Buy Low, Sell High: The Worst Financial Advice of All Time

As someone who’s given a number of talks on personal finance, and managing your investments, there’s one piece of advice that I keep hearing from people over and over again. “Buy low, sell high”, they usually whisper to me in a sagely tone, as though they have discovered some profound truth that will solve all their investment problems. I’ve always nodded along politely, but it always gnawed at me in the back of my mind as a not-very-useful piece of advice. Until one day, as I spent some time seriously considering this maxim, when I came to the startling realization that not only is this advice cliched to the point of ridiculousness, it is in fact, one of the worst pieces of financial advice you can ever give to a lay person.

First, let’s get something trivial out of the way: “buy low sell high” is indeed factually accurate and a mathematical tautology. The only way to make money on the financial markets is to buy at a (split/dividend/spin-off adjusted) price that is lower than the price you sell it for. This is just as true a statement as “1+1=2”, and unfortunately, just as useful too. Every single person already knows that they need to invest in something that is going to grow. You telling them that they need to buy at a lower price than what they sell it for, is doing just as much good as stating that the sun rises in the east and sets in the west. In order for any advice to be useful, it has to provide information that someone can act upon, in order to make better decisions. And in this regard, telling someone to “buy low and sell high” is utterly useless as advice.

Or at least that’s what I used to think, until I realized one day that I was wrong. Yes, on a mathematical level, buying low and selling high is a tautological way to make money. But going beyond that, and looking at the implicit meaning behind the phrase, it actually does influence people towards making different investment decisions. It subtly influences them to make investment decisions that are bad. Decisions that are harmful. Decisions that 99.9% of the public should never ever make. And that is exactly why I term this piece of advice not just useless, but in fact, the worst financial advice of all time.

To understand why, let’s explore the implicit suggestion behind this advice, and how most people try to put it into practice. What is your first instinct when you hear the words “buy low, sell high”? Your first instinct is to ask yourself whether the market is currently low or high. If you answered that the market is currently low, you would then act on this by investing any liquid assets you have. And if you answered that the market is currently high, you would conversely act on this by selling off some of your portfolio and parking your money in liquid/safe assets. This is after all, the most straightforward way to “buy low sell high.”

Unfortunately, this is also exactly the wrong thing to do.

Consider a few examples. Suppose the stock market has dropped 25% in the past year. Does that mean that stocks are now “low” and therefore, you should start buying more of it? If you answered yes, you’ve arrived just in time to lose another 25% from 2002-03. Suppose instead that the stock market has doubled in value in the last 3 years. Does this mean that stocks are now “high” and therefore, you should sell your investments or at least stop buying new ones? If you answered yes, you just missed out on the 50% growth that occurred from 2012-15.

So how exactly does one go about predicting when the stock markets are “low” or “high”? Here’s a dirty little secret in the financial industry: no one has a clue. There are armies of Harvard-MBA-educated financial wizards working on Wall Street, at hundreds of mutual funds, earning millions of dollars, trying to time the market and predict its highs and lows, and the vast vast majority of them are no better at it than a monkey throwing darts. If you think that you have somehow cracked the code and have some special insight in predicting market highs and lows, you need to quit your job and start working in finance where every Hedge Fund will welcome you like the second coming of Christ. (Warning: Don’t quit your day job – you’re not Christ.)

The amount of damage that people have done to themselves, by futilely trying to time the market, is immense. By constantly buying and selling, they incur unnecessary transaction costs and tax liabilities. By parking their money in low-yielding investments, waiting for the “right time” to buy stocks, they are foregoing the 7% annual returns that the stock market yields on average. Every time someone allows their investment decisions to be guided by the “buy low sell high” philosophy, they succeed only in hurting themselves.

Which brings me to the advice which you should actually follow. The advice that should replace and put to rest the dangerous “buy low sell high” snake oil. The advice that will actually protect you and your long term investment prospects. “Buy when you have money to invest, and sell when you need the money“. Don’t try to guess whether the stock market is high or low. Invest your money when you have disposable cash. And liquidate your investments when you need the cash. Everything else is bunk.

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The Chinese Hegemony

Given the frantic pace of the 24 hour news cycle, stepping back from it all and looking at history provides some immensely valuable perspective. The modern news cycle may care only about what happened in the past few years, but in reality, World History is measured in centuries. First there was the Roman empire. Then the Chinese, Mongol, British empires, and now the US. The current American hegemony is impressive in its peak, but just like all its predecessors, is bound to come to an end. The coming century is going to be marked by a Chinese hegemony. It’s not a question of if. It’s a question of when.

To anyone who thinks that today’s America can continue to be the global superpower that it is, let’s look at the facts. Our military and diplomatic power, while impressive, is built on a foundation of economic power. For the past 60 years, our economic power has come from one single fact: we are the largest developed nation in the world. With 320 million people, we dwarf the next closest developed nation: Japan with a mere 125 million. But this is about to change.

China is developing rapidly, and will continue to do so. Even if their per capita income never matches that of America, it doesn’t need to. With 1.3 billion people, they will dwarf the united States, 4-to-1. Even if their per capita GDP permanently lags America’s by 30%, their population alone would give them an economic power 3 times greater than America’s. They will be to America what America is to Britain.

And this economic superpower status can buy many things. With such massive economic power will come technological power, diplomatic power, and inevitably, military power. And short of America invading China before it can happen, a completely barbaric and preposterous idea, there’s nothing we can do to stop this. In the coming decades, China will be the world’s single most powerful nation. It will be the next world superpower, the way America is today.

This may seem like a frightening thought to many, but it doesn’t have to be. If we start acting today, to prepare for this inevitability. The United States, and its allies in America, Europe, Japan and Korea, combined, will have populations and economic powers that match China’s. India, an emerging democracy, also has a population that rivals China. Southeast Asia, a rapidly developing region with 600 Million people, is also wary of Chinese imperialism, and could serve as allies in a coalition to contain Chinese hegemony. On a global scale, China’s population of 1.3 billion is still only 15% of the global population.

Historically, coalitions like the ones described have been completely toothless in combating the war mongering of superpower nations. But this has always been by design. Such coalitions, and partner international institutions, have always been built by the world’s leading superpower of the day, and kept deliberately weak in order to ensure the continued immunity and privileges that the superpower enjoys.

Consider for example, America’s attitude towards organizations like the UN. Smaller nations would like to see these organizations given dramatically more enforcement power, in order to deter aggression from, and the impunity which larger countries enjoy. The US currently, is completely opposed to any such measures precisely because it would challenge that same impunity that it currently enjoys. When the US invaded Iraq, in violation of UN laws, it suffered no consequences from any international organization or coalition. When the US was found to have been invading the privacy of every country in the world, even that of its allies’ heads of state, it again suffered no consequences at all to speak of. Toothless international organizations serve the US interests just fine, hence why they are toothless by design.

It’s easy for us to excuse and justify such behavior with the implicit trust that we have in America. But let’s step back for a second and examine this from a historical perspective. In the year 2060, when China dwarfs the US the way the US currently dwarfs Britain, what do we want to see happen when China unilaterally invades a sovereign nation? What do we want to see happen when China is found to be hacking and surveilling all electronic communication around the world? What do we want to see happen when China starts torturing and indefinitely detaining foreign nationals? Would we still want to live in a world of toothless international institutions?

Let’s face facts. America’s days of being a sole international superpower are numbered. China is going to replace America as the world’s leading superpower, in the coming decades. As unpalatable as these facts might be, burying our heads in the sand does nothing to change it.

But this doesn’t mean that we have to be helpless. By acting now, we can start building international coalitions, organizations and institutions with teeth. Institutions that can face up to any individual superpower, and adequately punish them for misbehavior. Institutions powerful enough to deter, and engender respect from, any country in the world. As the current global superpower, this will involve us giving up the privileges and immunities that we currently enjoy… for the moment. But when the day comes that China supplants us as the world’s hegemon, we will be safer for it.


Addendum: Please do not misinterpret this as a rant against China. Many in the west do indeed see China as a bogeyman, which makes it a convenient metaphor for this essay. But in truth, we should be wary of any one country serving unilaterally as the world’s policeman. If there’s one thing to be learned from the Iraq debacle and the Snowden revelations, it is that no country can be trusted with absolute power. It’s time we put in place checks and balances to prevent such occurrences from ever happening again.

