Too often, people mix up the ideas of risk (or riskiness) and complexity - they aren't the same and they shouldn't be mixed up. When you don't understand the difference between the two, you're liable to make errors in judgment and/or decision-making related to your investing portfolio, your career, and even your overall life.
Complexity in our current context is when things are complicated, multifaceted, and difficult to grasp mentally in an all-encompassing way. Complex things need to be broken down to be understood, but they aren’t necessarily probabilistic (or stochastic) in nature.
Risky things, however, could be complex or they could be simple – there is an overlapping area where things are both risky and complex, but risky things definitely don’t need to be complex. Risk arises when there is a probabilistic (or stochastic) distribution of outcomes, some of which are unpleasant or detrimental in some way.
The reason people often mix the two up is because understanding and dealing with complex things requires mental energy – this means a human needs to exert real mental energy to deal with, process, or utilize complex things/concepts. This can be inherently unpleasant, since the conscious mind seems to want to be in a constant state of pleasant ambivalence and rumination (this rumination has a way of often becoming quite unpleasant, but that’s for a different day). Our minds might simply shut down in a sense when dealing with complex things, similar to how they’d shut down when working through risky things from a probabilistic sense.
The problem arises in that it makes a lot of sense to break risky things down into their underlying probabilistic components (assuming these components can even be understood), but it doesn’t always make sense to break complex things down in such a way if you’re only concerned about risk. It only makes sense when the complex things are risky; if they aren’t risky, there’s no reason to break things down to understand risk. Some mental discipline and clarity could help you take a few steps back and see the bigger picture. Ask yourself if this complex thing is in fact risky – if it is, analyze; if it isn’t, step back and don’t get bogged down in unnecessary details if your primary concern is risk-related.
The simplest things in the world (for example, whether the stock price will be above or below a certain strike price X) can be incredibly difficult to understand from a risk perspective. But, things that appear incredibly complex in their operation nature (for example, the fault rate of complex self-driving software) might be very simple from a risk perspective. In the self-driving example, maybe you only care about the error rate, which can be easily determined (and probably already has been by the firm producing the software) and utilized in downstream analyses, calculations, etc.
How to use historical stock market data to build your investing intuition, and move one step closer to becoming an investing superhero
On Monday, October 17, 1987, the S&P 500 dropped a little over 20%. Going back to 1950, this was the single worst one-day drop in the stock market. It showed and taught a lot then, and it can still teach market participants and investors today if they are willing to listen.
Historical financial data can be magical - it can help you travel into the past and see the forests from the trees. By listening to historical data, we can more easily understand that a single-day drop of 20% in an index such as the S&P 500 is possible. By knowing that a 20% stock market drop is possible -- and by seeing the number present itself to us in the data -- we can better understand the risks we face by investing and participating in the financial world.
How do we know whats or of stock market drops are possible?
What exactly does possible mean in the context of investing and considering severe market declines? Sure, we know it's "possible" for the S&P 500 to drop by this amount or that amount. But until you ground your understanding in some historical data, you're not going understand this possibility at a deep level.
Observing the S&P 500's daily price movements will help you learn what sort of severe drops are possible for your portfolio
First, a quick note on using the S&P 500: The S&P 500 is a great place to start because it's a reasonable proxy for the market. The S&P 500 surely doesn't represent the entire market of equities, financial assets, and let alone of all assets; but, it's a reasonable and easily-manipulatable proxy for "the market."
If we care about how bad things can get in a single day (eg. an extremely severe yet plausible one day decline in your portfolio), we'll want to look at daily price data. This type of data is readily available online. There's a lot of free data, but you'll have to pay to access longer time horizons or more esoteric data.
Below, we have S&P 500 data April 3, 1950 to September 6, 2019. This represents an almost 70-year time horizon, a bit less than the expected lifespan of a person today. You can see this in the screenshots below (bottom and top of the table shown; table ordered earliest to latest).
The data has three columns - one shows the date, the other the closing price of the S&P 500 on that date, and the last column is the day-over-day change int he S&P 500 stated as a percent. The day-over-day change is easy to calculate - it's merely the one day change divided by the previous day's closing price. Declared as a formula, it is: [Day 2 - Day 1]/Day 1
This is called the arithmetic return. More complex return types -- namely the geometric return -- exist, but they are outside the scope of this discussion. The simple arithmetic return above is sufficient for our purposes.
