 95 percentile for incremental life span is 47 years and if he is on the healthier side it is 50 years. If you are married you should consider the lifespan of the last survivor. The 95 percentile for the last survivor is 51.

Assuming lifespan of 100 instead of 80 the Funds Required jump from $1,953,000to $2,247,000

If you are a person who says, “I don’t want to die rich, I can’t take it with me!”, then you may be wondering if you really need to plan for such a long period and if there is a way to get away with saving less. This is called reduction of longevity risk. Well technically there is, but is it the right choice for you? You need to decide. One way would be to purchase an annuity that would pay you benefits until death. You can be certain about the payments and can feel comfortable that you are not leaving money on the table. However, they don’t come cheap. The amount you need to protect yourself with annuities often comes out to be even more than the funds we have estimated you would need to cover yourself until the age of 100 as the underlying interest rates they offer tend to be lower than what you may potentially earn in the stock market.

However annuities may still be appropriate for people that are risk averse and would like that certainty. See the Appendix A at the end for further discussion, if interested.


Inflation rate 2% vs GDP growth rate 3.5%

Using Inflation rate as the deflator is probably the most common error, especially for folks wanting to retire early. You may expect your needs to go up with inflation, but in reality they go up by a greater degree. We propose using expected nominal GDP growth rate as the deflator to reflect increasing standard of living and new necessities that arise over time.

As the economy expands in a few decades several new necessities will be forced on to you. Microwaves, Cell Phones, Fax Machines, Internet, personal printers have all become necessities in a lifetime. Before the days of the cell phones shopping malls had pay phones that you can use to call someone in an emergency. They don’t exist anymore. So even if you are willing to live with only things you had in the past, it may not be n option for you.

What then is a reasonable deflator? Nominal GDP growth is probably a decent proxy for this. GDP growth is comprised of Inflation, Population growth and Productivity improvements. Since US population is flattening out, we can expect GDP growth to track inflation + productivity improvements. Productivity improvements are likely to be around 1.5%. It is hard to know what the inflation will be but if we are assuming to be 2% the appropriate deflator for our calculations will be 3.5%.

So, plugging 3.5% instead of 2% (for inflation) the Funds Required move up to $3,190,000.


Rate of Return Assumption (6% vs 5%):

We were assuming 6% as the rate of return in our Simple Model. Based on our past history of the stock market 8% or higher may seem reasonable and 6% may even seem too conservative.  But let’s examine this a bit.

A reasonable estimate of stock market returns in the long run can be approximated by the equation:

Stock Market Returns = Nominal GDP growth + dividends + P/E expansion. 

Nominal GDP growth = Population growth + Productivity growth + Inflation.

Next few decades the population in US and much of Western Europe is expected to flatten out. What we are left with then is productivity growth which we may expect around 1.5% and inflation, admittedly difficult to predict, of about 2% which FED seems to be striving for. This brings us the Nominal GDP growth of 3.5%.

Dividends S&P 500 historically have been around 2%.

Many value investors have been warning that the current P/E ratios are unsustainable in the long term and that they are a result of present low interest rate environment and that they would revert back to lower values in the future. However there are those that argue that this low interest rate environment is the new normal as a fall out from the excesses of the previous decades as well as the aging of the developed world. If one were to look at Japan which experienced similar forces, one can’t be too optimistic about the stock market growth. In the absence of a crystal ball, let’s assume that the PE ratios will remain constant.

So 3.5% GDP growth and 2% inflation will bring us to 5.5% stock market return and since one wouldn’t hold 100% of their assets in the stock market, more than 5% is not realistic return on the overall portfolio.

Charles Schwab’s site has following estimates for what to expect in terms of future returns which we think are a bit too aggressive but should give you a decent idea of what the investment world is expecting. You will certainly notice that they are lot less than the historical results.


Note that even if stocks or some other asset were to return more than 5%, since no one can consistently predict which asset class outperforms, one should assume that their portfolio would underperform the best asset class. Besides it would be fool hardy not to maintain some cash or conservative investments.

If we reduce the ROI from 6% to 5% theFunds Required jump to $3,844,000.


Long Term Care Expenses:

As people are living longer more and more people are affected by disabilities that require long term care either in the home or in a nursing facility. The type of disability that prevent you from performing your normal daily activities like, eating, bathing etc… without assistance are called PADL (Physical Activity Daily Activity) disabilities. PADL affects people as follows:

20% of people over 70 and 50% of people over 85 are affected.


You would need to set aside funds for possible long term care expenses. There are many products out there that offer Long Term Care Insurance. Most of them have restrictions on how long they pay and in what conditions trigger and whether it would be in a nursing facility or at home and so on. These products are somewhat controversial, and require sufficient research to find one that you can be comfortable with. One option is to self-insure or in other words save enough.

Without being too precise in order to cover additional long term care expenses based on various estimates for premiums in different articles and working backwards it is probably reasonable to set aside $150,000 if you are a 50 year old single person and about $300,000 if you are married and trying to cover both of you.  Our number moves up to $4,144,000.

Throw in some unanticipated expenses, like your children needing some help or someone suing over some negligence and so on, we are staring at a $4.5 million figure.

A question often asked is, “Is this including your home or excluding your home?” The answer depends on whether you estimated your annual expenses, in our example of $100,000, considering home ownership or renting. If you need $100,000 a year even after owning a home, then the amount we have come up is in addition to your home. However when you are ready to proverbially kick the bucket you still own your house, therefore the Funds-Required is overestimated somewhat.


APPENDIX B: Annuities

An article on inflation adjusted income annuity


An inflation-adjusted annuity aims to solve the problem by giving you an automatic cost-of-living increase every year. But the cost is steep. A $100,000 inflation-adjusted annuity policy from Principal Life Insurance offers a $379 monthly payout for a 65-year-old man; American General offers a $363 monthly check.