Related Links: The UN, by design, being forced to cave to pressure from even mid-tier powers

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Caucus: The Next-Generation Community-Discussion Forum

Regular readers have probably noticed my extremely low posting frequency lately. I would usually explain this with some excuse about being busy, but this time, I actually have a good reason behind it. I’ve been spending the past couple of months building a site of my own.

For years, I’ve been frustrated by the state of online discussions, and the platforms that host them. For years, I just sat back and complained, but this time, I thought I should take a stab at it myself, and try to build something better. I’m now proud to say that the site’s version-1 is now complete!

For those of you wondering why you should visit this site, and what makes it unique, here’s a summary of the guiding principles behind the site. I’m sure you’ll agree that this is indeed an ambitious project, never been attempted before, and I’m very curious to see how it shapes out.

Why Caucus

How often have you seen content that is highly rated online, despite being inaccurate, misleading or inflammatory?

How often have you seen an online discussion resembling an echo chamber, with dissenting views being systematically silenced and suppressed?

How often have you seen a great online community crumble because its very success attracts swarms of new members who do not share the community’s values?

These are the problems that caucus was specifically designed to solve. By applying sophisticated Reputation-System based algorithms to rank crowd-sourced content, we aim to develop healthy online communities, and foster truly constructive and thought provoking dialogue.

Our Principles

Reputation Matters

The success of real world communities derives ultimately from reputation, and reputation-enhanced speech. The advice given by the wise is awarded greater reverence and prominence, than that of an angsty troublemaker. The converse of this, in the reputation-free internet, is vitriol and lowest-common-denominator mob rule. We believe that in order to effectively build online communities, and foster constructive discussion, we need digital reputations as well, and reputation-enhanced online speech.

Discussion Matters

Constructive discussion keeps the world spinning. Both the spreading of verified knowledge, as well as the discussion and synthesis of new ideas. Announcing to the world that you love Vanilla, is a very safe and popular thing to say. But there has to be more to life than simply discussing how awesome Vanilla is. The most important things in life can also be contentious. And that is exactly why they need to be discussed. Popular content is worth highlighting, but so too is controversial content. Only with a mix of both, can we engage in true dialogue.

Community Matters

In our increasingly anonymous online world, communities still matter as much as ever. Systems work best when people are allowed to self-organize into communities. Communities that have their own distinct principles, personalities, values and reputations. Communities composed of regulars, who embody the character of the community itself. Communities that are free to welcome outsiders who are a good cultural fit, and safeguard themselves against outsiders who are not. Communities that socially compete with one another, in order to provide its members with the best experience. And out of this competition, the greatest benefit for individuals: The freedom to pick and choose a community that best reflects her values and needs.

Site Features

Crowd-sourced Content Ranking

Through voting, you decide which content is worth being on the front page, and which content should be buried in the archives.

Earned Reputation

By posting content, and getting votes from others in the community, you can over time, build up your own reputation.

Reputation Enhanced Speech

The extent to which content is highlighted will depend on the reputation of the people posting and voting for it. We trust those, who are trusted by their community.

Fair Airtime

Some people post every thought that comes into their head, and others are more deliberate about posting things that are well thought out. Some people have an opinion on everything, and others only vote on things that they feel strongly about. We account for such posting/voting patterns to ensure that every person gets a fair voice in the community.

Merit Based Scoring

Some content may have accumulated more votes simply because it was posted at a better time, and thus, seen by more people. We normalize for such biases and ensure that every content is judged fairly on its own merit.

Promoting Controversy

Popular content has its place, but so too does controversial content. Only with a mix of both, can we engage in true, informative dialogue.

Community Specific Reputation

A person’s reputation is specific to each community. Together with reputation-enhanced-speech, this ensures that communities can retain their own unique culture, and not be deluged by outsiders.

If you’ve read this far, you must be curious to see the above ideas put into practice. Take a look for yourself!

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Conscience Driven Politics

Around the world, xenophobia seems to be everywhere. In the US, anti-immigration rhetoric fills the airwaves in half the country. People like Donald Trump, the leading republican Presidential nominee, describe Mexican immigrants as rapists and drug dealers. Eastern European countries like Hungary are not only politically lobbying to restrict the rights of asylum seekers escaping violent war, they are even shutting down the train stations that would ferry them to their final destinations. Right wing anti-immigration groups like the UKIP and the Greek neo-nazi party are popping up everywhere we look.

Almost every country in the world is divided on the topic of immigration and welcoming foreigners. And even in the faction that is welcoming of them, we often find a cold selfish political calculus in its heart. Business leaders who simply want cheap labor, and politicians trying to appeal to specific ethnic demographics.

Hence why it’s heartwarming to see something so completely contrary, like what’s happening in Germany. As a country, they have nothing tangible to gain from taking in tens of thousands of hungry, impoverished refugees. And yet, not only are they welcoming them, they are fighting for them. They are lobbying for them in the European Union. They are using their political capital to go up against the Eastern European bloc that is resisting their every move. They are confronting their own local xenophobes and budget-tightwads, in order to welcome asylum seekers and provide them with the basic services they need to get back on their feet.

It’s easy to fall into cynicism when looking at politics and foreign policy theater. After all, the reasons for cynicism are so prevalent. But every now and then, something like this comes along, and it is touching to see a country act, not out of political calculus, but simply out of respect for human dignity.

A few months ago, during the Greek economic crisis, many were drawing unfair parallels between Germans and Nazi domination of Europe. Today, Germany has permanently laid to rest any such inflammatory accusations, and proven that when it comes to moral high ground, no other country in Europe has the right to lecture them. Kudos to you Germany. You have warmed the heart of even this cynic.

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Avoiding the next Financial Meltdown

In a previous article, we discussed the problem with banks guaranteeing fixed deposits while actually investing the money into speculative, long-term ventures, and how such an arrangement naturally leads to bank runs. There is a second problem in this scenario as well; one that is so commonplace that most people do not even stop to ask this question: Why are banks even in the business of making investments?

When you as a consumer deposit money in a bank, what service exactly are you seeking from the bank? If you’re anything like most people, you just want the bank to store your money in a safe & liquid manner, easily accessible for transactions through checks, debit cards, ATMs and such. And banks do indeed excel at this role. They do an excellent job of physically safeguarding money and greasing the wheels of commerce by acting as a convenient and trusted middleman.

So why are they stepping beyond this role and engaging in loans and other investment activities as well? To put it simply, the problem with banks is that they do too much. They provide an essential administrative service to the public: Safely keeping people’s money and enabling transactions to occur in the marketplace. The problem is, instead of simply safeguarding this money, they are simultaneously also engaged in a completely different service: gambling this money on speculative investments. It would be as if the mailman not only delivered letters from person A to person B, but also opened the letter, read its contents, and rewrote portions of it based on what you really needed to hear.

There is no ostensible reason why the administrative services provided by the bank should be forcibly tied together with their investing services, particularly when considering the risks involved, by definition, in all investment activity. If consumers want to loan out or invest their money, 3rd party investment funds such as Bond Funds already exist for this express purpose. These are extremely stable funds, immune to bank runs by design. Banks could have services tying in to these 3rd party funds, allowing consumers to invest their deposits into these funds the same way they currently do in Savings Accounts. And the bank for its part, could avoid all the associated loan/investment risks, and focus on the one service it does best: Safeguarding financial assets and being a middle-man greasing the wheels of commerce.

In fact, this problem isn’t limited to commercial banks alone. Many other financial institutions, such as Investment Banks, share the same problem as well. Similar to commercial banks, Investment Banks also provide a number of vital administrative services. They help startups with the IPO process, aid established companies with issuing new securities, and help matchmake the buyers and sellers of financial instruments. They perform an essential role in the economy, hence why the collapse of Lehman Brothers and Bear Stearns sparked such widespread panic.

Unfortunately, that’s not all they do. Investment banks have also been engaging in speculative investments, with profits and losses accruing directly to the firm itself. Such forms of risk taking helped pad their profits during times of calm, but led to the financial meltdown during the last market crash. Eventually, we the taxpayers had to come to their rescue, simply to keep the wheels of commerce turning.

