jankythoughts2

Foreword

Unless you are extremely lucky, building wealth will likely be a long term process, something you work towards over long periods of time, possibly your whole career.

Once you’ve built your wealth, retaining it will require just as much, if not more effort. Without the discipline to control your budget, invest wisely and manage your risks, whatever wealth you may have built, can easily be squandered away.

As usual, a reminder that I am not a financial professional by training — I am a software engineer by training, and by trade. The following is based on my personal understanding, which is gained through self-study and working in finance for a few years.

If you find anything that you feel is incorrect, please feel free to leave a comment, and discuss your thoughts.

Expected returns

Let’s say there is a game, where you have to bet your entire liquid net worth every turn, but the expected return to whatever you bet is 10% (i.e. the expected value of a $1 bet is $1.10). Would you play this game? And if you would, how many rounds would you play?

Given the positive expected returns, I’m guessing a large number of people will play at least one game, and a good number of people will play until they are rich enough to retire.

What if I say that every turn, you have a 99% chance of winning 11.11% of your bet, and a 1% chance of losing everything (expected return is still 10% per turn)?

I’m guessing that most of those who would play at least once, will still play at least once, but most people will only play a relatively small number of games, somewhere in the 1-50 games range, certainly not enough to let most people retire.

What if every turn, you have a 1% chance of winning 110x of your bet and 99% chance of losing everything (expected return is still 10% per turn)?

I’m guessing close to nobody would play the game now.

The key to remember here is that positive expected return is not nearly enough information to determine if something is a good bet. Volatility of returns is important too!

The longest race

From the day you start accumulating wealth, to the day you pass from the world, the need for financial discipline is constant — it is the race that never ends, until you literally do.

If you become fabulously wealthy, then yes, you can probably be more reckless and still get away with it. But not too reckless! History is replete with famous rich people who manage to gamble away unimaginably large fortunes.

But no matter if you have $500k saved for retirement or $5b, the fact remains that you need to maintain some financial discipline. Simply betting your entire liquid net worth on a lark is probably not a winning strategy!

If you are making a one time risky bet, you may certainly get lucky — even better if the odds are in your favor. But no matter how small the chance of ruin, if you keep making that same bet, and if every single bet is an independent event and thus has the same odds, then that small chance of ruin will eventually catch up with you — the law of large numbers practically guarantees it.

It is with this in mind, that I view with horror at how some people are betting large portions of their net worth on options. Yes, in the short run, you can quickly grow your money by a few multiples, maybe even a few orders of magnitude — as long as you remain lucky. But once your luck runs out, one bad bet can easily ruin you. To make matters worse, buying options generally has negative expected returns — options are generally priced such that options sellers have positive expected returns, while buyers have negative expected returns.

Viable strategies

That’s not to say that risky bets are totally off the table. The crux of the matter is that the event of ruin, no matter how unlikely, will eventually occur if we tempt fate enough times. So, naturally, the strategies to counter involve trying to reduce or completely remove the chance of ruin.

For example:

• Diversification
  • By spreading out your bets, the probability of all of them going sour at the same time is reduced, hence reducing your chance of ruin.
• Taking profits
  • For speculative bets, including investments that have gone beyond rational exuberance, taking some profits off the table gives you cash to redeploy as and when the markets regain some sanity.
• Buying insurance
  • Insurance in the financial markets tend to be expensive, but if you have a position that has a large chance of ruin, it may make sense to buy some insurance against that event. For example, if your portfolio is heavily concentrated in technology stocks, it may make sense to hedge that exposure by buying puts against QQQ.
• Rebalancing, position sizing
  • A combination of taking profits and diversification, regularly rebalancing your portfolio and making sure the value in each position is a limited part of your entire portfolio will ensure that no single blow up will wipe you out.

Marathon

At the end of the day, it is important to recognize that getting “there” and staying “there” are two sides of the same coin. It is a journey from the first dollar you make, to when you are laid to rest. It is a marathon, and you need to treat it as such — making rational, long term decisions, instead of trying to bet the farm on random whims.

