jankythoughts2

Foreword

Financial planning, portfolio management and wealth management are often used interchangeably, but they are actually different disciplines in finance.

In this post, we look at the differences between the three, and how they should be employed.

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.

Financial planning

Financial planning, as the name implies, is a process where you plan out your finances. First, you come up with financial goals that you want to achieve, for example:

• Save for a house down payment by age 30
• Pay for children’s college
• Financial independence by 45
• Retire by 55
• etc.

These goals should have a dollar amount attached, estimated to the best of your abilities. They should also have a deadline. In effect, all of these goals can be translated into a statement of the form:

I want to have $D by year Y.

Once you have your list of goals, you’ll effectively have a list of net worth dollar amounts that you’ll need, by certain years.

The next step is to take stock of what your assets are, right now. You should be able to then assess the viability of your financial plan, by just applying aggressive assumptions for your assets, for example, 15% annual growth year over year, every year. You should also factor in your expected annual income from a job, trust, allowance, etc., as well as your annual expenditures, again, use aggressive assumptions — your income will grow 2-4% a year, your expenditures will only grow 1.5-3% a year, etc.

If your financial plan fails even with the aggressive assumptions, i.e.: you miss one or more goals even with such aggressive assumptions, then your goals are likely unreasonable, and you should re-evaluate the goals and try and make them more reasonable. For example, maybe delaying retirement by a few years?

Finally, you need to figure out how much risk you need to take on, and how much you need to increase your income by, and how much you need to limit your expenditures by, in order to give your financial plan the highest probability of success. This is important! You are not trying to maximize the return of your assets/investments, but rather, under the set of goals, you are trying to figure out what is the least risky way for you to achieve it.

This last step is where you start making more conservative assumptions. Is 15% annual growth in investments reasonable? There certainly are stocks that grow 15% or more a year for long periods of time. But how likely are you to identify them ahead of time? Also, these stocks tend to be more risky — either small/mid caps, highly levered, etc. Also, how likely are you to get a 2-4% raise every year? How much harder will you have to work to achieve that? Are you willing to work that much harder? And how much will you have to sacrifice in terms of living standards to keep your expenditures low? Are you sure you can maintain such low expenditures for long periods of time?

These are all questions you need to ask yourself honestly, and answer honestly. Make the necessary adjustments to what kind of risks you are willing to take with your investments, how much you are willing to put into your job to try and achieve the raises you target, and how much you are willing to forsake in current standards of living in order to meet your goals.

Remember always, that you are trying to maximize the probability that your plan works! Yes, if you work 20hours a day, you may get a 6% raise every year. But is that reasonable? What are the chances that you work yourself into serious health issues, and then have to take months or even years off of work to recover? Think about all these issues, then ask yourself, is it reasonable to expect yourself to work 20hours a day for 2 years? 5 years? 10 years? Probably not!

As you are probably thinking now, this is an iterative process. As you figure out the kind of sacrifices, risks and adjustments you’ll have to make, you’ll find that perhaps you are willing to trade off some goals to reduce the amount of sacrifices, risks and adjustments you’ll need to make, which in turn will likely increase the probability of success.

After a few rounds of adjusting goals, making more conservative assumptions, you’ll have a better picture of the tradeoffs that you need to make — either reducing your goals, or increasing your risk, sacrifices and adjustments.

And once you are done, once you are happy with the final result, you’ll have a financial plan.

That’s not the end, though! Life is unpredictable and things often change without warning. After you have a financial plan, you need to re-evaluate your plan periodically — I like to do it once a year or when I have to make major financial decisions. Figure out if you are on track for your plan, and if not, go through the iterative process again, and figure out what you need to do to get yourself back on track.

Portfolio management

Portfolio management is the curation of your investment assets. For example, let’s say you have a financial plan in place, and you have devoted $100,000 to investing. What assets should you buy? In what ratio? Should you have excess cash lying around to opportunistically time market downturns? Or will you stay 100% invested at all times? Or will you even lever your position to be more than 100% invested?

These are all questions that you’ll answer when you are managing your portfolio.

In order to answer these questions, though, you’ll need to have an idea of the different asset classes. Largely they are:

• Cash
• Equity (stocks, or ownership of private businesses)
• Bonds (or other types of debt(-like) instruments such as loan, preferred equity, etc.)
• Real estate
• Commodities (such as precious metals, agricultural products, energy commodities, or more likely derivatives of these)
• More exotic forms such as fine wine, rare art, etc.

Each of these behave differently in different environments. For example, in inflationary environments, commodities and real estate tends to do well, equity decently, but bonds and cash tend to suffer. In reducing interest rate environments, bonds and equity tend to do well, real estate decently, commodities and cash maybe not so much, etc.