Observing financial market data can teach you a lot and help to build a bit of market-related intuition
Just observing stock market data like this can be useful. Exploring data visually without graphing it can give us some interesting and potentially-valuable preliminary insights. This is especially true for people who haven't done this sort of data analysis before. For example, we can observe that in the very beginning of our data set (the first few days of April 1950), the S&P 500 was around $18. This is in sharp contrast to the almost $3000 S&P 500 level we observe below for September 2019. This plainly shows us that there has been some dramatic growth over the last 70 years in absolute metrics.
Although we can see some things by observing the financial data, it's hard to determine summary statistics about the S&P 500 data set visually. Stats like mean, median, minimum, and maximum are hard to see because all of the data needs to be taken into account. Taking all of the data into account can't easily be done relying on the human mind - it's just not what it's made to do. The data set has almost 17,500 rows - that's simply too much to comprehend without the use of computing devices/methods (or without a considerable amount of time to devote to this endeavor). Luckily, such devices/methods are easily available for free (eg. Google Sheets) or cheap (eg. Microsoft Excel) in the form of software. More complex options are available that are both free and paid (eg. R, Matlab, Tableau, etc.). Something like Microsoft Excel would be enough for the vast majority of use cases, however.
Finding the minimum, or the worst stock market day over the last 70 years
Some relatively easy functions can be used in Excel -- the tool of choice for most finance people -- to get some stats on the data. In the screenshot below, you can see the average, the max, and the min. The min is what we care about most here - it represents the lowest day-over-day S&P 500 change; it represents the most severe single-day drop in the S&P 500 over the last 70 years.
We can see that the worst drop is -20.47%. That means that in one single day, the stock market effectively dropped by over 20%.
Black Monday - an over 20% one day drop in the stock market
We can see the drop occurred on Monday, October 19, 1987, by examing our data set in greater detail. By filtering the data from largest to smallest, we can see what date corresponds to the worst stock market drop. Once we have the date, we can observe what happened around it in the days before and after Black Monday, which is what Monday, October 19, 1987is called in the financial industry.
The image below is the copied and pasted data from around Black Monday. It's interesting and useful to observe what happened around that time. We can see in the 10 days around Black Monday, 7 out of 10 days were losing days. We can also combine the losses to see what the cumulative loss over the 10-day period would have been. We can see that it's even worse - over the 10 days, the stock market dropped over 26%.
That means you could wake up one day over the course of your investing life and see that your portfolio is down 20% in a single day. That event would be tough to deal with - you'd be in for a very rough day and rough week. It would take some time to recover from the loss, but recovery would definitely be possible. A mistake, however, would be to panic and deviate form your long term investment strategy for no real reason beyond the fact that you're freaked out.
Use this knowledge to avoid panic sales and other forms of freaking out during the next inevitable stock market disaster
We all get freaked out in investing - it's your money that's on the line, and you don't want to lose it. Even small drops can seem bad. Even times where there's no movement could be perceived as bad if you were anticipating gains. You can't let these investing difficulties make you make investing mistakes, however. You've got to do your best to maintain a long-term perspective on investing. Something that helps us do that is exercises like the one we just went through. Looking at historical market data, understanding how the markets have moved over time, and understanding how markets may tend to move int he future are all essential things that will buffer you from foolish investing mistakes made out of fear.
If you'd like to explore the Excel file form which the above screenshots originated, you can download the file here. You'll be able to copy and paste the S&P 500 data to do your own data analysis work, like finding the maximum one-day increase.
At the beginning of your wealth-building lifetime, it's your rate of saving and investing that matters more than your rate of return
People in the investing and financial world fetishize rates of return. Often cited and mentioned in financial articles is financial/investing genius Warren Buffet. Since 1965, Buffet has generated (thru 2017) approximately 21% annually. This is astonishing and deserves both praise and diligent study, but for most people who are in the early stages of their investing lifespan, it isn't relevant or useful.
The reason it's not relevant or useful for most people who are in the earlier stages of their investing timeline is that a focus on investing rates of return is useless and distracting. It's not the rate of return that matters most for a twenty-something or thirty-something investor. Instead, it's their rate of saving and investing that matters far more.
Barring ridiculously large and deeply improbably investing returns, getting more return won't be as beneficial as saving more. Imagine you have $1000 today, you can get an astonishingly high 50% return, or you can save another $1000 and get a100% gain effectively. If you've got $10,000, this becomes harder to do unless your income is very high. At $100,000, it's very hard to save an additional $100,000 - you'd likely want to start giving proper focus to investing returns. At $1 million, you'd likely begin to see more gains from investing than from saving. Obviously, these numbers need to be adjusted depending on income, but the core principle remains the same - if you don't have a lot of capital to work with, stashing away more capital is going to be better for you than trying to finesse something with the small amount of capital you do have.