Foreword

How do business ventures get funded? Who’s paying for the overhead when the company is first starting out and has no revenue? And what do they get out of this?

As usual, a reminder that I am not a financial professional by training — I am a software engineer by training, and by trade. The following is based on my personal understanding, which is gained through self-study and working in finance for a few years.

If you find anything that you feel is incorrect, please feel free to leave a comment, and discuss your thoughts.

Decent proposal

Let’s say you have a fantastic new business idea, but to get the business started will require $50,000 right now, which you do not have. How could you fund your new venture?

Traditionally, there are 2 main avenues:

1. Take a loan from a bank
2. Take on some partners who have deeper pockets (i.e.: sell a portion of your new company)

The former is also known as debt financing, and the latter is equity financing.

When you take on debt, you agree to pay the lender some amounts of money on some fixed timeline. For example, 1% of the loan amount every month (interest payment), and then 100% of the loan amount at the end of 10 years (principal payment).

When you take on partners, they share in the profits (or losses!) of the entire enterprise. So, if after paying off all your bills (which may include debt payments), you are left with $1,000 to distribute between the partners, then you and your partner can(1) get up to $1,000 in total. Who gets how much depends on your partnership agreement, as well as how much of the company each of you own.

First come, maybe not first served

Who gets how much money, and when, is one of the 2 central differences between debt vs equity financing.

Debts must always be paid back, on the timeline agreed upon when the loan is taken out. If you fail to make even a single payment on the debt, it is technically in default, and may officially be in default after some grace period. At that point, the lender generally has some set of rights they can exercise, up to and including forcing you to give up ownership of your company to them.

Equity partners, on the other hand, generally have no fixed payments due. A company can very well never return a single cent to the equity partners! The main considerations are the partnership agreement(2), which will detail how any payments, if made, will be distributed amongst the partners, and fairness — in general, in the absence of any details about how profits are shared, then all dividends will be made pro rata, i.e.: if each of the partners own 50% of the company, then every dollar distributed will see 50c go to each partner.

One way of thinking about this, is that debt investors have the first dibs on revenue generated by the business. Once all debt payments are made, and all other costs are paid, whatever is left over (which may be nothing, or even negative — a loss) can be distributed to the equity partners. In exchange for this “seniority” in terms of payment, debt investors typically settle for a smaller and shorter-term profit — interest rates are generally much lower than what the business can be expected to return over the long term.

Control your enthusiasm

The other central difference between debt and equity financing is that of control, or rather rights — who has rights to do what with the company?

Debt investors generally have no rights on the company other than their regular payments (sometimes known as coupons). If, however, a payment was missed for long enough that the company is in default of the loan agreement, then debt investors generally have additional rights to recover their investment, such as forcing the equity partners to give up ownership of the company, or forcing a sale of the business to 3rd parties to repay the loan.

Equity investors are generally split into 2 groups — the general partners(3) who oversee the actual running of the company, and may even be personally responsible if the company goes bankrupt, and the limited partners, who generally provide the funding for the business, but otherwise have no say in the day to day running of the company.

Mix ‘n match

When you think carefully about it, debt investors and equity investors are very similar at a very high level. Each of them:

• Provide capital for a company …
• … and, in return, receives some promise of cash flow at a future time, …
• … along with some rights with regards to the company.

And at this abstract level, it shouldn’t be surprising, then, to learn that the tradition little boxes that debt and equity investors fit in, are not nearly that clean cut in practice.

In practice, an investor in a company is labeled debt or equity based mostly on their rights to call an event of default on the company. If an investor can call an event of default on the company when their promised distribution is not received, then they are typically labeled debt investors. Otherwise, they are an equity investor.