Figuring out what to invest in, and in what ratio, is non-trivial! Happily, for most people, the answer need not be very nuanced. A 60/40 portfolio of 60% equities and 40% bonds (1), with maybe a few percentage taken out of each to invest in real estate will generally be a fairly good trade off between risk undertaken and potential reward. However, if you are willing to spend more time on the topic, you may be able to eek out more return without increasing risk or reduce your risk without reducing your return. Unless you have a substantial amount of assets under you care, however, you may find that the results are simply not worth the effort.

Remember that when you are planning your portfolio, you are effectively aiming for some goal from your financial plan — say you need to get 10% returns every year. This goal may severely hamper the choice of assets that you can invest in! If you aim for 10% returns every year, for example, leaving your portfolio entirely in cash is unlikely to work.

Finally, unlikely financial planning, where the focus is mainly on trying to maximize the probability of success (i.e.: reducing risk), portfolio management takes a more balanced approach and looks more at expected returns of assets, before figuring out how to reconcile that with expected risk (i.e.: trading off risk vs return).

Wealth management

Wealth management is generally spoken of as a service provided by a professional, a wealth manager. It’s not really something someone does for themselves.

In effect, wealth management is a service which combines aspects of financial planning and portfolio management. The wealth manager will work with you to figure out what you are comfortable doing for yourself, and what you would prefer professional help with, and then work through the financial planning and portfolio management process with you. At the extreme, you may simply give the manager power of attorney over your assets, and they will then manage everything towards the goals you’ve discussed, and perhaps send you a regular stipend for living expenses.

In practice, wealth management services tend to be very expensive, as they involve a lot of risk for the manager (legal and liability risks mostly), which need to be defrayed with increased fees. Also, ongoing portfolio management and financial planning services tend to be labor intensive, while also requiring fairly specialized skills, again pointing to high fees. So, in general, wealth management services are typically only offered to those who are wealthy, and for most managers, the minimum assets a client must have is generally in the $2-10m range.

How they intertwine

Financial planning can be thought of as your “life’s goals”, finance-wise. It is the targets that you’d like to hit, if you think of your financial life as a business. Portfolio management is, then, the actual steps you’d take to achieve those targets (though focusing only on investments, while a financial plan often involves incomes and expenditures as well).

Wealth management, in our little analogy, will then be the hiring of external consultants or vendors to advice on or run part of your business for you.

Do I need a financial plan?

Probably yes! Everyone has goals they’d want to meet in the future, and unless you are so incredibly wealthy that almost any goal you can think of can be trivially met financially, you’ll probably want to develop a financial plan to figure out where you stand, and what you need to work on.

Do I need to manage my portfolio?

Probably yes, but this may not be that hard. Unlike financial planning which often involves taking stock of your current situation and trying to figure out what goals are feasible and how much effort/risk you need to take on, portfolio management can be fairly straightforward.

For most people, a passive (or mostly passive) investment portfolio may be appropriate — unless you have specialized knowledge about the financial markets, or you are personally interested in finance, or if you have a large amount of assets already where even a marginal increase in returns is a meaningful absolute number, you may find that effort spent on managing your portfolio to optimize it more, may be wasted. Instead, for most people, it may be more bang-for-the-buck if you spend more of your efforts on trying to increase your income, for example, taking on more at work to aim for a promotion, or taking on a side gig, etc., or by spending time going through your expenses to try and reduce your expenditures.

A passive investment portfolio may be as simple as figuring a ratio between stocks/bonds that you’d like to hold, and then buying the respective indices in the decided ratio. (2)

Do I need a wealth manager?

Probably not. The pre-requisite net worth for a wealth manager to be even willing to work with you is often a bar most people do not meet. And honestly, unless you are incredibly wealthy and have a very complicated financial situation, it probably isn’t worth the money hiring a wealth manager in the first place.

However, if you do happen to have the requisite $2-10m lying around (check your couch!), and you don’t happen to be interested in finance and just want to enjoy what life has to offer, then a wealth manager may indeed be just what you need.

Footnotes

1. For those who are younger, you may want to take on more equity risk, say, 70/30, or even up to 90/10, depending on your risk tolerance. For those who are closer to retirement, you may want to reduce equity risk, say, 50/50, etc.
2. It irks a lot of people, but I generally will not provide financial advice except to people I am close to. This is for conscience reasons (I may be wrong), legal reasons (I am not licensed to provide financial advice) and for liability reasons (you may sue me if I’m wrong). Therefore, this is about as specific as I will go.

Foreword

How much money can you spend every year, if you want your money to last 30 years?

Does this change if you invest 100% in stocks? 100% in bonds? 60/40 in stocks/bonds?