Similar to commercial banks, there is absolutely no reason for Investment Banks to engage in such investment activity. Mutual funds and Hedge Funds already exist for this express purpose. Individual hedge funds make bad bets and go out of business all the time. No one bats an eyelid when they do, because we don’t depend on them for any other vital services. They might be risky, but at least their risk is contained, and that makes them expendable. With Investment Banks on the other hand, because of the wide array of other essential services that they perform, they end up being Too Big To Fail. Which really is just a fancy way of saying that they can do anything they want, and we the taxpayers will be the ones cleaning up after them. Heads they win, tails we lose.

A ray of hope: Some politicians are starting to come around and recognize this problem. The Volcker Rule was specifically created to ban Investment Banks from engaging in investment activity, precisely for these reasons. Unfortunately, the bank lobbyists have been hacking away at the bill, and exemptions have been created allowing Investment Banks to invest in Hedge Funds, Private Equity Funds, Treasuries, Municipal Bonds, and GSE Bonds such as those of Fannie Mae/Freddie Mac. Exemptions have also been added allowing Investment Banks to engage in market-making activities. The net effect has been to dilute the Volcker Rule, and leave Investment Banks vulnerable once again to the near meltdown that we experienced in 2008.

Software Engineers have spent the past decades painfully learning how to build massively complex systems, that are also robust and resilient. One of their central learnings is known as the Single Responsibility Principle. To summarize crudely, it teaches us that every entity should be responsible one thing, and one thing only. Trying to pack a wide variety of completely unrelated features, into a single entity, is a recipe for chaos and disaster. We would be wise to learn from these lessons and apply them to our financial systems.

Commercial and Investment Banks provide a number of essential services, that are absolutely vital to the healthy functioning of our economy. Hence why they need to be completely decoupled from any investment activity. Investing is fundamentally a risky process, and any large scale investment is prone to sudden and catastrophic failures. Individual investment funds can and will implode from time to time, but as long as the administrative services of the financial industry are completely decoupled and left intact, the wheels of commerce can still continue running and will eventually recover again. Only by enforcing a strict separation between administrative/transactional services, and investment activities, can we hope to avoid the financial panics that have been hitting us regularly every decade.

Related links:

Too Big To Fail: Still a problem today

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A Financial System with Solid Foundations

The story of financial crises is one that’s as old as time. Bank runs have been occurring since the time of the renaissance, were a key factor in the great depression, and its variants have necessitated billions of dollars in bailouts in the past decade after the subprime crisis. Is this really inevitable? Is this really something that we simply need to accept and live with? I will be making the argument here that this is not the case.

Bank runs, and its derivative financial crises, all share one common root. A fundamental cause revealing the cracks in the system’s foundations. The dependency on public sentiment.

To put it simply, our banking system of present simply cannot function without people’s confidence. Even if the bank operations and balance sheet are perfectly sound, if enough people believe that they are in trouble and start withdrawing their money, these rumours and misguided fears will promptly turn into reality.


To understand why this is true, consider what actually happens at a bank. Joe deposits $100 at his bank, in order to safeguard his money. The bank however, is not providing a simple service of safeguarding this money. It is also investing the money. The bank approves Mark for a mortgage, and lends him $80 to be repaid over the next 20 years. The bank now no longer has the full $100 that Joe deposits. It has only $20, and the other $80 is pawned away as a speculative long-term investment.

Now at this point, you may be wondering what would happen if Joe were to return the following week, and withdraw his $100. The bank no longer has it. It has only $20 of Joe’s money available. Thankfully, the bank is exceedingly clever, and has a solution for this. Joe is not the only depositor at the bank. So too are Alison, Adam and Amanda. So when Joe tries to withdraw his $100, the bank gives him back his original $20, together with $80 that actually belongs to Alison, Adam and Amanda. Over time, this $80 will be repaid by Mark through his mortgage payments, and Alison, Adam & Amanda will never even know the difference.

99% of the time, the system works exceedingly well. There are only 2 problems:

  1. What would the bank do if Mark defaults on his loan and does not pay back his $80?
  2. What would the bank do if Alison and Amanda also tried to withdraw their money the next day?

First, let’s consider case 1. The bank has 4 depositors, and using their pooled money, it had made a $80 loan to Mark. If Mark now defaults, the reasonable outcome should be for all 4 depositors to lose $20 each. However, that’s not how banks work. Losses are never accrued to the depositors, and banks simply return the entire balance to customers in a first-come-first-serve manner. The first 3 people to withdraw their money will get back their full $100, and the last person to do so will end up with only the $20 that’s remaining. Hence the term “bank run.” People are literally racing against each other to be the first few lucky ones, and not be the last one holding an empty bag.

Now let’s consider case 2. The bank has 4 depositors, with deposits totaling $400. Out of this $400, $250 has been loaned out as mortgages, and only $150 is sitting in the bank as cash. All the loans made are perfectly healthy, and the bank is receiving all payments as scheduled. Everything seems to be going fine.

However, a rumor starts that loans are being defaulted on. Most of the depositors know the rumor to be false, but Adam believes it and withdraws his entire $100. After all, he doesn’t want to be the one holding an empty bag if the rumor is true. Amanda knows that Adam withdrew his money, and that there is only only $50 remaining in the bank, so she rushes to the bank as well and withdraws the full $50. Alison and Joe, the only ones who were “responsible” and didn’t fall for false rumors, are now unable to withdraw anything from the bank because all the cash is completely gone. Despite their prudence, and also because of it, it will now be many years before they can ever recover their money.

These two cases perfectly illustrate why bank runs happen: During bad times, it devolves into a winner-takes-all and loser-gets-nothing situation, which leaves everyone scrambling to withdraw their money and not be one of the losers. And even during good times: uncertainty, fear, rumors and the mere threat of the above, can all send people similarly rushing to the bank, creating the very problem that was rumored to exist.


For centuries, governments have tried to fix the problem by sweet talking people, whispering sweet nothings, and providing artificial government backed “guarantees” that promise more than they can ever deliver during a real panic. Consider for example, that the FDIC is responsible for insuring $9294 Billion worth of bank deposits, but it has only $25 Billion in its coffers to make good on this promise.

To put it generously, these “solutions” are mere hacks; temporary bandaids hiding the real problem. Any system of guaranteed fixed-deposits backed by speculative investments, is inherently an unstable one. It’s fundamentally predicated on the idea of “borrowing from Paul to pay Peter.” It may seem great during periods of calm. But during times of trouble, the bank’s guaranteed deposits simply do not line up with their assets, and no amount of sweet talking or confidence building can make up for this mismatch.

As an alternative, consider, how bond-funds work. These funds have been remarkably stable for decades. Despite lacking the type of guarantees provided by the FDIC, bond funds have never experienced any form of bank runs. The reason for this is simple: If some of the loans in their portfolio go bad, the loss is immediately borne out by everyone invested into the fund. It doesn’t matter how early or late you are in withdrawing, everyone loses the same relatively small amount. The fund’s liabilities to their investors, are always perfectly matched by their assets. This is what gives people the confidence to remain invested and stay with the fund, even while a select few panic and rush for the exits. Contrast this with banks, where the bank runs are in fact the rational response to times of panic.


The problem with banks is that they promise more than they can deliver. They know it, the government knows it, and their customers certainly know it as well. But things don’t have to be this way. Let’s imagine an alternative banking system, that’s built on solid fundamentals and transparency.

If consumers want their money held for safekeeping in a risk-free, liquid manner, in checking accounts, it should be locked away in a metaphorical vault, and left to gather dust. It can still be accessible at any time using debit cards, checks, or bank withdrawals. But it should never be invested or loaned out to anyone. Your money should literally be sitting there, untouched by anyone else, waiting for you to withdraw it anytime you choose. In return, the same way you pay the postal service for delivering your mail, you should also be paying the bank some fees for storing and safeguarding your money.

If consumers instead want to loan their money out and earn interest in the process, through savings accounts, the money should be placed into equivalent bond funds, with the disclaimer that all profits and losses will be immediately and equally accrued to all fund-investors, on a daily basis. Customers wanting safe investments can choose funds that invest only in short-term government bonds, while more aggressive customers can choose funds that invest in long-term corporate bonds or mortgage loans. Each customer will be able to choose their desired fund, based on the amount of risk they want to take on, and the corresponding amount of interest they would like to earn.