Immediateannuity.com has the quotes you may want to refer to.

Joint Life with 20 year certain for 50 year old female and 54 year old man $3720 before tax if one invests $1 million. That means they would need to invest about $3 million to guarantee $100k per year after tax (assuming 25% tax rate). This does not protect against inflation.


Non Dualism, Advaita and Physics


Scientific model for Vedanta metaphysics

Delving into the interconnections between various branches of knowledge is always interesting, especially interesting is the connection between scientific laws and Vedantic metaphysics.  Two themes, dualism and non-dualism had been debated by Vedantic scholars fiercely for generations. In this blog we will look at dualism and non-dualism through a scientific lens.

Two branches of metaphysics, dualism and non-dualism are as different as the scientific laws in classical physics and quantum physics. Surprisingly each of these two branches of Vedanta map rather well to the underlying notions in the two branches of physics. That, primarily is the subject of this blog.

We will first look at Advaita (non-dualism) which maps to laws of classical physics and Vishistdvaita (qualified non-dualism) and Dvaita (dualism) next, which seem to map to quantum physics.

Advaita – Classical Physics – No Free Will — Non Dualism

Image result for shankaracharya


Issac Newton

Advaita school holds that there is One Soul that connects and exists in all living beings, regardless of their shapes or forms, there is no distinction, no superior, no inferior, no separate devotee soul (Atman), no separate God soul (Brahman).The Oneness unifies all beings, there is divine in every being, and that all existence is a single Reality. (Source: w

In classical Physics, specific cause produces a specific effect on an object. For example, Newton’s First Law of Motion states that an object stays at rest or in uniform motion unless compelled by an external force. Second and Third Laws of Newton specify what the outcome will be once the external force is applied. Similarly in chemistry, we expect a combination of specific elements in specific proportions to produce same specific reaction each time. And so is the case in most other branches of Science. Causes produce effects and they are specific and predictable.

Imagine a world, filled only with inanimate objects, things won’t be still. Wind will still blow, rivers will still run. Stones will still turn to dust and dust will still morph into mountains. However nothing happens by itself or unexpectedly. Every change and movement in an object will be the result of some other force acting on it, a continuum of actions and reactions inexorably, proceeding as if with a purpose. Each atom and molecule busily doing what have to or compelled to by the forces acting on them which it turn were set in motion by something else that acted on them before.


You can see that by mapping out every physical force in play in the universe on any given day, you can predict everything that would happen the day after.  And forever into the future. Therefore all changes are dependent on the previous changes and the outcomes are preordained and predictable. In this system there is no freewill. All actions and reactions are connected inextricably as one unit with no force, change or thing having a choice to alter course of what is to be.

Physical vs Psychological?

Perhaps inanimate objects are pushed, pulled and altered by forces beyond their control, but surely we humans control our destiny, right? Even animals and plants don’t follow predictable paths. They adapt, change their course — deer runs from a tiger, elephant travel for miles seeking waterholes in Serengeti. While some manage to survive others perish. Surely, there is no way that this model of predictability and interdependency that applies to inanimate world applies to animals and humans. Or does it?

Let’s look at humans as we are likely the most free willed species. Isn’t our current thought merely an outcome of the interaction between our previous thought, external and internal inputs, signals that reach our brain, our memory, and our biological and psychological constitution?

Our physical, biological and emotional makeup is what we are born with. Encoded in our genes are our proclivities that we don’t choose but inherit.  From the moment we gain consciousness we begin to react to stimuli. Stimuli leading to sensations, thoughts, conclusions and updated memory. Sometimes thoughts might lead to action and other times they don’t. But regardless, our memory and personality are modified. Each state (becomes a cause) leads us to next step (an effect). Is there a point where we make a choice? Do we say, “I won’t think that way but this way”? Isn’t such a thought itself an outcome of a previous thought and experience that happens automatically? How can this cycle automatic cycle be broken?

Can a thought spring from nowhere? Without a stimulus, without a previous thought, a new thought can occur only then can we say we are able to make a choice.  If not, we are as much guided by cause and effect laws as inanimate objects are by laws of motion.

If our thoughts and hence our destiny can’t be controlled by us, how can there be free will?

Without getting mired in semantics, one can draw an analogy between the set of forces and laws of nature and the universal soul aka Brahman aka Ishvara. Under this model we just follow these laws of nature and an interconnected part of the whole along with all the other life forms and non life forms. Therefore the laws of classical physics seems to be consistent with the non-dualism (Advaita) model.

Dvaita (Dualism) — Quantum Mechanics — Free Will — Dualism

Neils Bohr

After all, we intuitively feel that we are choice makers and not just automatons. Therefore, modeling brain as a machine doesn’t seem right. Perhaps brain does not follow the cause and effect laws like physical objects. May be there is no explanation or analogy in science for its behavior. Wait! maybe there is.

Models in Quantum Mechanics that deal with sub atomic particles do in fact allow for the possibility of multiple simultaneous outcomes which only collapse into a single state when observed. Perhaps, our brain too takes in all the inputs and comes to a conclusion by choosing between multiple alternatives. May be that choice is not made without the interference of some mysterious entity that may or may not be within us. Hence the decision cannot be predicted even if we can replicate the position and movement of every atom and molecule inside and outside our body and every signal  the brain receives. May be it has certain independence to make a choice guided by some mysterious force that manifests itself that is not strictly bound by laws of nature.

quantum weirdness.jpg

Shooting a photon on to a screen makes it land at different places on the screen each time even if all the variables are controlled. However it lands at some locations more often than others. Similarly we too based on our past experience are more likely to make certain decisions than others, but even if we can go back in time with all the conditions being same up to that point as the last time a decision was made, maybe we can make a different decision like the electrons or photons. But what accounts for this variability (or freedom if we can call it that)?