Do you even know what the historical returns of stocks are?

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.

Raw data

Here is the annual total return (1) of the S&P500 index since 1926, taken from https://www.slickcharts.com/sp500/returns. I haven’t verified the data, but a quick glance suggests it’s probably close enough for our purposes. I’ve excluded 2021 because the year hasn’t ended yet. All numbers are in percentage terms.

  18.40,  # 2020
  31.49,  # 2019
  -4.38,  # 2018
  21.83,  # 2017
  11.96,  # 2016
  1.38,  # 2015
  13.69,  # 2014
  32.39,  # 2013
  16.00,  # 2012
  2.11,  # 2011
  15.06,  # 2010
  26.46,  # 2009
  -37.00,  # 2008
  5.49,  # 2007
  15.79,  # 2006
  4.91,  # 2005
  10.88,  # 2004
  28.68,  # 2003
  -22.10,  # 2002
  -11.89,  # 2001
  -9.10,  # 2000
  21.04,  # 1999
  28.58,  # 1998
  33.36,  # 1997
  22.96,  # 1996
  37.58,  # 1995
  1.32,  # 1994
  10.08,  # 1993
  7.62,  # 1992
  30.47,  # 1991
  -3.10,  # 1990
  31.69,  # 1989
  16.61,  # 1988
  5.25,  # 1987
  18.67,  # 1986
  31.73,  # 1985
  6.27,  # 1984
  22.56,  # 1983
  21.55,  # 1982
  -4.91,  # 1981
  32.42,  # 1980
  18.44,  # 1979
  6.56,  # 1978
  -7.18,  # 1977
  23.84,  # 1976
  37.20,  # 1975
  -26.47,  # 1974
  -14.66,  # 1973
  18.98,  # 1972
  14.31,  # 1971
  4.01,  # 1970
  -8.50,  # 1969
  11.06,  # 1968
  23.98,  # 1967
  -10.06,  # 1966
  12.45,  # 1965
  16.48,  # 1964
  22.80,  # 1963
  -8.73,  # 1962
  26.89,  # 1961
  0.47,  # 1960
  11.96,  # 1959
  43.36,  # 1958
  -10.78,  # 1957
  6.56,  # 1956
  31.56,  # 1955
  52.62,  # 1954
  -0.99,  # 1953
  18.37,  # 1952
  24.02,  # 1951
  31.71,  # 1950
  18.79,  # 1949
  5.50,  # 1948
  5.71,  # 1947
  -8.07,  # 1946
  36.44,  # 1945
  19.75,  # 1944
  25.90,  # 1943
  20.34,  # 1942
  -11.59,  # 1941
  -9.78,  # 1940
  -0.41,  # 1939
  31.12,  # 1938
  -35.03,  # 1937
  33.92,  # 1936
  47.67,  # 1935
  -1.44,  # 1934
  53.99,  # 1933
  -8.19,  # 1932
  -43.34,  # 1931
  -24.90,  # 1930
  -8.42,  # 1929
  43.61,  # 1928
  37.49,  # 1927
  11.62,  # 1926

Pop quiz 1

You can refer to the numbers above, but don’t use a calculator or anything, just try to estimate the answers:

1. What do you think is the average annual return over the period covered?
2. What do you think is the median annual return over the period covered?
3. What do you think is the CAGR(2) over the period covered?
4. Which of the following 3 numbers above should you use, if you want to estimate how much returns you’ll get over the next 10 years?

The answers are:

1. 12.2%
2. 14.3%
3. 10.3%
4. CAGR, because total returns over a period of time compounds multiplicatively. Average and median are non-compounding measures.

Are those numbers surprising? Most people find it surprising that the CAGR is so much lower than the other 2 measures, because they generally hear about the average/median returns thrown around in the media, but CAGR is a number that’s less frequently used, even though it’s more important. Some people, especially those who started investing since 2010, may find it surprising that the numbers are so low, because they are used to 15+% returns, in most years since 2010. However, because returns compound multiplicatively, a down year dramatically skews the CAGR, which is why we see these numbers.

Pop quiz 2

Now, let’s say we have some amount of money, $R, to retire on, and assume inflation rate of 3% (3), which is to say, if you need $X in year one, you’ll need $(1.03 * X) in year 2, and $(1.03^2 * X) in year 3, and so on.

The ratio X/R is your withdrawal rate in the first year. The safe withdrawal rate (or SWR) is the ratio X/R, such that you have a high probability of not running out of money within your retirement — in our case, 30 years.