One of the most significant risks related to house flipping is holding period market risk - it's the risk that during the time in which you're holding the property you intend to "flip," the property value will decline.
The decline in property value can be caused by a variety of reasons (macro recessions, localized events, etc.), but that's not the point of this short piece. The point being made here is that house flipping exposes the "flippers" to significant market risk.
Not taking this real estate market risk to which you're exposed to when pursuing a house flipping strategy into proper account and consideration may have some serious negative consequences. The negative consequences are rare - they only arise in market downturns, which happen once every number of years. But, although the chances of the risk coming to fruition are small, the severity of the negative consequences (should there be a real estate market decline) are severe. The consequences can be severe enough to wipe out investors that are not well-capitalized and in positions of strong liquidity.
This is pretty easy to see if we think about a hypothetical example. Let's say you're doing house flipping and you buy a $200,000 property. The timeline might look something like this:
The risk exposure continues until you sell the house. So, in the above example with the relatively rapid renovation and resale (likely in a good real estate market; very unlikely in a real estate downturn), the investor or flipper would be exposed to market risk arising from adverse moves in the real estate market for at least a few months. If the investor is new, inexperienced, or doesn't have a lot of capital/liquidity in reserve, things might be over in one serious real estate or economic downturn.
If you're holding a property that's worth less than you bought it for -- even with the improvements you made or might make -- you'll have to (1) either accept a loss on this investment or (2) you'll have to continue making mortgage payments on the note until the market recovers.
In the first case, you'd lose real money - you'd possibly lose your entire down payment and in the worst scenarios you might be so underwater that you'd have to add additional funds to be able to get rid of it. This isn't far-fetched. Many people all across the United States experienced this during the Great Recession that started in 2007/8.
In the second case, you'd avoid having a severe capital loss, but you'd have to outlay money every month to keep the mortgage note current. This can be costly, especially if this is done for many months or even many years.
Of course, you might have bought the house in cash - in that case, you still may experience a severe loss (you'll just never be underwater on the mortgage). Renting might also help mitigate the risk - if there's a downturn, you might abandon your initial house flipping strategy and put a tenant(s) in the property for several months or years to help with the mortgage payments.
A prudent house flipper or potential house flipper would take these risks into account. Everything is exposed to risk, so this article isn't attempting to say that real estate investing in general, or house flipping specifically, are imprudent investments or that there's undue risk in a house flipping strategy. The article simply attempts to highlight a particular type of risk that house flippers are and will be exposed to.
Can investing in your career provide more financial benefits than investing in the financial markets? Maybe...
For most people -- especially for those in the 1st half of their working lives/careers -- investing time, energy, and even money into their careers might prove to be very valuable investments. For many, investments in their careers might prove more rewarding than typical financial investments.
The reasons why this is the case for many people are two-fold. First, most people don't have a lot of initial capital to start off with - saving and investing is key for them, but with so little capital there's not much that can be achieved in the short run for the typical retail investor. Second, investments in your career (e.g., investments in your skills and knowledge) have compounding effects over time as one progresses in his/her career.
It's hard to give a useful guide on what to pour your money, your time, and your energy into because each job is different and careers are diverse. However, it's a safe bet that building the following skills/attributes within yourself will prove very beneficial over time:
With each economic cycle in modern economies, we experience the same thing - there's a boom, then a bust, then a recovery, and then another boom...
It's typical after a long period of growth for investors, the financial media, and your everyday Joe Shmo to start thinking that a recession looms on the horizon. But, recessions don't like fear - people freaking out doesn't usually beckon a recession.
In actuality, recessions are more often seen right after periods of intense euphoria in the economic and financial worlds. These times are marked by excessive optimism and a fear of missing out (FOMO) by many market participants. During such times you'll hear people traditionally not involved in finance or investing talking about investing - this is markedly different than how people act during times of fear or caution.
Thinking that a recession is near when most others think this is an error in most cases - one likely based on not understanding financial market history well enough. Although real panics will very likely have macroeconomic consequences (and might cause a recession or even a depression), general but relatively subdued caution and fear is not likely going to be the cause of a recession. It's when people expect it the least do macroeconomic downturns start to brew.