If the thought is coming from outside, who or what is it coming from? Is that still our thought? Are we in fact two? Us with the physical part that reacts and another part that we may call soul? Or is there something outside of us that guides all our actions, call it god or some super soul? If there is a super soul how much choice do we have in our actions?


Vedantic  philosophy has an answer for this. Vishistadvaita (qualified non dualism) differentiates between our physical being (ajiva) and our soul (jiva). This soul (jiva) is capable of introducing this randomness or free will which lets us not be totally bound by strict rules of nature but have a little bit of freedom albeit bound by a probabality distribution, sort of like a teenager allowed to go out once a week on weekends, but they get to choose whether it is on Saturday or Sunday.

In quantum mechanics world, electrons and photons behave as if they have a soul of their own, not bound by the force that ejected them onto the screen.  They reach a spot that can’t be predicted exactly although bound by a probabilistic distribution. Therefore quantum physics model seems to be consistent with VishistAdvaita and Dvaita models.


Some thoughts on free will

Although I don’t intend to get into the spiritual aspects of these schools of thought too much, it is interesting that ultimate goal of human existence is to achieve Mukti or salvation, a release from human bondage by surrender in vishistAdvaita and deep understanding of interconnectedness in Advaita.

Since surrender seems to imply giving in, sort of like the teen saying, dad/mom you decide when I can go out as if the freedom to make a choice is a burden.

The third school of thought Dvaita (dualism) goes a little bit further. Not only believes in the existence of souls that are distinct from the Univerversal soul/laws of nature but classifies the souls into three categories. There too the goal seems to be to give up your free will and let the universal soul express itself through you and there by merge or cease to exist as an independent soul.

I am digressing a bit from a strict scientific analogy into the spiritual beliefs, but it is relevant to understanding the scope and value of free will as it relates to dualism and non dualism and spiritual and religious beliefs.

Counter intuitive to western thought, where the desire is to live as long as possible, struggle and fight with passion as many battles as possible, skydive and drive fast cars to feel alive and exercise your freewill and uniqueness to make a mark on the world, the Vedantic notions seem more in line with the notion of either identifying yourself with all of the world, universal soul or surrendering yourself depending on the school of thought, but a common theme is not to celebrate uniqueness and free will but to eschew it and detach oneself from his or her own soul to merge with or give in to the universal soul.

Ancient Greeks and Ancient Indians:

Another extremely interesting connection one finds while inquiring into these themes is the similarity in the types of questions Greek philosophers were asking and the notions they had come up with starting with  4th century BC and the ideas in Hindu Vedas. This by the way is also true with ancient Indian medicine and ancient Greek medicine. In the ancient world Greeks and Indians seem to have shared ideas or were inspired by each other.

Capturing Closed End Fund Discounts

Every wave regardless of how high and forceful it crests,

must eventually collapse within itself.

Stefan Zweig



  • Closed-end funds rarely trade in line with their net asset values. They trade at a discount or a premium. Most trade at a discount with the discount itself raising and falling with the alternating optimism and pessimism of the investors. Buying a fund when the discount widens beyond its long term average and selling when it narrows has produced excess returns for professional investors. These excess returns are made possible by the tendency for the discounts to mean-revert. Multiple academic studies have confirmed this phenomena.However I think in the current environment in which the interest rates are more likely to go up than down over the coming years, this strategy carries with it significant interest rate risk as many of these closed-end funds are income oriented funds that are sensitive to interest rates.
  • A strategy outlined in this blog, although doesn’t remove the interest rate risk completely, could reduce uncertainty, by identifying funds whose discounts reduce in defined time frames. This involves buying funds  after (or when possible before) they have  announced steps to reduce the discount.

Some basics:

  • If you are not familiar with what a closed-end fund is, you may want to make yourself familiar with them by reading up on the net. You can also begin here:



The idea behind buying closed-end funds trading at a discount is as follows. Open-end fund shares trade at their Net Asset Values, where as closed-end funds can trade at a discount or premium to their Net Asset Values. Any discount reduction adds to your over all return. The rest of the nuance is about deciding when to buy and sell and what type of funds to buy.


Fund A: Type: Open End Fund B: Type: Closed End
Net Assets (1/1/00): $10 Net Assets (1/1/00): $10
Price (1/1/00): $10 Price (1/1/00): $8 $8
Discount (1/1/00): 0% 0% Discount (1/1/00): 20%
Net Assets (12/31/00): $10.30 Net Assets(12/31/00): $10.30
Price (12/31/00): $10.30 Price (12/31/00): $9.0
Discount: (12/31/00): 0% Discount (12/31/00): 10%
Dividends: $0.20 Dividends: $0.20
Total Return: ($0.30 +$0.20)/$10 = 5% Total Return: ($.30+$0.2+($9-$8))/$10 = 15%


Trading Strategies:

Strategy I: Buying funds whose current discount is much greater than their long term average discount.

Most professionals use the strategy, as also mentioned  in the above article, which involves buying a closed-end fund when it trades at a discount that is greater than its long term average discount. For example, if the fund’s average discount over last 3-years has been 10% and the current discount is a 2 sigma deviations below it, it might be a good time to buy and sell it when the discount gets back to 10%.

There is considerable academic research that has documented this phenomena of mean reversion and the opportunities it provides to vigilant investors.

There are couple of risks that need to be highlighted:

  • It is possible that any gain accrued due to discount reduction can be offset by decrease in the Net Asset Value of that fund.
  • Another concern is that many of the studies that observed exceptionally high positive even over long periods were conducted in an environment of secularly declining interest rates an environment in which Net Asset Values are also likely to go up. This may not be the case in the future.