Assuming we used $R to buy the S&P 500 index on day 1 of our retirement, and ignoring transaction costs, taxes, etc.,

1. What do you think is the SWR if you want a 90% probability of not running out of money in 30 years?
2. What about if we want a 95% probability?
3. 99% probability?

Now, if you are like most people, you’ll probably do something like take average/median/CAGR of stocks return, subtract the inflation rate, and that’s your SWR. That’ll give you a number that is either 9.2%, 11.3% or 7.3%, depending on which measure of stocks return you used.

And all 3 answers are wrong. The correct answers are:

1. 3.8%
2. 3.1%
3. 1.9%

Hopefully, you are surprised (4).

Whadafuqjuzhappened!?

The reason the numbers are so small, is because of volatility. Stocks don’t go up in a straight line, they often take little detours where the annual total returns is the wrong shade of green (5). During the years where stocks are down, you are actually spending a much larger percentage of your assets to maintain your lifestyle — since your spending strictly goes up due to inflation, X/R (or your withdrawal rate) goes up if X goes up and R goes down.

So, if you want to maintain the same lifestyle over time, you’ll need to start off by just withdrawing a smaller portion of your portfolio in the first year, i.e.: a lower SWR, to compensate for these episodic underperformance of stocks.

This is sometimes called “sequencing risk”.

I am never gonna retire

Well, maybe don’t despair yet — it’s not as bad as it sounds. Recall that you don’t have to invest (just) in stocks. You can also invest in bonds! Or real estate! Or fine art! Or in this blog! I take donations! (6)

Now, as we know, bonds have, in recent history, really low yields. At the time of this writing, the 30y US Treasury is yielding only 1.93%. Can bonds really help?

Pop quiz 3

Let’s say you use your entire retirement fund of $R to buy a 30y US Treasury yielding 2% (7). So, what do you think your SWR is for

1. 90% probability of not running out of money in 30 years?
2. 95% probability?
3. 99% probability?

And the answers are… 2.9%. For all 3. Note that we are assuming US Treasuries won’t default, and you’ll always get your money back, on top of all the other assumptions above.

So yea, for 90/95%, it’s not as good as stocks, but the stability of bonds help in the 99% case.

What’s going on here?

Recall that I said the main reason why SWR for stocks is so low, is because of volatility and sequencing risk — you need money every year to survive, even if the stock market is being uncooperative. But bonds, being so helpfully stable (at least in our made up model world with semi-unrealistic assumptions), means that even at 99% (and 100%!) percentile levels, we can have the same SWR of 2.9%, higher, in fact, than their CAGR (which is 2%)!

To hammer home this point, I ran simulations of various scenarios, and the results are summarized below:

“Sampled stocks” is stocks using actual historical returns, uniformly sampled for each simulation year.

“Normalized stocks” is stocks using a random returns sampled from a normal distribution with 12.16% mean and 19.66% standard deviation (which is the mean/standard deviation of our historical data above). As you can see, these numbers are fairly similar. Because it’s easier to model different scenarios using a normal distribution, all other simulations involving stocks use variations of “normalized stocks”.

“Low vol stocks” is stocks where we simply halved the standard deviation for modeling purposes. “Low vol, low return stocks” is stocks where we halved both the standard deviation and the mean. “High vol, high return stocks” is stocks where we doubled both standard deviation and mean.

“2/6/10% bonds” are bonds where the yield is 2%, 6% or 10%. (8)

The remaining rows show composite portfolios where we have some percentage of assets in stocks, bonds or cash, and where we may apply leverage (buying 50% of the portfolio’s value on margin) at different margin interest rates.

Observations

If you go through the data carefully, you’ll quickly see that:

1. Expected returns (either via average, median or CAGR) is not a good predictor of SWR at all, especially at the higher confidences.
2. Instead, volatility, or lack thereof, is a much better predictor of SWR, again, especially at the higher confidences.
3. So, you can sacrifice some expected returns, and get a higher SWR 99% rate, by swapping out some stocks for bonds, or even cash!
4. If you can get cheap leverage, then some mild application of leverage on a balanced portfolio (for example, 60/40 1.5x leverage with 1% margin) can yield even better results.
5. But using leverage without first tamping down volatility is a recipe for disaster (not shown here, but the high vol, high return stocks scenario is a good approximate).

Wrapping up

For a very long time, people have been asking me why I’m “leaving money on the table” by not being more aggressive in stocks, or why I’m not levering 100% into stocks, etc. Some have even suggested a portfolio of 100% UPRO (which is a 3x daily balanced SPY product).