Figure our your "why" for saving, investing, and building wealth - it'll help you financially and emotionally
A lot of well-educated people in today's modern economies save and invest a lot of money relative to their less-educated or less well-off counterparts. But, too often, these people in advanced economies lose sight of what they are saving and investing for.
It's not for anyone -- especially this blog -- to opine on why people should be saving and investing. But, it is troubling when most people can't come up with an answer quickly.
When you can't think of an answer quickly, it means you haven't thought about the question/problem long enough. In the case of saving, investing, and attempting to build wealth, that's a problem - if you haven't thought about "why" you're trying to build wealth, you're doing a disservice to yourself and your community (e.g. your immediate family, broad family, friends, etc.).
The point of building wealth is to use it - you can use it soon, you can use it far into the future, or you can put measures in place so that your wealth is used when you are dead. If your wealth is never used, it is clearly wasteful. If you don't think about how it's going to be used, that doesn't mean it won't be used; that doesn't mean you're wasteful. You're not - you're saving and building wealth. BUT, by failing to think about how you'll use your wealth, you fail to
It would do you a lot of good -- both financially and emotionally -- to grab a cup of coffee once a year and go for a long calm walk while thinking about your "why" (or any similar clam and contemplative activity).
From a mathematical perspective, those in Finance can clearly show you how not being diversified -- in an economy that allows for diversification -- is not prudent. Why isn't it prudent? Because, for most investors, not having all of their eggs in one basket will prevent them from devastating loss should some baskets break. Baskets break all the time.
Although diversification is an ancient concept, the modern idea of financial diversification in the context of creating an effective investment portfolio can be attributed to Harry Markowitz. Markowitz published his seminal paper titled Portfolio Selection in 1952. Check it out here, and other places online.
Some investors, however, feel that they don't need this rule. Some investors think the rule, or more precisely, the nature of the world in the investing space, doesn't apply to them. They feel that they know more than the typical investor or investing firm knows - they think they're somehow better at picking stocks or making investment decisions. These people -- and they are everywhere -- believe that they're just different. It's a common thing in humanity, and it might not change.
In the context of investing -- and specifically retail or family office investing -- portfolio concentration risk is the risk that you are overly exposed to something. That something can be any of the following and more:
Inappropriate portfolio concentrations are those that expose your portfolio to more risk than you would like or more risk than would be prudent. As such, assessing the concentration levels within your investment portfolio and taking steps to ensure that they are in line with your goals is a smart thing that should be done every so often.
The good thing is that it’s pretty easy and straightforward to determine the concentration levels for a lot of things like stocks, sectors, and countries (things like determining the concentration to strategies and assumptions is a bit more complex).
Step 1: Compile your entire investment portfolio
This might be the most difficult part as modern investors often have portfolios spread out amongst different account or different institutions. For example, you might have a brokerage account, a savings account for an emergency fund, some random savings accounts, and a 401k plan at work – this isn’t unreasonably complex but it does mean you’ll need to do a bit of work compiling things initially.
In fact – you should have done this already; the info should already be complied! If you’re investing and you don’t have a single source that is updated at least occasionally where you can get a high-level picture of your portfolio, you’re making a mistake. Spending some time on this will be beneficial in many ways, beyond just understanding concentrations and concentration risk.
Step 2: Pick a concentration category (eg. stocks, countries, sectors, etc.)
Next, pick a category against which you'd like to determine concentration levels in your portfolio. Don't start with complex things - start with basic things and move towards more complexity as you slowly get a better understanding of the risk nature of your portfolio.
For example, a great place to start would be sectors - you don't want to be exposed to a particular sector too much. If you're only in tech stocks or only in blue chips, you might want to diversify at bit more, depending on your risk tolerance and investing horizon. At the very least you'll want to know that you're heavily concentrated in particular sectors.
Other key concentrations are for individual stocks (eg. the investor who's absurdly exposed to one particular stock they love at the detriment to proper portfolio risk management and diversification).
Step 3: Simply make a list
For a retail investor doing simple portfolio concentration risk analysis, once you have your portfolio in one place and once you decide what you want to examine, it's very simple to proceed.
All you need to do is make a list with two columns - the particular investment product in the right column and the percent of the portfolio that the investment product represents. This is best illustrated by the table below.