Some examples, in order of decreasing priority when profits are being distributed (i.e.: an investor at a lower row is not paid, until all investors in higher rows are paid according to the agreement):

A table where a company lists all its debt and equity investors, according to their priority in terms of payment and their contributions to the venture, is called a “capitalization table” (or “cap table” for short). A table or description detailing how the profits are actually distributed (assuming there are any profits to distribute) is called the “waterfall”.

In general, as you go down a cap table, risk increases, but potential return also increases.

To each their own

Which tier you want to invest in, is entirely up to you and your personal situation.

If you are a retiree, and you need stability of income, you may opt to give up some upside, but get more protection by going up the capital stack (i.e.: going up the rows in the cap table).

But if you are investing for the long term, and you are diversified such that your investment in a single company is a relatively small part of your entire portfolio, then it may make sense to take on the additional risks involved in the lower tiers, for a chance at a higher return — even if this particular company goes bankrupt and you lose all your money in it, hopefully, enough other companies that you’ve also invested in will succeed, such that you still make a greater return than investing at a higher tier.

In the end, where each investor ends up on the capital stack depends on their expectations of how the company will perform, as well as their personal financial situation (generally, their ability to withstand uncertain cash flow and/or losses).

Footnotes

1. “Can”, not “will”, because in most cases, distributions (or dividends) are not paid on new companies. New companies tend to be very cash hungry, as they need cash to spin up their factories, advertising, research, etc., and more cash is almost always better. As such, equity partners generally don’t tend to see a single cent of profits until years 2-3 or beyond. The exact timeline depends on the nature of the business — some cash intensive businesses may not see a dividend for decades!
2. Technically, a “partnership agreement” is only used in a partnership (this is a legal term). LLC’s (limited liability company) and corporations use “operating agreements” instead. However, for purely financing purposes, the basic principles remain the same — a group of people got together to fund the equity tier of a company, and there’s a document that describes what they can expect to get out of that venture. I’ll use partnerships for simplicity going forward. Understand that the issues discussed affects LLC’s and corporations as well, though perhaps with minor differences.
3. As with “partnership agreement”, “general partner” and “limited partner” are terms used in partnerships (the legal entity). LLC’s and corporations have different names for these roles (board of directors, executive team vs shareholders, etc.). Despite the naming differences, the roles are mostly the same and for simplicity, I’ll stick with the nomenclature for partnerships.

Foreword

Real estate vs stocks, the perennial debate. Which one should you invest in?

As usual, a reminder that I am not a financial professional by training — I am a software engineer by training, and by trade. The following is based on my personal understanding, which is gained through self-study and working in finance for a few years.

If you find anything that you feel is incorrect, please feel free to leave a comment, and discuss your thoughts.

Caveats

Before we go deeper into the discussion, I’d like to address some criticisms of “Monte Carlo“. To be absolutely clear, in “Monte Carlo” and in this post, I use simplified models to represent returns from various assets. In particular, stock returns have been modeled as normal distributions, which isn’t quite correct:

As you can see from the histograms, actual stock markets total returns (left) is quite different from the stylized normal distribution with similar mean and standard deviation.

Separately, assumptions that stocks and bonds (and in this post, real estate) returns are completely uncorrelated are clearly too permissive. In reality, stocks, bonds and real estate are somewhat (negatively) correlated over short periods of time, as all of them are generally affected by politics, inflation and interest rates, amongst other things.

That said, the point of “Monte Carlo” and this post isn’t to build a perfect model for anyone’s financial planning purposes. Instead, these 2 posts are meant to explore various aspects of portfolio construction — how you should think about expected returns, CAGR, SWR, and how volatility affects these metrics. With this rather more modest goal, I believe the simplified models used are more than adequate.

My my, what low returns you have!

In “My Personal Portfolio“, I mentioned that I invest heavily in real estate, generally via private real estate syndications.

In some private discussions about real estate syndications, others have noted that the pro forma returns presented by some real estate syndications that I invest with (generally in the 10-15% range) are lower than what the stock markets have returned in the past 20 years or so.