But think of it this way — when you retire, you’ll depend essentially 100% on your portfolio for cashflow to survive. And as we discussed in “net worth“, net worth is only useful if it can be used somehow to generate cash flow. Because, say it with me now, you cannot eat net worth. Therefore, “expected net worth”, based on whatever modeling of expected returns from a risky portfolio, is only useful if I can depend on it, at retirement, to generate cash flow. It doesn’t matter if the expected value of my portfolio is $1B at retirement, if there’s a 50% probability I’d go bankrupt — What? Am I supposed to eat caviar on my mega yacht off Monaco 50% of the time and then jump off a building the other 50%? (9)

What about levering up now and then selling everything at retirement to buy safer assets? Sure, if you happen to retire when the stock markets are at a high. But I’m not inclined to time my retirement based on the whims of the stock market. Also, since I don’t have a crystal ball, that means I’ll have to go with a more conservative strategy.

Which is to say, in general, as you approach retirement, it is a good idea to reduce volatility in your portfolio, so that you can smooth out market madness and thus achieve a higher level of stable cash flow (higher SWR) from your portfolio. (10)

Monte Carlo

By now, you’re probably wondering why this post is titled “Monte Carlo”. That’s simply the name of the methodology I used to run the simulation for the numbers above. The code for the simulation is attached, feel free to play with the assumptions yourself to see what comes up.

Note that for all the stocks based portfolios, the inputs are random (which is why we need Monte Carlo in the first place), so your numbers may differ slightly. But I’ve found that the differences are relatively minor, typically in the 5-10bps range.

#!/usr/bin/python3.8

import numpy


# Number of times to run each simulation.
TOTAL_ITERATIONS = 10000
# Ratio of runs where we must end up with more than $0, before we consider the test a success.
THRESHOLDS = [0.9, 0.95, 0.99, 1]

# Number of years to run for in each simulation.
NUM_YEARS = 30
# Inflation rate of cash withdrawal.
INFLATION = 0.03

# This should be mostly irrelevant.  Just use a large number.
START_CASH = 1000000

# Data from https://www.slickcharts.com/sp500/returns
HISTORICAL_RETURNS = numpy.array([
  18.40,  # 2020
  31.49,  # 2019
  -4.38,  # 2018
  21.83,  # 2017
  11.96,  # 2016
  1.38,  # 2015
  13.69,  # 2014
  32.39,  # 2013
  16.00,  # 2012
  2.11,  # 2011
  15.06,  # 2010
  26.46,  # 2009
  -37.00,  # 2008
  5.49,  # 2007
  15.79,  # 2006
  4.91,  # 2005
  10.88,  # 2004
  28.68,  # 2003
  -22.10,  # 2002
  -11.89,  # 2001
  -9.10,  # 2000
  21.04,  # 1999
  28.58,  # 1998
  33.36,  # 1997
  22.96,  # 1996
  37.58,  # 1995
  1.32,  # 1994
  10.08,  # 1993
  7.62,  # 1992
  30.47,  # 1991
  -3.10,  # 1990
  31.69,  # 1989
  16.61,  # 1988
  5.25,  # 1987
  18.67,  # 1986
  31.73,  # 1985
  6.27,  # 1984
  22.56,  # 1983
  21.55,  # 1982
  -4.91,  # 1981
  32.42,  # 1980
  18.44,  # 1979
  6.56,  # 1978
  -7.18,  # 1977
  23.84,  # 1976
  37.20,  # 1975
  -26.47,  # 1974
  -14.66,  # 1973
  18.98,  # 1972
  14.31,  # 1971
  4.01,  # 1970
  -8.50,  # 1969
  11.06,  # 1968
  23.98,  # 1967
  -10.06,  # 1966
  12.45,  # 1965
  16.48,  # 1964
  22.80,  # 1963
  -8.73,  # 1962
  26.89,  # 1961
  0.47,  # 1960
  11.96,  # 1959
  43.36,  # 1958
  -10.78,  # 1957
  6.56,  # 1956
  31.56,  # 1955
  52.62,  # 1954
  -0.99,  # 1953
  18.37,  # 1952
  24.02,  # 1951
  31.71,  # 1950
  18.79,  # 1949
  5.50,  # 1948
  5.71,  # 1947
  -8.07,  # 1946
  36.44,  # 1945
  19.75,  # 1944
  25.90,  # 1943
  20.34,  # 1942
  -11.59,  # 1941
  -9.78,  # 1940
  -0.41,  # 1939
  31.12,  # 1938
  -35.03,  # 1937
  33.92,  # 1936
  47.67,  # 1935
  -1.44,  # 1934
  53.99,  # 1933
  -8.19,  # 1932
  -43.34,  # 1931
  -24.90,  # 1930
  -8.42,  # 1929
  43.61,  # 1928
  37.49,  # 1927
  11.62,  # 1926
])
HISTORICAL_RETURNS /= 100