The above discussion has so far been concentrated on banks, but the same principle can be generalized to other financial systems as well. Any form of fixed guarantees, backed by speculative long-term investments, fundamentally leads to an unstable situation. As long as such systems exist, guarantees are bound to be broken, and panics are bound to occur.

The subprime crisis of 2008 has been an ominous precursor to bigger and more dangerous possibilities that await us. Whenever we’re dealing with unstable systems, it’s only a matter of time before a loose spark blows everything up. Let’s learn from 2008, and not repeat our mistakes all over again.

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Life Lessons from Machine Learning

What comes to mind when you hear the term “Machine Learning”? A bunch of programmers hunched over their computers in a dark room, working on something completely virtual & divorced from reality? A group of scientists creating a Frankenstein monster that has no resemblance to us whatsoever?

It may certainly seem that way, but you’d be wrong. The accomplishments of Machine Learning (Self-driving cars, human handwriting parsing, IBM Watson) are certainly very technological in nature. But in truth, Machine Learning is equal parts Art and Philosophy, incorporating deep Epistemological insights in order to better make sense of the world. Machine Learning is in essence, a simplified & structured version of what goes on in our minds every single day, in our quest for knowledge.

If this “quest for knowledge” sounds like a bunch of mumbo jumbo and you’re wondering how it’s actually relevant to us, consider the following: We were all born without any knowledge whatsoever of how the world works. Since then, every single day, every single thing we observe around us, is a data point that we accumulate. And by interpreting these data points, we are able to gain knowledge about the underlying mechanisms that lead to these data points, and more abstractly, “how the world works.”

Life is a massive swarm of data points, and consciously or subconsciously, we are engaged, every single day, in an epistemological quest for knowledge. And one of the most central challenges, in this quest for knowledge, is knowing how to correctly interpret all this data. And that is exactly where Machine Learning comes in.

Overfitting: Keep it Simple

If this all seems overly abstract, let’s consider a concrete example. Imagine that you’re a biologist running a bunch of experiments on the relationship between temperature & enzyme activity.  You collect a variety of data points, that looks like the following:

Screen Shot 2015-03-15 at 6.36.58 PM

Well, that’s great. We now have a bunch of data. But what do these data points really mean? How should we interpret them, and what knowledge can we gain from them? Even though it may seem obvious, there’s actually infinitely many ways to interpret these data points, all of them radically different from each other. For example, you could draw a simple straight line which seems to fit the data pretty well.

Screen Shot 2015-03-15 at 6.38.52 PM

You could draw a very finely tuned curving function which fits the data even more closely.

Screen Shot 2015-03-15 at 6.39.24 PM

You could even draw crazy zig zag lines that fit the data points perfectly. All 3 options fit the data well, but lead to wildly different conclusions on how the world actually works. And there are thousands of other such options possible as well. How do we actually know which of these options to pick?

There’s actually an answer to this dilemma, and it forms the bedrock of all science. It’s a very simple principle known as Occam’s Razor, which sure enough, says that anytime you have a choice between 2 explanations, you should pick the one that is simpler. For those of us who are lazy, this seems like a godsend. The simpler option is much less work to understand & model, so that sure saves us a lot of time & effort!

But there’s also a more powerful factor at play. Not only is the simpler explanation the lazier option, it is also the more accurate one. If you have to choose between 2 explanations that equally match the data, the simpler one is the one that is most likely to be true! Hence why in science & math, there is so much importance placed on “beautiful” and “elegant” answers, as opposed to overly complicated ones. Albert Einstein said it best: “Everything should be as simple as it can be”.

And this is a lesson we can apply in our lives as well. When trying to understand something, always go for the simplest explanation that fits. If you went on a date with some guy, and he never called you back, did he meet with an accident? Was he kidnapped by the KGB and held in a gulag somewhere in Siberia? Or maybe he’s simply not interested in you? If 5 different people tell you that your new shirt looks very odd on you, are they jealous & trying to keep you down? Is there a massive behind-the-scenes conspiracy to fool you into throwing away a great shirt? Or maybe the shirt is actually not all that great? Always go with the simplest explanation.

Underfitting: Oversimplifying

Now suppose we go one step further. You look at all your data from before, remind yourself of Occam’s razor, and convince yourself that enzyme activity keeps going up with temperature. But then, as you run more and more experiment, something odd happens. At some point, the data seems to start diverging from your straight line.

Screen Shot 2015-03-15 at 6.39.42 PM

You try to redraw your line in a different way, but no matter how much you try, no straight line seems to match the data that you’re now seeing.

Screen Shot 2015-03-15 at 6.40.00 PM

In Machine Learning, this is known as the “underfitting problem.” Ie, you’ve taken simplicity too far. You’re trying to model a very complex phenomenon with an explanation that is far too simple. In order to deal with this problem, you have to loosen up on your pursuit of simplicity, and search for a more complex explanation that better matches the data you’re seeing. You still don’t want to go overboard and pick an overly complicated explanation. But something that is slightly more complicated than your earlier straight-line hypothesis would now serve you best.

Screen Shot 2015-03-15 at 6.40.24 PM

Once again, Albert Einstein said it best: “Everything should be as simple as it can be, but not simpler!” Pick the simplest explanation out there, but make sure it’s sophisticated enough to explain what you’re seeing.

This is something that will serve us well in our personal lives too. The best example of this, is something we all do subconsciously to some extent: Judging a book by its cover, generalizing, and stereotyping. We all do it to some extent. We constantly judge people & size them up based on such superficial factors like race, gender, religion, age, profession, height, weight, looks, and even the way we dress. The most dangerous thing about all these generalizations, is that they are always based on a little kernel of truth. That’s why people believe them, and that’s why they keep persisting.

And yet, despite this kernel of truth, the problem with generalizations is that they are overly simplistic, just like the straight line above. As human beings, we are all enormously complex and extremely varied. Anytime you try to lump together millions of people into one overly simplified bucket, you’re going to wind up with an extremely distorted vision of reality. And so it is too, with all knowledge. Always strive to find the simplest explanation possible, but no simpler.

Data is King

If this seems like quite the challenge, it certainly is! One the one hand, we always want to find the simplest explanation possible. But on the other hand, we don’t want it to be too simple either. How do we walk this fine line?

Let’s recall the experiments we were doing with enzymes earlier. First, we mistakenly believed that enzyme activity will always keep increasing with temperature. Then as we collected more data, we realized that this is only true up to a certain point, and that it eventually plateaus off. In fact, the truth is even worse; beyond a certain point, if you increase temperature even slightly, the curve plunges all the way down to zero. How can we avoid falling into such traps?

The answer to both puzzles is the same: Get more data. If the amount of data you have is too small, or if all your data falls into a very small range, it doesn’t matter how smart you are, or how great your data-processing capabilities are. You’ll keep making errors of both kinds, and continually misunderstand how the world really works. There’s even an Indian metaphor describing this, roughly translated as being a “Frog-in-a-well.” If you’re a frog living in a well for your entire life, then the entirety of your knowledge will be applicable only to the well that you’re in. You would think that the whole world consists of damp, dark conditions, with cylindrical walls & a small hole of light at the top.

In order to truly understand the world, you have to leave your well and start collecting much more data, from much more varied sources. Hence the common saying in Machine Learning that the amount of data you have, is even more important than how well you can process it. And so it is in our personal lives too. If you’ve spent your whole life in a small farming town in Ohio, then the entirety of your knowledge will be limited to life in small farming towns in the midwest. If you’ve spent your entire life in San Francisco, then the entirety of your knowledge will be limited to life in liberal American cities. If the entirety of your experiences with Mormons consist of the 2 people who came to your door to preach to you, you’d be much more prone to stereotyping them, than if you had 20 different Mormon friends.

The best way you can fight this problem? Get more data! Read more books. Watch more documentaries. Travel the country, travel the world. Make friends with people who are different from you. Read the NYTimes, and read WSJ. Watch MSNBC, and watch Fox News. Read the Bible, read the Quran, and read Richard Dawkins. Only by collecting as much data as possible, from as many varied sources as possible, can we best begin to make sense of how the world works.