If you pick up a calculator, you’ll find that from 2009 – 2020 stocks have returned about 15.5% on average every year, with a CAGR of about 15%. Compared to the 10-15% pro forma returns, it seems silly to even consider real estate.

Therefore, we should just invest 100% in stocks… right?

Expected returns

The first problem with the 100% stocks assertion, is that expected returns are misleading — expected returns are merely “expected” as opposed to “realized”. The future is always uncertain, and it is entirely possible that the next N years see returns dramatically below expected returns based on the past N years.

That is why in “Monte Carlo“, each test is done 10,000 times and the metrics reported are the averages of the 10,000 simulations. However, since the average person cannot live 10,000 lives and pick the best/median/average lives (1), these numbers should be taken with a pinch of salt — they are expected values, not realized nor even predicted values. In the context of a single lifetime, the law of large numbers simply does not hold.

Looking further

The next problem with the 100% stocks assertion is that only looking at the expected returns of the past ~11 years is misleading. Typically, expected returns are the arithmetic means of historical returns. In effect, they tell you “given a random year, what is the expected returns of that year”. Stock markets, however, do not always go up uninterrupted — periods of growth are punctuated with periods of declines.

In the context of historical stock markets performance, the past ~11 years have been unusually kind to stock investors, and it is currently not clear if future years will be as kind.

Since returns are multiplicative, a few years of subpar returns in the future will reduce lifetime CAGR significantly. In “Monte Carlo“, I presented historical total returns of the S&P 500, which suggests that long term CAGR is closer to 10%, with mean annual total returns of around 12.2%. Suddenly real estate is looking much better(2)!

Volatility

As we’ve discussed above and in “Monte Carlo“, volatility in the portfolio, as represented by standard deviation of annual total returns, can dramatically curtail the safe withdrawal rate from that portfolio. To illustrate this point, let’s look at some example scenarios.

In each of these, stocks are represented by both their sampled historical returns as well as their normally distributed returns (mean 12.1%, standard deviation 19.7%). The 2 alternate universes is a hypothetical scenario, where we invest 50% of our portfolio each in 2 completely independent stock markets (i.e.: each stock market in its own alternate universe). 5 alternate universes is where we invest 20% of our portfolio each in 5 completely independent stock markets. Real estate is represented by a normally distributed model with mean of 9% and standard deviation of 10% (3).

In each case, the portfolio is rebalanced annually so that the portfolio is distributed across the assets according to the description.

The histogram on the left is when we use sampled historical stock returns for the simulation, and the histogram on the right is when we use normalized stock returns.

Portfolio	Average returns	Standard deviation of returns	Histogram of returns
100% stocks	Sampled – 12.1% Normalized – 12.1%	Sampled – 19.7% Normalized – 19.7%
80% stocks 20% cash	Sampled – 9.7% Normalized – 9.7%	Sampled – 15.6% Normalized – 15.7%
2 alternate universes	Sampled – 12.2% Normalized – 12.2%	Sampled – 13.8% Normalized – 13.9%
5 alternate universes	Sampled – 12.1% Normalized – 12.2%	Sampled – 8.75% Normalized – 8.79%
50% stocks 50% real estate	Sampled – 10.6% Normalized – 10.6%	Sampled – 11.00% Normalized – 11.00%

And for the same 5 portfolios, we compute the CAGR and SWR over 30 years (see “Monte Carlo” for a full description of the methodology details).

Some interesting results:

• If we invest in 2 or more independent assets, then the sampled returns approximate the normally distributed model.
  • This is why the differences between using sampled stock returns and normally distributed model is generally small, especially when we consider a diversified portfolio.
• If you just put 20% of your assets in cash, and 80% in stocks, your expected returns will suffer. However, somewhere in the 95-99%-ile range, your SWR will actually go up.
• If you can invest in stock markets in 2 alternate universes, then your expected annual returns will remain roughly the same. But your CAGR and SWR will increase dramatically.
• This is even more pronounced if you can invest in 5 alternate universes.
• Since I am a mere mortal, the best I can do is invest 50% in stocks and 50% in real estate, which definitely helps SWR, and maybe helps with CAGR as well(3).