The following paper listed below is a more technical sophisticated version of buying funds that are trading well below their long term average discount while at the same time short selling funds that are trading well above their long term averages.

This reduces some of the interest rate risk but is not easy for casual investors to implement.


As the technique outlined above involves shorting that has significant risks, I do not recommend it for casual investors. It is particularly risky to short closed-end funds as they tend to be illiquid, may be hard to and expensive to borrow, and you may also be forced to cover your shorts at inopportune times.  Additionally, lot of closed-end funds have large distributions/dividends that as a short seller you owe the buyer until you close your position.

It is however a good paper that provides several interesting insights, even if you skip over the math. One important one is that fixed income and international CEFs exhibit mean reversion of discounts better than domestic equity CEFs.

Coming back to the main purpose of this blog is to highlight strategy II that is usually not talked about much in the literature, perhaps because the opportunities to apply it come by only occasionally. Given the current environment of low interest rates in which closed-end fund fees are being viewed with skepticism by the investors and the growing clout of activists I think will make these opportunities come up more frequently in the coming years.

Strategy II: Buy when you expect or even after announcement that a fund is taking steps to narrow or eliminate the discount.

There is something to be said for capturing the smaller discount that exists after a fund has announced definite plans to reduce the discount than trying to capture a larger discount by buying a fund trading at a large discount and waiting for the “mean reversion” to do its trick. In a normal set of conditions I wouldn’t have much of a preference between the two strategies but in the current conditions in which we are unable to predict when the interest rates will rise, but know that they will, being nimble has its appeal.

Implementing Strategy II:

There are couple of different ways this can be implemented:

(A) Easiest is to buy these funds immediately after the announcement of liquidation, open-ending, conversion to and ETF or some such discount reducing move. Even though significant amount of the discount gets narrowed on announcement, usually there is still a 4 to 5% discount even after a day or two. You need to take the time factor into consideration and figure out how long it would take for the discount to go to reduce or go to zero. If it takes eight months for the discount to go to zero from 4%, due to liquidation, that is equivalent of a 6% reduction on an annualized basis.

This discount reduction adds to whatever the fund was otherwise going to yield. If the fund was going to yield 3% either in terms of dividends or increase in the net asset value, a discount reduction of 6% (annualized) would add to that 3% and make it 9%.

Table below shows some of the closed-end funds in various stages of the discount reduction process after the fund has declared some sort of discount reduction steps:

Symb Discount Reduction Action


Date of Announcement Disc Two Days After Disc on 6/16/16 Disc Redn. Tot Retn.


Days Annualized tot. retn.
JGV Company agreed to put up a proposal to open end at Annual Meeting in late May’16. 5/16/16 -4.36% -3.14% 1.22% 1.97% 31 24.8%
ZF Buy back 15% of shares at 98% of NAV and conditionally 10% in the coming year. 4/5/16 -9.74% -8.48%1 1.27% 1.63% 72 8.5%
FAV Merging with ETF by Oct 30th ’16. Will receive NAV worth of ETF shares. 3/18/16 -4.37% -2.64% 1.73% 5.61% 90 23.3%
KHI Plans to liquidate. First liquidation distribution by Nov 30th, 2016. Some shareholders want to convert to ETF. 2/26/16 -4.26% -2.02% 2.24% 6.98% 111 23.4%
HYF Liquidating. Expected to be completed by June 30th, 2016. 10/13/15 -6.53% -1.06% 5.47% 4.47% 247 6.7%


RIT Will open endby June 30th, 2016. Redemptions subject to 1% fee.


9/30/15 -4.74% -0.0% 4.74% 19.42% 260 27.5%
LBF Liquidate by about Sept 2017. Lengthy wait might explain smaller discount reduction


7/10/15 -6.4% -4.5% 1.9% 3.46% 342 3.7%
DHG Liquidate by about March 2018. Lengthy wait might explain smaller discount reduction.


7/10/15 -7.5% -7.05% .45% -2.18% 342 -2.3%
CTF Is converting to ETF. Regulatory approvals taking long time. 12/19/14 -8.17% -3.4% 4.76% 3.58% 545 2.4%
Avg Annualized Return             13.1%
  1. ZF’s current discount is adjusted to account for the roughly 38% of the offered shares that were bought back at 98% of NAV recently.

Average Annualized Return: 13.1%

You shouldn’t take this number too seriously though as it is based on a small set and also, annualizing returns based on small holding periods as it was done for a few of the funds in the table above can skew the results easily.

The purpose is to demonstrate how the discount reduction enhances the yield.


(B) Although somewhat harder and more time consuming, if you can identify situations where you can predict with at least a 50% certainty that a fund is about to announce discount reduction steps, it is worth taking the risk and buying the shares.

For the same set of data listed in the above table if you could have bought each of the funds two days before the discount reduction announcement as opposed to two days after the Average Annualized Return would have been 28.4% as opposed to the 13.1%.

Often you will notice an activist investor pressuring the management to do something about the discount. If you have high confidence that the activist would succeed, it is worth taking the risk and buy before the announcement. You of course need to make sure that the discount hasn’t unduly narrowed based on too much optimism that the activist will succeed. If they don’t the discounts can go back to where they were before the activist’s involvement. Best place to identify such opportunities is by tracking the “13D” filings. There are websites that provide this information.


As only a few “activists” are really effective, you would want to be careful not to get excited every time you see a 13D filing.

The following are the most common steps CEFs take to reduce the discount:

(1) Converting the fund to an ETF

                (2) Converting it into an open end mutual fund

                (2) Liquidation of the fund

                (3) Merging  into one of their other funds

                (4) Buying back a percentage of shares close to NAV from the shareholders.