Test Yourself

So you’ve now done all of the above. You’ve collected a wide array of data points. You’ve parsed all this data, and come up with a beautiful model for how the world works. A model that is as simple as possible, but also nicely fits all the data that you have. Is it now time to pop the champagne & bask in your supreme wisdom?

Not quite. Everyone in the world reaches this stage at some point in their life. In fact, this is the default stage that everyone is in for most of their life. They think they have enough data for their needs. They are confident that they interpretation of this data is a beautiful blend of simplicity and accuracy. After all, hindsight is 20/20. Everyone’s an expert after the fact.

But are you really an expert? Is your vision limited to great hindsight, or do you actually have great foresight as well? In order to know, you have to constantly test yourself. Ask yourself questions for which you don’t know the answer. Make a prediction based on your knowledge & beliefs. Then collect the data, and see if it matches your prediction. Anytime you come across a new piece of data, ask yourself whether it matches what you would have predicted.

If these answers don’t quite match your predictions, don’t just rationalize it or sweep it under a rug. Admit that your beliefs have been incorrect, or imprecise. Alter them to fit the new data, in a manner that still makes overall coherent sense. Be willing to throw your beliefs out entirely and start from scratch, if the situation calls for it. Pick explanations that are as simple as possible, while still being complex enough to explain what you’re seeing. And once you’re done with all that, gather even more data, and test yourself all over again. It’s a never ending loop, but with every lap that you take, you’ll find yourself a wiser person for it.

Life is the greatest epistemological problem of all. There are mountains of data that we’re constantly collecting everyday, and oceans more that is out there waiting to be collected. We arrive into this world not knowing anything, and using only these data points, we try to put them together in a way that makes this massive, immensely complex world, slightly more understandable.

This is exactly the same problem that Machine Learning scientists have been tackling for decades, in a much more structured format. They still have a long way to go, but their insights have been powerful enough to produce computer programs that can recognize human handwriting and self-drive cars. By learning from and applying these insights to our own lives, we too, can hope to make slightly better sense of this mysterious and magical world that we live in.

Related links:

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All Lives Matter

There’s been a number of slogans trending recently. Black lives matter. Muslim lives matter. Let’s try this on for size: All Lives Matter.

Sounds like a platitude that we can all get behind, doesn’t it. But what does it actually mean to practice this as a matter of policy?


Every year, 33,000 people die in the US from motor vehicle accidents.

Every year, 15,000 people die in the US from homicides.

Every year, 300,000 people die in the US due to medical errors.


Anna dies due to a motor vehicle accident involving a drunk driver. The world moves on.

Alice dies due to the actions of a lunatic while running the Boston Marathon. The entire world mourns her death & embarks on a manhunt to avenge it.


Trevor dies while walking back home, in a botched robbery. He gets a small note in the crime section of his local newspaper the next day.

Trayvon dies while walking back home, in a struggle with an armed man. The entire world is glued to their television sets as the trial unfolds.


Paul goes to the hospital for a routine operation, and dies from a preventable medical error. His family mourns his loss privately.

Peter goes to school at Columbine and dies at the hands of a mentally unstable shooter. The President of the United States discusses potential legislative changes in response.


Every year, a saddening number of people die all over the world from tragic & preventable causes. Car accidents, crime, medical errors, lack of access to Healthcare, poverty, malnutrition, drugs, suicide, the list goes on. We mourn their loss when it happens to someone we know. Some of us go a step further & discuss legislative or societal efforts we can undertake to mitigate these tragic losses. But for the most part, we accept these mortalities as the inevitability of life, and move on with our own.

And yet, when it comes to sensational deaths, the script is completely flipped. Deaths caused by terrorism, school shootings, police malpractice, and plane crashes, are given wall-to-wall coverage in the media and our minds. In spite of the relatively tiny number of deaths involved, or perhaps because of it, they receive a massively disproportionate amount of attention, coverage & discussion.

This is an insult to our basic sense of fairness. All preventable deaths are equally tragic, and to passionately mourn one while sweeping the other under the rug, devalues the worthiness of life itself.

But beyond that, this obsession over certain forms of deaths, distorts our entire perception of the problems plaguing our world, and how best to address them. The time and energy that we spend obsessing over the few plane crashes that happen every year, can have an exponentially greater impact if it were directed towards vehicular accidents instead. The trillions of dollars that we’ve spent in our “War on Terror” could have made the world a much greater place, if it were directed towards a “War on Crime” or “War on Malnutrition” instead. We’re obsessing over the warts on our forehead while collectively ignoring the tumor in our lungs.

In an ideal world, we would all get together every Sunday, mourn the loss of every life individually, and discuss what should be done as an appropriate response. Given the 400,000+ deaths that occur every year from tragic causes, this is hopelessly impractical. Mourning is best left as a personal & private matter, for the people who actually knew the individuals involved.

The purpose of our media coverage shouldn’t be to shock, entertain & captivate with the most sensational deaths that have occurred. The goal of any serious journalistic organization should be to focus on the most pressing & widespread issues that affect our lives most directly. Every event and issue should be reported by the media in proportion to the number of people directly affected by it. As a rule of thumb, a national cable channel has no business reporting on an issue that has impacted less people than local crime.

All lives matter, regardless of race, gender, or cause of death. All deaths from preventable causes are equally tragic, and it’s time this fact reflected itself in our national discourse.


Related Links:

Casey Anthony

Trayvon Martin

Chapel Hill shooting

Malaysia Airlines Flight 17

The Atlantic tackling this same issue

The Political Side of selective mourning

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Lies, Damned Lies, and Statistics

We live in a world today, with statistics all around us. Opinion polls. Confidence Intervals. Margin of Error. Risk estimates. But do we actually understand what any of these things mean?

I must have been in college when I first heard the quote popularized by Mark Twain: “There are lies, there are damned lies, and then there are statistics.” As an engineering student with a passion for mathematics, I found myself very confused. After all, the numbers don’t lie. How can anyone be so skeptical of math & statistics?

It was only as I grew older, that I started to better appreciate the insight in that quote. It’s true that the numbers don’t lie… but our minds certainly do. You see, we all think that we understand statistics. We all think we have an intuitive feel for it. But more often than not, our intuition turns out to be completely wrong. Too often, our intuition leads us completely astray, without us even realizing it.

Don’t believe me? Well, let’s play a game and find out.


Welcome to the Monty Hall Game Show! Up for grabs, is a fancy new car that could be all yours. We have below, 3 doors. Behind one of these doors, is the car. And behind the other 2 doors, is a goat. If you guess right, the car is all yours. What’s your guess going to be?


Door 3 you say? Well, here at the Monty Hall Game Show, we want to give you the best possible odds of winning. So as a show policy, after you’ve made your guess, we will always show you one of the other 2 doors, which contains the goat. And in this case, that’s door 1:


Now, you no longer have to choose between 3 doors. You only have to choose between 2. Would you like to stick to your original guess of door 3? Or would you like to change your guess to Door 2?

Now comes the million dollar question. What are your odds of winning? And does it matter whether you stick to your original guess?

Our intuition might tell us that our odds of winning are 50%, and it doesn’t matter whether or not we switch. But that intuition, would be completely wrong. And here comes the key takeaway of this entire piece: If you ever find yourself in such a situation, don’t think of it as a single event with a single outcome. Instead, ask yourself what would happen if you replayed this event 100 different times, with a different outcome each time.

Imagine yourself playing the game 100 times, and always sticking to your original guess. 33% of the time, you will guess the right door on your very first attempt. And because you always stuck to your original guess, you will end up winning the car 33% of the time. Ironically, the fact that the host showed you one of the empty doors, doesn’t change your odds of winning at all.


Instead, imagine yourself playing the game 100 times, and always changing your guess after the host opens one of the doors. 66% of the time, you will start off with one of the empty doors. And after the host has revealed the other empty door, your switching will result in you picking the door with the car behind it. Thus, your odds of winning actually increase all the way to 66%. At no point is your odds of winning ever going to be 50%.