As you can clearly see, this isn't a healthy portfolio. The vast majority of the portfolio is concentrated on
The portfolio has home country bias and seems to biased toward popular or newsworthy tech stocks and friend/family tips. Only 30% (broad market ETF + global ETF) of the portfolio is in a broad, well-diversified, investment product while 55% of the portfolio is in just 3 stocks. That's simply absurd for most investors - unless you're an excellent/skilled investor with a very long time horizon and a high risk tolerance, that sort of exposure is unacceptable.
Step 4: Take prudent risk-mitigating steps to reduce the concentration risk within your portfolio
Finally, after the analysis, you would take action - you'd act in ways to adjust your portfolio to reduce concentration risk. Of course, in doing this you'd want to be prudently confident in the insights on which you base your decisions and you'll want to take other factors into account - these other factors might include tax implications and macroeconomic assumptions.
In our example above, a prudent investor would sell off some of the tech stock exposure and re-assess weather the family member's energy stock tip was actually a good tip (eg. is the stock worth owning). Then, the investor might take the proceeds from these sales and invest them into more well-diversified products like ETFs, focusing both on foreign and domestic ETFs. The investor would also want to make sure to focus on both small cap and large cap ETFs, keeping in mind their risk tolerance and adjusting appropriately.
Finally, the investor might see that they are only in equities - this might make sense but putting some money in bonds or alternatives might make sense for some investors. These decisions are all individual - one needs to act prudently based on their own circumstances.
Concentration risk is only one type of investment portfolio risk, but it's an easy one to spot and fix. A lot of investors are prone to taking on too much concentration risk. They don't do it intentionally - they just lack an investing plan or approach and instead buy stocks here and there based on emotions. This is hard to remedy - not everyone is going to create an investing approach and monitor it over time. But, people easily -- and enjoyably -- do the above exercise once in a while (at least once a year) to see if their portfolio is too concentrated on one stock, one sector, or one economy.
Newton said there's inertia in the universe, so we now know more about our world and physics is better for it. That's not the inertia we're talking about here. Forget the universe for a second - focus on inertia in your mind.
Mental or spiritual inertia is a real thing. We won't try to define it here, but everyone who has experienced it knows what it is. It's when
Here are some examples of using interim in your own favor and taking quick, small, but intense bursts forward in whatever you'd like to achieve:
Devastating portfolio declines and what it takes to recover from them – the math isn’t in your favor
Everyone thinks about gaining money when they invest, but too often we neglect how important it is to not lose money. Not losing money is so important, in fact, that one of the greatest financial investors in history (and very likely the greatest one alive today) espouses the following as his Rule No 1:
Don’t lose money.
What’s Rule No 2?
Remember Rule No 1.
Rule No 2 is obviously meant to be a little humorous, but Buffet is a serious man when it comes to investing and his rules are meant to illustrate a fundamental truth about investing – that truth is that it’s very hard to recover from a loss and that it gets harder and harder the deeper the loss.
This is all best illustrated with examples. Sometimes, a good set of examples can do more for contributing to understanding than pages and pages of text. So, let’s go over three examples, each with increasing levels of severity of initial losses.
In each example, we’ll break things down into 3 time periods – Time 0, Time 1, and Time 2:
A 25% Loss – Somewhat severe, but recoverable
With a 25%loss, your $1000 declines to $750 – this represents a one-quarter decline in your portfolio and would obviously be an unwelcome occurrence. Now, let’s take a look at what sort of returns you’ll need to recover by Time 2; let’s see what sort of returns in the subsequent time period you’ll need to make you whole again.
As you can see from the table, a 33.33% gain is required in order for you to recover and get back to the initial $1000. A 10% return, 20% return, or even a strong 30%return in one time period simply won’t do it.
That means if each time period is 1 year, even a 30% return in the year subsequent to your 25% loss won’t be enough. 30% is a solid return. The fact that it’s not enough should be the first hint that getting back to whole is a lot harder than dropping, from a mathematical/percentage perspective. It’s only going to get worse.
A 50% Loss – Very severe, but you can recover if you stay prudent over the long term
With a 50% loss, it’s a lot harder to recover. Now, it takes a 100% gain (doubling your post-loss portfolio value) to get back to whole again. If you halve your portfolio, you’ll need to double it to bring it back to its original value.
So, if a time period is one year, you’ll need to double your post-loss portfolio value to get back to your Time 0 initial value. That’s very hard. You’d be far better off having avoided such a decline because it’ll be an uphill climb getting back to baseline again. This is what Warren Buffet’s Rule No 1 points to.