Note that not all the discount reduction announcements are the same. Buying back shares might decrease the discount after the announcement and go back to where it was again if the buyback is small.


Liquidation announcements are interesting as there is a finite time frame in which the discount will go to zero, but there are also couple of negatives:

  • Assets the fund sells do not earn anymore, which means NAV doesn’t increase as much.
  • If the fund has illiquid or hard to value assets then the liquidation value may be less than NAV on the books.

Conversion to an ETF and open-ending somewhat similar, but you want to make sure that it is not a drawn out process like it happened with CTF.

It’s worth noting that you do not have to wait for the liquidation or  the process of conversion to ETF to complete. You can get out if the discount narrows significantly and the additional return in waiting out to conclusion is not worthwhile.

Disclosure: I do own JGV, FAV, KHI, DHG and CTF, however I not offering any opinion on whether they are a good buy at this time. They are only mentioned to illustrate the general strategy.

Special Theory of Relative Distances

 Paradoxes in Theory of Special Relativity:

Theory of Special Relativity is counter intuitive for most of us mortals. I like finding analogies to make sense of it. Is there something in our experiential domain that exhibits similar weirdness? I think I have an example. This is not strict analogy but there is enough similarity to help you get comfortable with the Theory of Special Relativity.

Let me first list a few concepts from Theory of Special Relativity that are strange.

  • If you are travelling at velocity v1 and someone else is travelling at velocity v2 the relative velocity is not exactly (v2-v1) but it is slightly more. The difference between the real relative velocity and (v2-v1) is too small to measure at lower speeds but becomes apparent at high speeds.
  • Speed of light is constant relative to anything. No matter how fast you travel next to it, the relative velocity of light is always the same relative to you.
  • Nothing can travel faster than the speed of light.
  • If one twin travels at very high speed (something closer to the speed of light) and comes back, he or she would be younger than his/her twin who stayed back.
  • Time and Distance or not constant, at high speeds time slows and length contracts.
  • Relative Velocity does not does not change in a linear fashion. For example if you are travelling at 100 million miles/hour and your friend is travelling at 200 million miles per hour the relative velocity is 104.7 million miles per hour (note it is not 100 million miles per hour as mentioned in point 1). But also if your friend is travelling at 300 million miles per hour the relative velocity will be 214.3 miles per hour. Note that it is not 2*104.7 but even more.

A similar phenomenon on earth:

Is there a phenomenon that we can think of or experience that we can relate to more easily? I have such a thing for you in this article.

Let’s suppose that you and your friend have a cell phone app on your phones that can measure the linear distance between the caller and the receiver. He goes on a road trip by himself. He calls you once in a while to let you know he is safe and how far has travelled. He averages exactly 60 miles per hour and drives for 10 hours every day. Let us further suppose that you are living in a future time where the roads are perfectly flat and perfectly straight.

What results do we expect?

If he called you after an hour of driving, his odometer should read 60miles and your cellphone app should show the same number. If he called you after two hours, his odometer should read 120 miles and your cellphone app should show the same result.

If d1 is the distance he travelled before he called you first time and d2 is the distance he called you before calling you the second time. The cellphone app and the odometer should both show d1+d2.

What if the cellphone app starts showing you different results than the odometer?

It would be strange, wouldn’t it?

What results will we actually see?

When your friend calls you after 1 hour his odometer will show 60 miles but your cell phone app will show 59.94 miles. This you may assume is due to some measurement error or because your friend might not have travelled in an exact straight line or the surface may not be perfectly flat. But, as the distance grows the results will be more mind-boggling, something like this:

Days Odometer Cellphone App
5 3000 2926
10 6000 5437
15 9000 7179
20 12000 7905
25 15000 7512
30 18000 6055
35 21000 3742
40 24000 899
45 27000 -2071

relative distances picodometer vs cell phone app

  • How does the linear distance shown by your cell phone increase and then start decreasing? After going further he is again closer – something like twin getting younger.
  • Why doesn’t it go up linearly just like relative velocities?
  • There seems to be a maximum relative distance just like the maximum speed (the speed of light)
  • What does the negative distance mean?

Why such weirdness?

Elementary! The earth is round?

Or in other words, we measure assuming the world is flat, oblivious of the curvature and it’s just as well for the most part when dealing with small distances. But it’s not so OK when dealing with large distances.

This would have been mind boggling if we didn’t know that. After all how is it possible that we think we can make a 200 meter straight beam by putting two 100 beams, but the math seems to be off if we believe in the “Special Theory of Relative Distances”? Well the math works because we don’t need exact measurements for normal construction. Otherwise we would need to make some adjustments, if we are dealing with very large beams in construction, say miles long we may need to be aware of the curvature of earth.

Space time curvature in Theory of Special Relativity when dealing with very high velocities requires adjustments that are not apparent when dealing with normal speeds. Similarly distance measurements can create complications if we were to deal with large linear distances due to curvature of the earth.

I am still trying to figure out what is the analogy for light? Would it be the center of the earth or any generic point that is diametrically on the opposite side of the earth? J

A Clueless Data Scientist Discovers the Theory of Special Relativity


I am not a Physics Major. A random thought that occurred the other day resulted in this post. What if a Data Scientist tried to reconcile constant speed of light with classical relativity? No disrespect for the awesome genius of Einstein and others who discovered the Theory of Special Relativity. It is written just for fun and may even have some errors.

Could a Data Scientist have come up with Theory of Special Relativity by looking at this graph?

Let’s suppose that he was given this graph and told to find the best fitting equation for the data in the graph below.