Think you got the hang of it? Let’s find out. You’re now sitting next to a stranger on the bus. She turns to you & tells you that she has 2 kids. What are the odds of her having 2 boys?

This seems easy enough:


The odds of each kid being a boy is 50%, so the odds of both being boys is 25/100 = 25%, also shown when you crunch the numbers as shown above.

Now let’s add a twist. You ask her whether she has at least one boy. She says yes. Now what are the odds of her having 2 boys? Is it still 25%? Is it 50%?

To find out, let’s go back to our previous way of tackling these problems. Imagine there being 100 mothers, all with 2 kids. And here’s how this number breaks down:


When the stranger on the bus tells you that she has a boy, all that tells you is that the very first case cannot be true. This mother does not have 2 girls. However, there are still 75 possibilities that remain, out of whom 25 have 2 boys. Hence, the odds of her having 2 boys is now 25/75 = 33%.

Keep in mind though that the context behind the information is crucial. Suppose the mother didn’t tell you she has a boy. Instead, you go to her house, knock on the door, and a boy opens the door. The numbers now break down differently:


The fact that a boy opened the door, and not a girl, now leaves only 50 possibilities open. Out of which, 25 have 2 boys. So the odds of her having 2 boys is no longer 33%, it’s instead 50%. Even though this problem seems extremely similar to the previous one, the small change in the way the information is presented causes the answer to dramatically change from 33% to 50%.

Which brings us to the next key takeaway: There is no such thing is a single “absolute” probability. Rather, it constantly & dynamically changes depending on the amount of information that is available, and the precise way in which that information was obtained.

Think you got the hang of it? Let’s throw yet another twist. You’re sitting next to a stranger on a bus who tells you she has 2 kids. You ask her if she has a boy born on a Tuesday. She says yes. What are the odds of her having 2 boys?

Once again, our intuition tells us that the “born on a Tuesday” makes absolutely no difference at all. After all, he has to be born on some day of the week, and what’s the relationship between Tuesday & having 2 boys? But once again, our intuition turns out to be completely wrong.

Imagine 100 mothers once again, and how this number breaks down:


Out of the 100, only 13.7 have a boy born on Tuesday. Out of these, 6.6 mothers have 2 boys, at least one of whom is born on Tuesday. Hence, the odds of her having 2 boys has now changed from 33% to 48%. Even something as seemingly trivial as a kid’s birthday, completely changes our answer.


At this point, you may be saying to yourself that these are contrived puzzles that would never happen in real life. That’s a fair point, so let’s look at a different puzzle that’s vitally relevant to our lives.

You go to see the doctor, and he decides to test you for a rare disease called Neurophilia. A few minutes later, he comes back with grave news. You have tested positive for Neurophilia. You ask the doctor how accurate the test is, and he replies that the test is 98% accurate. What are the odds of you actually having the disease?

Our intuition might tell us that the odds of us having the disease is 98%, just like the test’s accuracy. But once again, that is completely wrong. In fact, we can’t even predict our odds of having the disease, without asking a follow-up question. “How prevalent is Neurophilia?” The doctors replies that Neurophilia is indeed pretty rare, affecting only 1% of the population. At this point, imagine again 100 different people getting tested for the disease:


Out of the 100, only 1 actually has the disease. But because the test is only 98% accurate, 2 among the 99 who are disease-free, will wind up testing positive anyway. Thus, the odds of you actually having the disease, is only 33%. Even though the test’s 98% accuracy rate might seem so highly impressive, our actual odds of having the disease is a measly one third.

Which brings us to the second key takeaway: It’s not enough to simply test for something in a vacuum. We also need to estimate the odds of something being true, even before we get the test results back. Only by comparing our initial estimate with the test’s accuracy, can we arrive at the final answer.

To see why this is true, imagine if the doctor tells you that the 1% prevalence mentioned earlier is too optimistic. That the disease prevalence varies greatly with an individual’s circumstances, and that for someone of your age, weight & gender, the disease prevalence is actually 10%. The numbers now change completely:


Out of the imaginary 100 patients, 10 of them will now have the disease, and 2 others will test positive. The odds of you actually having the disease given that you tested positive, has now increased to 83%. If we assume that your initial odds of being diseased is 1%, the final odds of you being diseased is only 33%. But if we change our initial estimate from 1% to 10%, the final odds of you having the disease grows to 83%.

It might seem paradoxical & circular to place such importance on initial, naive estimates of someone having the disease, when we’re doing these tests precisely because we don’t know the answer. But that is the true nature of statistics. There is no “absolute right answer,” of the kind we find in other sciences & math. Our initial naive estimates will greatly influence the final answer, even though they are simply naive estimates to begin with.


Do you think you’ve now mastered the art of Statistics? Let’s find out. You’re a juror serving in a murder trial… the defendant’s life sits in your hands. The police detective testifies that some DNA fragments were gathered at the scene of the crime. The police ran this DNA on a random database of people who live in the same city, and the defendant came up as a perfect match. He goes on to state that the test is 99.9% accurate. What are the odds of the defendant being guilty?

Once again, we cannot even begin to answer this question without first forming an initial probability estimate. You ask the detective how large the city is, and he replies that there are 2 million people who live or work in the city.


Out of these 2 million people, only 1 person is actually guilty. However, because the test is only 99.9% accurate, 2000 people will be flagged as matching the DNA, even though they are innocent. The odds of the defendant being guilty is a paltry 0.05%.

At this point, the detective interjects. He tells you that the defendant isn’t simply some random person found in the city; he actually knows the victim personally. There are only 1000 people in the city who know the victim personally.


You crunch the numbers again, and find that 2 people out of the 1000 will test positive. One of whom is actually guilty, and another who was simply unlucky. Therefore, the odds of the defendant being guilty is still only 50%. Plenty of room for reasonable doubt.

Once again, the detective interjects. “No no no, you don’t understand. The defendant was born on a Tuesday. There are only 140 people who know the victim personally & were born on Tuesday. Out of these 140, only 0.14 will test falsely positive. Therefore, the odds of the defendant being guilty is actually 88%.”

“What do you mean, he was born on Tuesday? Why does that matter?” you reply.

“Remember that mother you met on the bus earlier? Well, her son being born on a Tuesday changed the answer from 33% to 48%. If that matters, then so does this.” the detective confidently states.

And if you find yourself unable to respond… if you find yourself on the verge of believing the detective’s blatant distortion… don’t feel bad. Statistics is hard. It’s confusing. And it’s downright non-intuitive. And that’s why there are lies… there are damned lies… and then there is statistics.


Related News:

Viral NYTimes article also discussing conditional probability, its subjective/dynamic nature, and the Monty Hall problem. What are the odds of NYTimes writing about these exact same topics, a month later, purely by coincidence?

Spurious correlations: Traffic Noise and Obesity

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The ABCs of Personal Finance

Do you want to be a millionaire?

The odds may certainly seem to be stacked against you. Less than 0.2% of the world’s population can claim to be millionaires. The average American household before the financial crisis in 2008 had a financial net worth of roughly $100,000. Today, the situation is even more dire, with half of all Americans having no assets whatsoever. Do you really think that you can buck the trend and be a millionaire?

The answer is yes. Becoming a millionaire is easier than you think, and within reach of the common man. You simply need to start young & learn the ABCs of Financial Planning.

Figure out your Goals

The very first step, is simply to figure out what your goals are. Do you want to retire at 65 with a million dollars? Retire at 65 as a multi-millionaire philanthropist? Retire at 45 with just enough money to live a frugal, relaxing life? Save up $200,000 in the next 20 years so that you can send your kids to the best private colleges? These are all equally valid answers, and there’s a different one out there for every person. You simply need to figure out what your own life goals are.

Some resources that can help you figure this out:

Guidelines for how much money you need in retirement

Calculator for how much money you’ll need in retirement

Guidelines for saving for your kids’ college

Budget your Savings

Once you have figured out your goals, the next step is to figure out how you can get there. Too many people spend whatever they feel like spending, and save the rest. The first step towards achieving your financial goals is to flip the equation.

First figure out what you need to save every month, in order to achieve your goals. And then, spend only whatever is remaining.

Calculators like this, can help you figure out exactly how much you need to save every month to achieve your goals.