# Uncomment to print average, median and CAGR of HISTORICAL_RETURNS.
#print(numpy.mean(HISTORICAL_RETURNS) * 100)
#print(numpy.median(HISTORICAL_RETURNS) * 100)
#print((numpy.prod(HISTORICAL_RETURNS + 1) ** (1 / len(HISTORICAL_RETURNS)) - 1) * 100)


class Sim():
  def __init__(self, label):
    self.__label = label

  def Name(self):
    return self.__label


class FixedRate(Sim):
  def __init__(self, label, interest_rate):
    Sim.__init__(self, label)
    self.__interest_rate = interest_rate

  def Return(self):
    return self.__interest_rate


class NormalDistribution(Sim):
  def __init__(self, label, mean, std_dev):
    Sim.__init__(self, label)
    self.__mean = mean
    self.__std_dev = std_dev

  def Return(self):
    return max(-1, numpy.random.normal(self.__mean, self.__std_dev))


class UniformSampling(Sim):
  def __init__(self, label, data):
    Sim.__init__(self, label)
    self.__data = data

  def Return(self):
    return numpy.random.choice(self.__data)


class Cash(FixedRate):
  def __init__(self, label):
    FixedRate.__init__(self, label, 0)


class FullLoss(FixedRate):
  def __init__(self, label):
    FixedRate.__init__(self, label, -1)


class Composite(Sim):
  def __init__(self, label, *args):
    Sim.__init__(self, label)
    self.__args = args

  def Return(self):
    result = 0
    for asset, ratio in self.__args:
      result += asset.Return() * ratio
    return result


def RunOneIteration(model, rate, returns):
  value = START_CASH
  required_cash = START_CASH * rate
  for i in range(NUM_YEARS):
    if value < required_cash:
      return False
    value -= required_cash
    value *= 1 + returns[i]
    required_cash *= (1 + INFLATION)
  return True


def RunSim(threshold, model, rate, returns):
  num_pass_required = TOTAL_ITERATIONS * threshold
  for i in range(TOTAL_ITERATIONS):
    if RunOneIteration(model, rate, returns[i]):
      num_pass_required -= 1
      if num_pass_required <= 0:
        return True
  return False


def GenerateReturns(model):
  output = numpy.empty([TOTAL_ITERATIONS, NUM_YEARS])

  for i in range(TOTAL_ITERATIONS):
    curr_results = output[i]
    for j in range(NUM_YEARS):
      curr_results[j] = model.Return()

  return output


def Report(model, output):
  print("{}:".format(model.Name()))

  while output:
    prefix = output[:5]
    output = output[5:]
    print("  " + "  ".join(["{:>8s}: {:<7s}".format(metric, "{:.2f}%".format(result * 100)) for (metric, result) in prefix]))
  print()



def MonteCarlo(model):
  returns = GenerateReturns(model)

  highest_rate = {}
  for threshold in THRESHOLDS:
    highest_rate[threshold] = float("nan")
    min_rate = 0
    max_rate = 1
    while round(min_rate, 4) < round(max_rate, 4):
      rate = (min_rate + max_rate) / 2
      if RunSim(threshold, model, rate, returns):
        min_rate = rate
        highest_rate[threshold] = rate
      else:
        max_rate = rate

  output = [
    ("Average", numpy.mean(numpy.mean(returns, axis=1))),
    ("Median", numpy.mean(numpy.median(returns, axis=1))),
    ("CAGR", numpy.mean(numpy.prod(returns + 1, axis=1) ** (1 / NUM_YEARS) - 1)),
  ]

  for threshold, rate in highest_rate.items():
    output.append(("SWR-{}%".format(int(threshold * 100)), rate))

  Report(model, output)


def MakeLabelParams(label, *params):
  full_label = label
  first = True
  for param in params:
    if first:
      first = False
      full_label += " {:.2f}".format(param * 100)
    else:
      full_label += "/{:.2f}".format(param * 100)

  return full_label, *params


def Main():
  cash = Cash("Cash")
  margin = FullLoss("MarginCost")

  bonds2 = FixedRate("2% Bonds", 0.02)
  MonteCarlo(bonds2)

  bonds6 = FixedRate("6% Bonds", 0.06)
  MonteCarlo(bonds6)

  bonds10 = FixedRate("10% Bonds", 0.1)
  MonteCarlo(bonds10)

  sampled_stocks = UniformSampling("SampledStocks", HISTORICAL_RETURNS)
  MonteCarlo(sampled_stocks)

  stocks_mean = numpy.mean(HISTORICAL_RETURNS)
  stocks_stdev = numpy.std(HISTORICAL_RETURNS, ddof=1)
  stocks = NormalDistribution(*MakeLabelParams("Stocks", stocks_mean, stocks_stdev))
  MonteCarlo(stocks)