Expected Rel. Velocity and Light above

First reaction may be to say that the straight line is a good fit and that the one point represented by green triangle above the line is a bad data point (an “outlier” per statisticians), or may be to consider it as a measurement error if the point is only slightly above the line, which is in fact the case in the above graph as explained below.

What this graph represents:

The graph shows relative velocity of the passing trains as you travel in a train at 2,000 miles/hour.

If you pass another train that is stationary then its relative velocity will be -2000 miles/hour (or in other words you will see the other train travelling at 2000 miles per hour in the opposite direction. Similarly, if a train travelling at 3,000 miles per hour passes yours, you will notice its velocity as 1000 miles/ hour.

In the graph above if Y is the relative velocity and your velocity is 2,000, then the relative velocity of the passing train is Y = X-2,000 except for one point: the green triangle!

This idea of relative velocity has been known at least since Galileo’s time. Einstein’s Special Theory of Relativity is something else. Surely you didn’t think Newton would have left such simple problems for Einstein to solve!

The green triangle represents the relative velocity of light as it passes you by. It is constant regardless of your velocity and is customarily denoted by letter ‘c’. The actual value is something close to 671 million miles per second. We are representing ‘ c’ as 10,000 miles/hour in the example above so that we can keep it from going off of our chart.

What is the problem? — Paradox of Constant Speed of Light:

The relative velocity Y= X – 2000 valid for every data point other than the one that corresponds to velocity of light? This exception is what needed reconciliation. That reconciliation is what the theory of Special Relativity did. Would you as a data scientist have you done it even without knowing Physics?


How about fitting a curve? Why don’t we try that?

What do we notice? The data points at lower speeds are approximated fairly well both by the straight line as well as the curve, but only the curve approximate the point corresponding to the velocity of light. Note that of the two points on the Y-axis corresponding to ‘c’ (i.e. 10,000) in our graph the lower point is only there only to highlight the estimate provided by the straight line, and is not the actual data point. The actual data point is the upper data point.

Relative Velocity Line and Curve fits

If someone was just trying to get a good fit for the data without knowing the physical meaning behind the data points being graphed, it would not have been impossible and in fact likely that they would have concluded that a curve is the best fit.

Einstein once wondered, “How can it be that mathematics, being after all a product of human thought which is independent of experience, is so admirably appropriate to the objects of reality?”

It is the experience and knowledge of the physical world that prevented other scientists from suggesting that a curve can fit this data rather than a straight line!

What way did Theory of Special Relativity contradict experience?

What does it mean for the data to be on the curve rather than the straight line? It meant that the relative velocity was not (v2-2000) but slightly more. One’s experience as well as experimental evidence until that point had established that the relative velocity of a train traveling next to you with velocity v2 would be (v2-2000). Within the limits of the normal measurement error involved in measuring this always seemed to be correct.

However the new theory based on fitting a curve says that this is incorrect. Greater the value of V2, greater was the difference between relative velocity and (v2-2000). It keeps increasing until it becomes equal to the speed of light as v2 increases close to ‘c’. When v2=c, relative velocity becomes exactly equal to c.

General equation that was later derived was

Relative velocity = (v2-v1) / (1-v1*v2/c^2) where v1 is your velocity, v2 is that of the other train or light and c is the speed of light.

Data scientist may have just fit a polynomial curve instead of the equation above. Nevertheless the implication of even a polynomial curve would have been equally astounding. It would have led to the ideas of time dilation and length contraction or both. If one were to accept that the relative velocity was not increasing in a linear fashion as the velocity of the passing train increased, one has to accept that either time or distance must be changing in a non-linear fashion relative to the two trains opening up the possibilities of dilation and contraction.

Looking at the graph was not how Einstein came to his conclusion, but it is interesting to think that a data scientist could have come to such a conclusion by merely looking at the data aided by his ignorance of the ramifications. Interesting, isn’t it?

Gold and Central Banks

What is gold, and what determines the gold price?

As Atahualpa’s loyal subjects carried the heavy gold to fill the 22 ft. X 17ft. X 8 ft. room, a ransom of 6.5 tons of gold on this day in 1532 to save their emperor, Spanish conquistador, Pizarro wasn’t wondering if gold was money, he knew it was.  He just took it and had Atahualpa strangled with a garrote anyway.

Atahualpa ransom

As HMS Enterprise came under German air attack, the captain wasn’t wondering if the 50 tons of gold that was his cargo, entrusted by the Norwegian government ,to be taken to Bank of England in 1940, the Captain had no doubt that it was.

For well over two thousand years gold was money. It is no wonder many people still think it is.

A persistent question the truculent US Congressman, Ron Paul kept asking every Fed Chairperson:

Is gold money?

Here is an exchange between then Fed Chairman, Ben Bernanke and Congressman Ron Paul, in 2011:

gold, reserve currencies, ron paul, bernanke, central banks
Is gold money?

Ron Paul:             The price of gold today is 1580 dollars. The dollar during these last three years has devalued by almost 50%. When you wake up in the morning, do you care about the price of gold?

Bernanke:           Well, I pay attention to the price of gold, but… I think it reflects a lot of things. It reflects global uncertainties. I think the reason people hold gold is as a protection against tail risk — really, really bad outcomes. And to the extent that last few years have made people more worried about the potential of a major crisis, then they have gold as a protection.

Ron Paul:             Do you think gold is money?

Bernanke:           No.

Ron Paul:             It’s not money? Even if it has been money for six thousand years and somebody reversed that, and eliminated that economic law?

Bernanke:           Well it’s an asset… it’s the same… would you say Treasury Bills are money? I don’t think they are money, but a financial asset.

Ron Paul (interrupting):                               Why do central banks hold it?

Bernanke:           Well, it’s a form of reserves.

Ron Paul:             Why don’t they hold diamonds?