Some of you may find this minimum-goal to be “too easy.” You may want to challenge yourself to save even more money, and are wondering how to strike the right balance between saving for the future & enjoying the present. If you’re one such person, give yourself a pat on the back. You’re on the right track. There is no single answer to this question, but the approach I’ve used is to split my money evenly between savings & luxury spending.

For example, suppose you’re making $5000 per month. Break down all your basic living expenses:

  • $1500 – taxes
  • $600  – rent and utilities
  • $75 – car insurance
  • $180 – medical insurance, life, ad&d
  • $500 – groceries
  • $1000 – minimum retirement savings to meet your goals

This leaves you with around $1000 left over. Split this money equally between your savings & luxury spending. Put an additional $500 into your savings every month, and allow yourself to spend the remaining $500 on whatever luxuries or hobbies you like, free of guilt. Whenever you get a raise or bonus at work, put half of it into your savings, and allow yourself to spend the other half on anything your heart desires. You may want to pick your own ratio, but I personally find this 50-50 balance helps me enjoy life to the fullest, while still sleeping soundly at night.

One quick note to mention here: There’s a huge difference between nominal dollars, and dollars indexed for inflation. One million dollars in 2040 is worth less than $500,000 when indexed for inflation. Whichever term you prefer to use when doing your calculations and looking up online tools, make sure to stay consistent.

Maintain Separate Accounts & Automate It

Once you know exactly how much you need/want to save, you need a surefire way of keeping your nest egg safe and separate from your spending money. Mixing the two of them together, is the easiest way to wreck all your careful plans & eat into your nest egg without even realizing it.

The best & easiest way I’ve found to do this, is to set up separate bank accounts. At the very minimum, set up one account for your savings, and another account for everything else. I personally keep 3 different accounts. One checking account for all my basic life expenses. Another checking account for luxury spending. And a third account on ETrade, where I keep & invest all my savings.

Once you have your different accounts in place, set up your paychecks to direct deposit money into each of the accounts automatically, from every paycheck. If you know you need $1500/month for your basic living expenses, have that much money direct deposited into your checking account directly from your paycheck. If you plan to save $1500/month, have that money direct deposited to your stock brokerage account directly from your paycheck every month. Arrange to have anything left over direct deposited to your luxury spending account.

If you ever find yourself wanting to go shopping or traveling, first look at your luxury account’s balance. Whatever money you see sitting there, is yours to spend guilt-free. But don’t even think about dipping into your savings, unless it’s an absolute necessity.

Minimize your Taxes

The average American pays $14,000 in taxes every year – enough money to become a millionaire over the course of their lifetime. Luckily, there are a number of tax benefits that we can all take advantage of, to reduce our tax bill. Every dollar not paid in taxes is an additional dollar earned & saved. Depending on how rich you are and how extensively you take advantage of these deductions, you can save tens of thousands of dollars every year. So definitely spend some time exploring these options fully.

The biggest tax benefit that you should definitely take advantage of, in order to save for your retirement, is the 401k and IRA plans. At the very minimum, these plans allow you to invest your savings without having to pay any capital gains taxes. That will single-handedly boost your savings by 15%. Another advantage of 401k plans is that many employers will match a good chunk of your contributions. Taking full advantage of these matching contributions is like getting a 5% wage raise for free; don’t ever leave that money sitting on the table.

Traditional 401k/IRA contributions are also exempt from Income Taxes for that year. This will significantly reduce your immediate tax bill, allowing you to save even more money. Keep in mind that you will eventually have to pay taxes on this during your retirement, but if you were to use it on charitable giving, significant medical expenses, or other such exempt uses, you may never have to pay taxes on it at all.

One tradeoff you make for getting all these benefits, is that the money in your 401k/IRA accounts can only be taken out after your retirement. This can be a blessing in disguise, preventing you from blowing your savings on unnecessary expenses. But if you do have legitimate expenses to handle before your retirement, you should save up for those expenses in a non-401k account.

There are quite a few exemptions that allow for early withdrawal, to account for unexpected hardships & life necessities. For example, you can withdraw money early from your 401k account to pay for qualified educational expenses, medical expenses, and to make the downpayment on your first house. If you plan to take advantage of these exemptions, make sure you research it thoroughly before committing your money to the 401k account. In general though, the 401k is an excellent way to save for your retirement, and significantly reduce your tax bill in the process.

If you’re investing your savings, as you definitely should be doing, you should certainly make sure to minimize your capital gains taxes as well. Whenever you buy a stock that appreciates in value, always hold on to it for at least one year before selling it. This will cut down your taxes by half, or even eliminate it completely. If you want to go one step further, there are other fancy tricks you can use, like Tax Loss Harvesting. I personally avoid it, because I find it too much trouble and too easy to get wrong, but it’s certainly an option that’s available.

The home mortgage interest deduction is another excellent way to minimize your tax bill, if you decide to buy a house. All you need to do is simply not pay off your mortgage early. This is a very good idea for other reasons as well, as covered later, but one additional tax benefit is that any money you spend in mortgage interest payments, qualifies as a tax deduction.

If you know for certain that you’ll be spending some amount of money on educational expenses or medical expenses in future, you can also set up special accounts for those. For educational expenses, you can set up a 529 plan. For long-term health expenses, you can set up a Health Savings Account. For immediate dependent-care and health expenses, you can set up a Flexible Savings Account. Be careful that if these expenses do not materialize, much of the money in the account could be penalized heavily. I don’t have first-hand experience with these special plans, but if you know for certain that you’ll have certain educational/medical/dependent-care expenses in future, you should explore these plans as a way of reducing your tax bill further.

The last and potentially more lucrative tax exemption of all, is Charitable Giving. Every dollar you give to charity is a dollar you will not have to pay taxes on. Note that your tax savings will always be smaller than the amount of money you’ve given to charity. So you will never become more wealthy by doing this. However, if you find yourself wanting to give back & help those less fortunate, this tax deduction is an excellent way to pay less in taxes while simultaneously making the world a better place.

Managing your Investments

In an earlier section, I linked to the following investment calculator. Try spending a few minutes playing with the Rate-of-Return field, and see what effect it has. Spoiler alert: It’s huge. Every 1% increase in your rate-of-return, can gain you an additional $100,000. Managing your savings & investing it wisely, will have an enormous impact on your retirement nest egg. Every small detail will make a difference of tens of thousands of dollars, so definitely educate yourself thoroughly on this topic.

There are some excellent services out there, that manage all your investments for you. If after reading this section, you still feel uncomfortable managing your own investments, you can further explore using such services. But knowing the basic principles of investing is still something that will serve you very well.

The very first decision you’ll want to make, is finding a balance between stocks and bonds. The stock market has historically averaged ~10% returns per year, but is also a lot more volatile. Long-term bonds (US Treasuries) have historically averaged ~6% returns per year, but are much less volatile (particularly if held to maturity).

As you earlier saw from the investment calculators, the difference between 10% and 6% can easily cost/gain you half a million dollars. Finding the right balance between the two depends on a lot of factors, such as your age, income and temperament. The conventional rule of thumb is that you should invest your (age-10)% in bonds, and the rest in stocks. There are also more sophisticated questionnaires out there, that will recommend a more customized asset allocation to fit your specific circumstances & outlook. You can use these to figure out the stock-bond balance that is right for you.

A quick note about CDs and savings accounts. In contrast to stocks and bonds, CDs cap out at ~2% returns, and bank savings accounts barely reach 1% returns. Their returns are so abysmal, that you should never rely on them except as temporary holdings. If you ever find yourself in an emergency where you need money immediately, you can always sell your stocks/bonds from your brokerage account, and raise the money you need within a day. Even if you were to realize a loss due to market conditions, it still beats tying up your money in savings accounts offering abysmal returns every single year.

At this point, if you don’t already have one, you should set up a brokerage account from which you’ll be able to buy & sell stocks/bonds. I personally use ETrade because of their low costs, and have always been fully satisfied with their service. Once you’ve set up your brokerage account, you can get the associated routing number, and have your savings be automatically direct deposited into it from every paycheck. ETrade also allows you to electronically transfer money for free, from any checking account to ETrade and vice-versa.