  low_vol = NormalDistribution(*MakeLabelParams("Stocks[LoVol]", stocks_mean, stocks_stdev * 0.5))
  MonteCarlo(low_vol)

  low_vol_mean = NormalDistribution(*MakeLabelParams("Stocks[LoVolMean]", stocks_mean * 0.5, stocks_stdev * 0.5))
  MonteCarlo(low_vol_mean)

  high_vol_mean = NormalDistribution(*MakeLabelParams("Stocks[HiVolMean]", stocks_mean * 2, stocks_stdev * 2))
  MonteCarlo(high_vol_mean)

  stocks60_bonds240 = Composite("60/40", (stocks, 0.6), (bonds2, 0.4))
  MonteCarlo(stocks60_bonds240)

  stocks55_bonds235_cash10 = Composite("55/35/10", (stocks, 0.55), (bonds2, 0.35), (cash, 0.1))
  MonteCarlo(stocks55_bonds235_cash10)

  # 50% margin loan, at 1% rate = 0.05% interest payments per year.
  stocks60_bonds240_x15 = Composite("60/40 x1.5", (stocks, 0.9), (bonds2, 0.6), (margin, 0.005))
  MonteCarlo(stocks60_bonds240_x15)

  # 50% margin loan, at 6% rate = 3% interest payments per year.
  stocks60_bonds240_x15 = Composite("60/40 x1.5", (stocks, 0.9), (bonds2, 0.6), (margin, 0.03))
  MonteCarlo(stocks60_bonds240_x15)


if __name__ == "__main__":
  Main()

Footnotes

1. Total return is equal to dividends + gains in asset price.
2. CAGR is “compounded annual growth rate”, which is, loosely speaking, the geometric mean of the returns, expressed in percentage terms.
3. I’ve been using 3% for modeling inflation for a while now. People used to laugh at me for this, especially during the 2009-2019 period. After 2020, they are still laughing at me. But for very different reasons. For those who are more conservative, feel free to jack up the value to 5% (or more!) in the simulation to see how that affects the numbers.
4. Look, buddy. I worked really hard to build up the suspense and everything. At least act surprised.
5. Also known as “red”.
6. I’m kidding, I don’t take donations.
7. I’m using 2% because it’s easier to type than 1.93%. Also, US Treasuries have some tax advantages, so it’s probably not THAT crazy an assumption. Finally, there are other “safe’ish” assets that can yield as high as 5-6% “safely”.
8. Yes, 6% and 10% bonds sound crazy in today’s low interest rates world. But there are assets (mostly for accredited investors) which can indeed yield up to 12%. They have varying degrees of risk, and certainly aren’t risk free like this modeling suggests. But they behave very similarly to bonds.
9. Interestingly, someone made the argument to me recently that if there’s an asset with a 25% probability of 10x, and 75% probability of going to 0, the expected value is still 2.5x, which means (paraphrased) “you almost have an obligation to buy that asset”. Hopefully this post and the discussion have shown that the question (and thus answer) is not so simple, and that there are a lot of other considerations other than “expected return”.
10. There are other withdrawal strategies that try to mitigate the sequencing risk issue. Most of them revolve around reducing your cash flow in bad market years (e.g.: keeping your withdrawal rate the same, or even reducing it). Some of them may work, but in general, I’m not really inclined to eat lobster one year and starve the next, just because the stock market decides to tank. I’d rather just have my daily, stable supply of ramen noodle.

Foreword

Contrary to the perception of many people, a lot of things go into a good trading strategy.

It is not simply just “a good idea”, but really, the orchestration of many different disciplines towards a common goal.

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.

Investing vs Speculating

Before we begin, let’s address the elephant in the room. Are we talking about investing or speculating?

Both. While most associate “trading” with speculation, in this particular post, I’m using the word in a more mechanical way — a “trade” is just a transaction, an exchange, in this case, of cash for some asset.

In the world of speculation, a “successful trade” is actually 2 (or more) separate trades — one or more to get into the “position”, and one or more to get out of it, sometimes also called a “roundtrip”. A speculative trade is never a success until you close out the position.

In the world of investing, most “successful trades” are also “roundtrips”. However, there is a separate class of trade which are perpetual, or near perpetual, where a “successful trade” is simply how you edge into a long term advantageous position. Recall that when investing, you are hoping to profit off the productive capacity of the asset. Therefore, a successful long term trade could simply just be getting into a long position with an asset that is productive and stable, at a good price — in such a trade, you are not looking to sell, instead, you are looking to hold the asset for an indefinite amount of time and let the productive capacity accrue profits.