Bernanke:           Well, it’s a tradition, long-term tradition.

Ron Paul (chuckling):     Well, some people think it is money!

Ex Fed Chairman, Alan Greenspan had a different take on it.

Alan Greenspan talking about gold in an interview in Oct, 2014 conducted by Gillian Tett, Managing Director, Financial Times.

“…Gold is a currency. It is still by all evidences the premier currency where fiat currency, including the dollar can’t match it. And so the issue is if you’re looking at a question of turmoil, you will find as we always have in the past, it moves into the gold price.” He also acknowledged its dual nature, “But the gold price is actually sort of half commodity price, so when the economy is weakening it goes down like copper. But it’s also got monetary characteristic… it behaves as though it is.”

What’s the difference? Why does it matter?

Ever since U.S. has gone off of the gold standard in 1971, and as most other countries too by 1974, gold has lost its perch.  During gold standard days, the amount of paper money printed was tied to the amount of gold in the treasury due to the gold standard. Money was good as gold and gold was good as money. But now a question has risen: what is gold now?

Is it just a commodity whose value is determined by the supply and demand for consumption?

Great deal of gold has been accumulated by central banks as a consequence of the gold standard and even greater amount of it has been accumulated by the people as it was money. As a highly hoarded commodity, its price would fall greatly if the hoarders – central banks and investors — decided to sell it. It would have been a no-brainer to write it off as a bad investment if not for the recent changes in the attitudes of some of the central banks towards it.

You can see from the chart below that the central banks have more than half the total amount of gold in the mines. Full 11 years of consumer demand (jewelry + industrial) can be satisfied by the gold in the central banks’ vaults.

central bank gold holdings vs yearly demand
Central Bank Gold Holdings vs. Yearly Demand

It should be apparent that any sales by central banks will have severe negative effect on the price.

An ounce of gold has averaged $650 in 1980, $384 in 1990, $279 in 2000. With such drops it is hard to see it as money when one of the core characteristic of money is that it should retain its value. However, great part of this drop has been caused by uncoordinated central bank sales in 1990s and the threat of more to come.

Central banks attitude determines the status of gold:

During this period of uncoordinated sales, when one central bank didn’t discuss their sales with the other, price of gold sank. UK’s central bank auctioned off about 400 tons of gold between 1999 and 2002. This was done at the direction of its then head Gordon Brown. Short sellers front ran these auctions and gold hit its multi-year low.

This low point was referred to by some as Brown’s bottom!


gold standard gold price
Post Gold Standard Gold Price

Central Banks, learnt from this experience and realizing that it would be a disaster if each tried to front run the other in selling it, formed as a group and do it in a coordinated fashion, little bit at a time so that the price doesn’t crash. This was the genesis of Central Bank Gold Agreement (CBGA1) made among several European central banks, that limited the sales by the members’ to less than 400 tons per year in total for the next five years 2000-2004.

Until the end of 2001 the price of gold was less than $300. Although one can’t dismiss the impact of Gold ETFs that made easy speculation in gold possible since 2004, we believe that the seed for significant upward movement in the price was sown when it became clear that Central Banks wouldn’t be dumping their hoard of 30,000 tons on to the market at once.

Even as these central banks were selling gold until 2009, the positive signal of CBGA1 and the introduction of ETFs that made it easy for public to buy and hold gold caused the price of gold to move up from the average price of $429 in 2005 to $954 in 2009.

central bank demand gold price

The 2008 recession, as well as some movements by the public to have their central banks hold on to their gold and even bring it back from other countries where some of countries have kept for safekeeping , have stopped the sales by European central banks.

At the same time the fear and mistrust of US dollar and Euro which made some of the non-European central banks to start buying of gold have led to reevaluation of gold’s status.

By 2011 the average price moved up to $1626.

This love for gold has by no means been universal. Central Banks differ significantly in whether gold should be a legitimate part of central bank portfolios, but the countries that don’t like to resurrect gold – the countries with reserve currencies – are also ironically the largest owners of gold and would not like to see the gold price drop dramatically.

Recent moves and motivation of non-European Central Banks:

After not disclosing the gold purchase data for last six years, China’s central bank had finally reported that they had bought 600 tons between 2009 and June 2015, which comes to about 100 tons per year on average. There had been speculation that they had been buying over 500 tons a year. Some don’t believe the Chinese numbers and think that Chinese Central Bank has actually bought over 2000 tons.

It is not clear if China’s central bank is buying gold to reestablish a legitimate position for gold among foreign reserves or merely as a negotiation tactic to get Yuan included as one of the reserve currencies in SDRs. Logic being that west would prefer including Yuan to gold in the list of reserve currencies.

Sanctions on Russia have also played a major role in Russian Central Bank buying gold from its miners who are unable to export it. Russia and its allies have been buying up almost 200 tons of gold per year to support their miners. This too may reverse, once the sanctions are removed.

Since the 2011 other central banks have also been adding about 300 tons.

china, russia, gold buying
China and Russia have been buying gold

Summarizing the buys mentioned above, net buying by Central Banks, between 2011 and 2014 has averaged about 500 tons (not including China’s 100 tons), in contrast to 450 tons of Sales between 2005 and 2008, for a swing of almost 950 tons per year.

We will explore in a future blog the quantitative relationship between the demand and the price of gold and show how almost all the price move of the gold from average $229 in 2005 to average $1626 in 2011 has been due to Central Bank buying and accompanying speculation from investors via ETFs and purchase of bars and coins in reaction to the perceived signal from Central Banks that gold is a legitimate asset.

One hears a lot about number of auspicious days, cost of production changes, exchange rates and many other factors in predicting future price of gold. These do matter in a steady state when the demand is not distorted by the sales or buys of central banks. We haven’t had this steady state over the last decade.