Once you’ve figured out your plans, set up your brokerage account and have the money to invest, let’s discuss the nuts and bolts of making an investment. There are all sorts of financial wizardry you can engage in, but since this is intended to be an introductory guide, I recommend the following bare bones approach to get yourself started

  1. For stocks, buy Vanguard Total World Stock ETF (Symbol: VT)
  2. For bonds, buy Vanguard Total Bond Market Index Fund (Symbol: BND)
  3. When placing an order:
    1. wait until the market is in session (M-F, 9.30am – 4pm, ET)
    2. set the order-type as “Market”
    3. the quantity at a integer number smaller than (investment_amount / market_price)
  4. Because ETrade charges a $10 commission for every trade, do not place small orders
    1. wait until you have ~$500-1000 saved up, before placing an order

Once you get more comfortable, you can deviate from the above and pursue other investment strategies. For example, you can invest specifically in Emerging Markets, International Developed Markets, the S&P 500, US small-cap, and various Bond Funds. I personally like to divide up my investments equally among all of the above. Quick note about Bond Funds: Ignore all numbers listed except for SEC Yield. The SEC Yield tells you what interest rate you can expect to receive on that fund, and that’s the only statistic that has any relevance whatsoever for the future.

You can do your own research before committing to  portfolio, but always keep in mind your two goals:

  1. Diversification, across all different companies, sectors, markets and locations
  2. Minimal expense ratios: 0.2% or lower

For example, when you invest $1000 in the Vanguard Total World Stock ETF, you are literally investing in thousands of companies, in every single market segment, across ~50 different countries. Even if a number of these companies were to go bankrupt, or their countries were to fall into civil war, your overall portfolio would still hold up reasonably. And you are getting all this for an extremely low expense ratio of 0.2%. In contrast, buying individual company stocks places a lot of risk on your portfolio, and actively managed mutual funds charge expense ratios of 1% of more, despite consistently getting trounced by passively managed funds. No matter what specific strategy you decide to pursue, always buy Index Funds & ETFs.

One last point to make here, and this might be the most important of all. We are absolutely horrendous when it comes to market timing. The average investor’s track record over the past 30 years is an abysmal 1.9% returns per year, in painful contrast to the 10% returns that the S&P-500 index has achieved during this same time. The reason for this? People consistently & repeatedly sell their stocks, or stop making new investments, whenever the markets are panicky. As a result, they then miss out on the dramatic upswings that happen right after a crash.

Do not let this happen to you. The smartest & most business savvy investors out there have tried very hard to time the market just right, and they have mostly failed. Once you’ve set up a 20 year plan for yourself, stick to it, paycheck to paycheck, no matter what the talking heads on television might be saying.

Buying vs Renting a home

Housing tends to be one of our biggest expenses and/or investments. Hence, the decisions you make about your housing situation, will have a very large impact on your long-term financial security.

It can also be one of the most complicated to figure out and get right. Under some circumstances, buying a house is an extremely wise move. Under other circumstances, it will prove to be a big financial setback. To figure out what is right for you, I highly recommend using the following NYTimes Rent-vs-Buy calculator. It can help you make sense of your local property market, and figure out whether buying a home is a financially savvy move for you.

One caveat to mention here, if you choose to rent a home. Renting is certainly cheaper than mortgage payments in the short term, and if you choose to rent, these calculators are all assuming that you’ll be investing the difference in stocks and bonds. Hence why renting can sometimes be a better decision than buying – investing the difference in stocks and bonds can sometimes be more lucrative than buying real estate.

However, this only works if you remain disciplined about maintaining your own personal savings plan. If you simply pay your rent and save a minimal amount of money on the side, you’ll be shooting yourself in the foot.

Buying a home & signing a mortgage is like enrolling yourself into a forced savings plan. Every month, the bank will give you a call and very forcefully suggest that you stick to your savings plan, by making your mortgage payment. Nobody likes others telling them what to do, but if you’re lacking in financial discipline, this can be a godsend. On the contrary, if you choose to rent your home, the pressure will be fully on you to make sure that you remain disciplined & invest significantly in your own savings plan.

To be sure, buying a home can certainly be an emotional decision, as well as a financial one. If you choose to buy (or rent) a home, despite the numbers recommending otherwise, that is certainly a valid choice to make. But be honest with yourself about what it really is – luxury spending. There’s nothing wrong with spending money on the things that make you happy, as long as you’re aware of the choice you’re making and can afford to do so.

Building up your credit score

If you ever find yourself wanting to buy a home, or take on a loan, having a great credit score can save you thousands of dollars in interest payments. Fortunately, it is also one of those things that don’t require much conscious effort to attain. With a few small tweaks, and good financial practices that you should be following anyway, you can be on your way to building a great credit score.

Always pay your bills on time, no matter what. In fact, I’ll go one step further and say that all credit card balances should be paid off in full, every month, no matter what. If you don’t, the interest rates on those balances will bleed you dry. If you can’t afford to pay off your credit card balance in full, you should not have spent the money in the first place.

If you ever have any loan that charges you 10% interest rates or more, you should similarly pay it off as soon as possible. On the flip side, if you have any loans that charge 4% interest rates or less, make all your minimum payments, but do not pay it off early. You’ll be better off investing the money in stocks & bonds instead, which offer 6-10% returns.

Use only a fraction of your available credit limit. Ideally, 10% or less. For example, if you have 2 different credit cards with a combined credit limit of $20,000, you should only use $2,000 of it. If that isn’t sufficient for your expenses, request a credit limit increase, or pay off your credit-card balance multiple times during a single month.

Build up your credit history, and hold on to it. Open up your first credit card as early as you possibly can, and hold on to it for decades. Use some amount of credit regularly. If you have the choice of paying for something using your credit card or cash, use your credit card. If you have the choice of buying your car outright or taking on a low-interest loan, take the loan. Every 2-3 years, ask your credit card company to raise your credit limit, even if you don’t need it.

You don’t want to have too many different credit cards or loans, but it does help to have around 3 sources of credit active at any one time. This will allow you to build up your credit history and establish your reputation as a reliable borrower.

There are websites out there that will give you free copies of your credit report, and others that will help you monitor your credit rating and give you customized recommendations on what you can do to improve it. It might be worth your while to explore these for a few months, just so you can better understand your credit score and what you can do next to improve it.

Career Planning

I’ve put this section last because it technically doesn’t fit into the category of personal finance, but it can have a larger impact on your finances than anything else mentioned above. The best possible investment you can ever make, is an investment in yourself. More specifically, an investment in your education & skills.

If you’re a high school dropout making $30,000 per year, you’ll have to scrimp and save just to have a financially stable future. In contrast, if you’re an MBA grad making 6 figures, you can afford to really enjoy life, while still saving for a luxurious retirement. Investing in yourself to bridge the gap between the two can be stressful in the short-term, but can pay off spectacularly within a decade or two.

A word of warning here: Bad investments do exist, and so too does bad educational expenses. If you’re spending $200,000 attending a private college and majoring in Art History, that may not be the best financial investment.

However, there are many other degrees and career paths that one can follow, which are very lucrative. For example, you can become a Registered Nurse simply by attending community college, and it pays $65,000 per year on average. Similarly, there are plenty of other lucrative career options that can be unlocked by enrolling yourself in an Associate’s Degree program at a nearby community college. If you’re willing to study longer and aim higher, there are plenty of college majors available at public universities, with extremely strong career prospects as well. For someone with a college degree and looking to grow their career further, doing a 1-2 year Master’s in a related field, or pursuing an MBA, can help them take their career to the next level.

There is no easy answer here, and the ideal way to grow your career will differ for each person. But considering the outsized impact it will have on your financial future, it’s certainly worth some serious thought, research and active planning.


There certainly is a lot of information covered here, and it’s very easy to feel overwhelmed if you’re coming across this information for the first time. Rest assured that there’s no way anyone can put into practice all the advice given here, in a single day. Start off slow, and start off small. Bookmark this page, or make a list of all the things that you need to do. Every day, look at the list and work towards ticking one item off of it.

It may take a few months to get everything done, and that’s completely fine. Life isn’t a sprint, it’s a marathon. Focus on taking just one step at a time, and before you realize it, you’ll be amazed by how far you’ve come.

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