There is an old trader’s adage which goes roughly, “An investment is a trade gone pear shaped”. And therein lies the difference as explained above, albeit with a tragicomedy twist.

Components of a trading strategy

So what are the components of a trading strategy? In broad terms, a good trading strategy should always have these 3 main components:

• Base thesis
  • Why are we even considering this trade?
  • What is the catalyst, or driver for this trade to perform well?
  • Examples:
    • Inflation trade, e.g.: we believe inflation is going up/down over the next N months/years
    • Macro trade, e.g.: we believe this country/industry/sector will go up/down over the next N months/years because of <reason>
• Execution
  • How would we translate the base thesis, from a purely analytical state, to one or more trades?
  • Embedded in this, are considerations such as:
    • Time horizon – How long are we holding the position in each roundtrip?
    • Instrument – What asset are we going to trade to express the base thesis?
    • Price – At what price are we looking to trade?
    • Trading – Are we going to edge into the position slowly? Or buy everything at once?
  • Example:
    • Base thesis: We believe that inflation will go up slightly in the next 2-3 years
    • Time horizon: 2-3 years
    • Instruments:
      • Short short/medium term Treasuries
      • Long stocks of businesses with fixed input costs and variable output prices
    • Price: At the market based on trading strategy.
    • Trading: Form a basket of the instruments with some ratio, rebalance every 3 months
• Risk management
  • How would we know that our base thesis/execution strategy was wrong?
  • And if one (or both) was wrong, what are we going to do to salvage the situation?
  • Example (follow up on the above):
    • We’ll know our inflation thesis is wrong if inflation does not go up at least 0.1% on a year over year basis every month for the next 6 months.
    • If our thesis is wrong, immediately close out the short Treasuries leg of the position, keep the long stock leg as long as it is still performing at or near broad market performance, and slowly close it out over 2-3 quarters.
    • We’ll know our execution strategy is wrong if inflation does go up as described, but out position does not appreciate faster than broad market performance over a 1 month moving window, sampled daily.
    • If our execution strategy is wrong, immediately close out all positions and rethink.

Case study – Inflation in the 1970s

Base thesis

We are currently in 1971, we predict inflation is going to be much higher for the rest of the decade into 1980.

Execution strategy

Buy near month exchange traded gold futures, and continually roll the contracts forward until expiration of thesis. We believe market pricing is currently fair, so we’ll trade at the market.

We’ll leverage our position by 3x of equity, rebalanced yearly.

Case study result

Anyone who predicted (in 1971) that high inflation will be a problem that decade would have been absolutely correct — inflation went from around 5% in 1971 to 12% in 1975, and finally around 14% in 1980.

However, this simple summary is misleading. Inflation actually fell after 1971 to a low of around 3% in mid 1972, before its enormous rise to 12% in 1975. After that, it again fell to around 5% in 1977, before another huge surge, before ending at around 14% in 1980.

So while the base thesis was, on the whole, correct, the sampling period and how we decide we were correct or wrong (risk management) may have led to us conclude that high inflation was over in 1972 or 1977!

The execution strategy, on the other hand, likely would have given us a roller coaster ride. From 1971 to 1975, gold prices raised from around $260 per ounce to $929 in early 1975. At 3x leverage balanced yearly, we’d have suffered a devastating 91% loss in 1976, ending up with a value worse than if we had simply just bought gold outright without leverage:

If we had closed our position then, however, we’d have lost out on a magnificent rise in value till 1980. True, it’s quite a bit less than 3x what the underlying did, but it was still pretty decent!

The astute reader will notice that in the case study, a section on risk management was left out. This is intentional, because since we are looking at the data in hindsight, any risk management strategy can be crafted to make any arbitrary point. That said, a good risk management strategy would hopefully have gotten us out of the trade either in 1972 (because the base thesis, at that point in time, looked like it might have been wrong), or in mid 1975, because gold prices and inflation were both turning down, or (albeit a very risky strategy) it could have given us the courage to held on to our convictions till 1980.

Why bother?

The reason why a good trading strategy plans out the base thesis, execution strategy and risk management way before even entering a trade, is so that these decisions can be made with a level head. Imagine if you were the portfolio manager of the strategy above. Would you have the conviction to hold in 1972, after a very decent (almost double) gain, but with inflation lower than expected? What about in 1976, after a devastating 91% drawdown? Or would you have folded, expecting gold prices to go even lower (as it did the next year by 1977, by another 12.8%)?

Laying out your strategies, and putting them to paper while you still have a clear head helps to eliminate emotional biases that creep in in the heat of the moment. This gives you a chance to at least think clearly about the issues, and decide what your risk tolerances are.