Size of the sales or purchases by central banks in a given year may not seem that big, but more than the magnitude, it is the direction that influences the other investors trading in ETFs and Coins & Bars that affects the gold price.  Central banks derive their disproportionate influence from the 30,000 tons they have available to sell should they choose to sell and the nearly unlimited resources they have, should they decide to buy and the fact that they tend to act in groups.

You can see a significant correlation between central bank buying and the gold price almost as strong as the correlation between the overall demand and the gold price.

Liner Regression gold price
Linear models: Central Bank demand vs Gold Price and Total Demand vs Gold Price

Central Banks tend to operate by consensus but lately there is a slight fissure. This makes the future predictions about the demand from central banks and hence the gold price difficult, but also offer some opportunities.

Whatever happens, the final status of gold and hence the gold price will be determined to a great degree, not by supply, demand or tradition, but by the outcome of the politics of reserve currencies.

Justice with Prejudice

Supreme CourtWhether it is the video evidence surfacing on the Internet showing the excesses of the Police Force or the news reports of citizens’ emails and phone calls being tapped by the government, we feel besieged. We fear that our law makers who run expensive campaigns are compromised and that they do not work for our interest but for the benefit of their sponsors.

However, one institution we take some comfort in is our Supreme Court. In most countries Gore v. Bush type of case would have resulted in riots if an election result were decided by a court. Despite the disappointment of losing such a hotly contested election, losing side accepted the decision calmly. This a testament to the unwavering trust Americans place in this institution.

Admittedly, our Supreme Court justices are highly qualified men and women, who could make fortunes in the private sector, but have chosen the path of public sector. Wherever their motivation may lie, it is not in fame and fortune and that’s perhaps one reason we trust them so.

Is there a possibility that our trust in the individuals is misplaced in the institution they are part of?

Let’s examine if the justices are in fact reaching their judgements through an unbiased interpretation of the laws. If the decisions are based on the constitution what should we expect? If we picked nine random fair minded judges from a pool of competent legal minds, the outcome should always be the same. Should there be some ambiguity, the justices should be able to reconcile the law and facts and come to a unanimous decision.

Do they agree?

If you let me define a clear decision as one which has at least eight justices agreeing, in only 30% of the cases a clear decision was rendered in the recent 20 cases I looked at. That means that in 70% of them there was no clear decision.

# of concurring judges # of cases
5 11
6 3
7 0
8 3
9 3


What could be the cause for the lack of consensus?

(1) Is the constitution vague?

(2) Do some justices are interpret the law incorrectly?

(3) Are the decisions ideological rather than legal?

How would each of these manifest themselves in the data?

If the constitution and body of law are vague, we could see disagreement, but unless it is the same section of the law the justices are disagreeing about, we should notice the disagreements to be randomly spread. In other words no two justices should always disagree.

If the problem is with one or two justices being incompetent, we should see that all others mostly agree but these one or two justices not being able to see the point.

Are the decisions ideological?

If on the other hand, the differences are ideological or personal then we should see one group of justices on one side of the issue with other on the other side. The justices within their group should agree with each other and disagree with justices in the other group frequently.

How much prejudice plays a part in the decision making despite long winded apparently scholarly opinions that often run over 100 pages of small print can easily be seen by looking at the correlation (positive or negative) between various justices.

No matter what the issue is, what the facts are, what the law is, one group of justices almost always come on one side and other group comes on the other side (see table below).

court close decisions

The split among the judges runs thus:

Group A: Alito, Scalia, Thomas, Roberts

Group B: Sotomayor, Ginsberg, Breyer, Kagan

Group C: Kennedy

Of the 14 close decisions with six or less judges agreeing, in twelve of them, judges from Group A came to an opposite conclusion as judges from Group B, give or take one or two defections. Two groups disagree consistently making you wonder if they are even looking at the same facts.

Do nominating Presidents define the tone?

It should be enlightening to note that how they decide a case seems to be predictable by looking at the political party of the President that nominated them and the justice’s religious background.

Remember reading a while back that Supreme Court justices surprise the Presidents that nominate them by unexpectedly leaning in an opposite direction than expected by the President. I was interested in signs of this phenomenon. After all, justices during their nomination hearings often proclaim that they haven’t made up their mind when asked about their opinions on controversial issues like abortion and death penalty and that they would adjudicate each by the specifics of the case.

Are they being forthcoming? What is the truth?

So, let us see how many acted in ways that are unexpected. It seems like only 1 out 9 did. Kennedy is the only one that can’t be classified into one of the two camps. 8 out of the 9 judges pretty much stay within the “party” lines, although Roberts breaks out infrequently. Generally they act in expected ways. It is a surprise why more judges are not “not confirmed” by the opposition party.

court composition

If two of the justices from Group A or Group B should perish in an accident, the party in power during that time will in effect get a stranglehold on future Supreme Court decisions for decades as the justices rarely retire, may be even centuries due to the impact of ‘precedents’.

Is this the type of Supreme Court we want? Are there ways of removing ambiguities in the law? Could the nomination process be improved? If there is no way to do either, shouldn’t we limit the terms of the justices so that fresh blood can come in that reflects the diversity and progress in the national thought?

In fact it even raises a question as to the value of Law Degrees as it pertains to being a Supreme Court Justice. If a Judgement is but an opinion, who doesn’t have one? Why not have a layman or Jury of Common people make the final decisions, by merely taking some input from subservient legal advisers in order to ensure that the decisions are not outside the limits of legal framework?

If Judges education is merely a tool to articulate and justify their biases is it disenfranchising other common folk who have equal right to enforce their prejudices as any on the bench? I don’t mean to say this is what I believe in, but certainly food for thought.