A drop of 50% in your portfolio value is very severe and detrimental to your long term investing goals. It will take a 100% increase -- doubling your portfolio -- to recover from a 50% loss. This is tough, but it's doable - it might not happen in a single time period but over time a prudent and disciplined investor stands a chance at recovery.
A 75% Loss – A devastating blow to a portfolio that will take some time to recover from
With a 75%, things get really bad. Now, in order to get back to whole, you’ll need a 300% gain. A 300% gain is the same as quadrupling your money (4x return). As any investor knows, a 300% return is very hard to get – it usually takes years to achieve such returns in a well-diversified portfolio.
Let’s think about this some more. As we keep increasing out Time 1 losses by 25% increments, the return needed to get back to whole by Time 2 goes up by way more than 25%. This is based on the underlying mathematics of portfolio returns, but we don’t need to get deep into that here. The above examples should clearly show how each time the loss gets more severe, the needed gain to get back to baseline gets more and more astounding.
If you lose 75% of your portfolio’s value in a single year due to a very severe recession or, far worse, due to investing blunders, you’re going to have to make some incredible returns (300%) to recover. What makes you think you’ll beable to do that? It’ll likely take a number of years and some serious investing discipline to be able to recover in this way.
A 75% portfolio decline is devastating to any portfolio. It will take a 300% return (quadrupling your money; a 4x return) to get back to whole again. This is very hard to do in a single time period. It might take years of prudent and disciplined long term investing to recover. This demonstrates why large portfolio declines are so detrimental and should be avoided.
A bit more mathematical, for the mathematically inclined
For those that are more mathematically inclined, let’s dig a bit deeper into the portfolio maths.
Let’s assume an initial portfolio value of a – this is your Time 0 value
For any portfolio change (decline or increase) d, where is greater than -1 but less than 1, the portfolio value in the immediately subsequent period (Time 1) will be a x (1 + d)
To get back to the initial portfolio value by Time 2, we’ll need to do something to the Time 1 value to get it back to a (which we stated above was our initial value)
We can simply divide the Time 1 value by (1 + d) to get back to a – that’s [a x (1 + d)]/(1 + d)
Dividing by (1 + d) is the same as multiplying by 1/(1 + d) – that’s the amount, no matter what our initial a is and what the change d ends up being, that we have to multiply the Time 1 portfolio value by
Now, notice that if d is less than 0, 1/(1 + d) will be larger than 1. So, if d is -0.25 (corresponding to a 25% decline in our first example above), then 1/(1 + d) is 1/(1 – 0.25) which is 1/0.75. What’s 1/0.75? It’s 1.3333. That means you’ll need 1.3333 times the Time 1 value – this exactly represents an aprox 33% increase.
Let’s do a 75% decline as in the third example above – now 1/(1 + d) is 1/0.25. That’s equal to 4, which represents a 300% increase over the Time 1 value.
We can see that as d approaches -1 (moving towards a total loss), 1/(1 + d) gets bigger, but by a disproportionate amount.
Can we derive a simple way to see how our 1/(1 + d) factor changes with changes in d? Yes – it’s easy using Calculus:
d/dx[1/(1 + d)] = d/dx[(1 + d)^-1] = [-(1 + d)^-2] x d/dx(1 + d) = [-(1 + d)^-2] x (0 + 1)
so, the derivative is -1/(1 + d)^2
Calculus can be applied to lots of situations to better understand how things change. F
We can see that by squaring the (1 + d) term, we’re increasing the effects of both positive and negative portfolio changes. If d < 0, then squaring (1 + d), which will be less than 1, will only make the factor smaller. By making that factor smaller, the entire factor gets bigger because dividing 1 by smaller and smaller numbers makes the result bigger and bigger.
This should be very discouraging – the numbers tell us that negative effects are magnified when we think about the returns needed to recover.
And now, given the rise of cyrptocurrencies and crypto assets to quasi-mainstream financial assets, we're dedicated to providing quality, relevant, and interesting material on cryptocurrencies and cryptoassets. Articles on Bitcoin, Ethereum, Ripple, Cardano, and many more cryptocurrencies and cryptoassets can be found on Pennies and Pounds - all that in addition to a plethora of information on what cryptoassets are, how the entire crypto industry came to be, blockchain/immutable ledger technology, mining, proof of work, proof of stake, and how to prudently invest in crypto if you are so inclined (based on your risk tolerance and ability to withstand the volatility that will come with a crypto portfolio).