Diversification

The basic idea behind the magical increase in CAGR and SWR beyond 100% stocks, is simply “diversification”. When you diversify, and you rebalance your portfolio periodically (4), what you are doing is essentially selling high (the asset which outperformed) and buying low (the asset which underperformed). Buying low and selling high is, historically, the winning strategy for investing (and speculating), and will likely remaining a winning strategy in the future (5).

So, the last problem with the 100% stocks strategy, is that even if real estate has a lower expected annual returns and lower expected CAGR than stocks (3), the very fact that they are not very correlated to stocks means that an allocation to real estate can help increase your portfolio’s CAGR and SWR.

This is the same principle in use when financial advisors recommend investing in index funds (as opposed to single name stocks) — diversification helps to reduce overall volatility and regular rebalancing forces you to buy low and sell high.

Side note: taking profits

A corollary that is not immediately obvious from the above, is the act of “taking profits”. Historically, when people have asked me for advice on what to do after some speculative asset they’ve bought appreciated by a huge amount (more than 100% increase in price), my general advice is something along the lines of “sell enough so that you take a decent profit, and won’t be sad if everything else drops back to your cost basis.”

The psychological effect of doing so is that you’ve now already realized a decent profit, and everything left in that asset is essentially “house money”. While a mathematical fallacy, I have found that this has made holding on to a speculative asset that much easier.

The financial/mathematical effect of doing so, is essentially the same as diversification. Assuming the money you take out is put into another (not very correlated) asset, then you have essentially achieved the “2 alternate universes” scenario.

Code

What kind of a nerd would I be, if I didn’t also present the code for the simulations mentioned above? Note that this builds upon the code in “Monte Carlo” — you’ll need to copy the code there and save it in a file titled “montecarlo.py” for the code below to work.

#!/usr/bin/python3.8

import matplotlib.pyplot as plt
import montecarlo
import numpy


HISTORICAL_RETURNS = montecarlo.HISTORICAL_RETURNS

NormalDistribution = montecarlo.NormalDistribution
UniformSampling = montecarlo.UniformSampling
Cash = montecarlo.Cash
Composite = montecarlo.Composite

GenerateReturns = montecarlo.GenerateReturns
MonteCarlo = montecarlo.MonteCarlo


def PlotHistogram(data):
  _, axs = plt.subplots(1, len(data))
  if len(data) == 1:
    axs.hist(data, bins=30)
  else:
    for i in range(len(data)):
      axs[i].hist(data[i], bins=30)
  plt.show()


def PrintStats(label, data):
  print("{}  Mean:{:.3g}%  StdDev:{:.3g}%".format(
    label,
    numpy.mean(data) * 100,
    numpy.std(data, ddof=1) * 100))


class NormalizedDistribution(NormalDistribution):
  def __init__(self, label, data):
    NormalDistribution.__init__(self, label, numpy.mean(data), numpy.std(data, ddof=1))


def Main():
  cash = Cash("Cash")

  sampled_stocks = UniformSampling("SampledStocks", HISTORICAL_RETURNS)
  normal_stocks = NormalizedDistribution("NormalizedStocks", HISTORICAL_RETURNS)
  normal_re = NormalDistribution("NormalizedRE", 0.09, 0.1)

  data = GenerateReturns(normal_stocks).flatten()
  PrintStats("Historical S&P 500", HISTORICAL_RETURNS)
  PrintStats("Normalized S&P 500", data)
  MonteCarlo(sampled_stocks)
  MonteCarlo(normal_stocks)
  PlotHistogram([HISTORICAL_RETURNS, data])

  sampled_stocks_80 = Composite("80% sampled", (sampled_stocks, 0.8), (cash, 0.2))
  normal_stocks_80 = Composite("80% normalized", (normal_stocks, 0.8), (cash, 0.2))
  s_data = GenerateReturns(sampled_stocks_80).flatten()
  n_data = GenerateReturns(normal_stocks_80).flatten()
  PrintStats("80% sampled stocks, 20% cash", s_data)
  PrintStats("80% normalized stocks, 20% cash", n_data)
  MonteCarlo(sampled_stocks_80)
  MonteCarlo(normal_stocks_80)
  PlotHistogram([s_data, n_data])

  sampled_stocks_alt2 = Composite("Alt2 sampled", (sampled_stocks, 0.5), (sampled_stocks, 0.5))
  normal_stocks_alt2 = Composite("Alt2 normalized", (normal_stocks, 0.5), (normal_stocks, 0.5))
  s_data = GenerateReturns(sampled_stocks_alt2).flatten()
  n_data = GenerateReturns(normal_stocks_alt2).flatten()
  PrintStats("2 alternate universes, sampled stocks", s_data)
  PrintStats("2 alternate universes, normalized stocks", n_data)
  MonteCarlo(sampled_stocks_alt2)
  MonteCarlo(normal_stocks_alt2)
  PlotHistogram([s_data, n_data])

  sampled_stocks_alt5 = Composite("Alt5 sampled",
                                  (sampled_stocks, 0.2), (sampled_stocks, 0.2), (sampled_stocks, 0.2),
                                  (sampled_stocks, 0.2), (sampled_stocks, 0.2))
  normal_stocks_alt5 = Composite("Alt5 normalized",
                                 (normal_stocks, 0.2), (normal_stocks, 0.2), (normal_stocks, 0.2),
                                 (normal_stocks, 0.2), (normal_stocks, 0.2))
  s_data = GenerateReturns(sampled_stocks_alt5).flatten()
  n_data = GenerateReturns(normal_stocks_alt5).flatten()
  PrintStats("5 alternate universes, sampled stocks", s_data)
  PrintStats("5 alternate universes, normalized stocks", n_data)
  MonteCarlo(sampled_stocks_alt5)
  MonteCarlo(normal_stocks_alt5)
  PlotHistogram([s_data, n_data])

  sampled_stocks_re = Composite("Stocks+RE sampled", (sampled_stocks, 0.5), (normal_re, 0.5))
  normal_stocks_re = Composite("Stocks+RE normalized", (normal_stocks, 0.5), (normal_re, 0.5))
  s_data = GenerateReturns(sampled_stocks_re).flatten()
  n_data = GenerateReturns(normal_stocks_re).flatten()
  PrintStats("Sampled stocks + normalized real estate", s_data)
  PrintStats("Normalized stocks + normalized real estate", n_data)
  MonteCarlo(sampled_stocks_re)
  MonteCarlo(normal_stocks_re)
  PlotHistogram([s_data, n_data])


if __name__ == "__main__":
  Main()

Footnotes

1. Not religious advice!
2. This is an imperfect comparison. The pro forma returns from syndications are estimates and may be wrong (though in my, very limited, experience good sponsors tend to underestimate returns). Also, the pro forma returns of syndications today have very little bearings on historical total returns of real estate over long periods of time. Certainly, the Great Financial Crisis of 2008 taught us that real estate prices can go down too!
3. Real estate returns are hard to measure, because real estate tends to illiquid and non-fungible, and the way depreciation affects accounting just confounds that matter even more. The 9% mean, 10% standard deviation modeled here is mostly out of thin air — I picked 9%/10% because it is a lower return with lower volatility than stocks. Some (unverified) data I’ve found suggests this is too pessimistic — historical real estate returns seems to be better than this.
4. Rebalancing periodically is key here! If you do not rebalance, then most, if not all, the benefits of diversification goes away. Every time I hear someone boast about how they are both “diversified” and “passive” (so passive that they do not rebalance), I die a little bit inside. I am already old, stop trying to help me along.
5. If you’ve managed to lose money by buying low and selling high, please let me know!