Financial Architects

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Types of Returns (Warning: Math Ahead)

I used this example in classes for financial advisors back in the day:

Client gives you $100,000 and it goes up 100% in period 1 so the balance is $200,000.

Client is excited then and gives you $1,000,000 more so the account has $1,200,000.

Account then goes down 25% in period 2 so $1,200,000 becomes $900,000.

You tell the client – we’re doing great! The average annual return has been 22.47%!

[((1+1)*(1-0.25))^(1/2) – 1= (2*0.75)^0.5 – 1 = 1.5^0.5 – 1 = 22.47% (for geometric – i.e. time-weighted – you add one to each return, take the product, then the nth root (the number of periods) then subtract 1)]

The client responds, “Are you smoking something hallucinogenic? I gave you $1,200,000 and you turned it into $900,000 and you have the audacity to tell me you made money?

The problem is the client’s. He/she should have given the advisor all the money up front! Since managers generally don’t have control over cash flows it is unfair to penalize (or reward) them for the timing. So that’s why all standard reporting is CAGR (Compound Annual Growth Rate) which doesn’t account for cash flows.

The client’s compound return is -13.40%

[What you got divided by what you paid for it to the nth root, minus 1, or ($900,000/$1,200,000)^(1/2) – 1 = 0.75^0.5 – 1 = -13.40%]

That’s still a compound (geometric) return, but it’s dollar weighted.

The arithmetic return is just the average like you learned around fifth grade or so. 100% + -25% = 75% / 2 = 37.5%.

To recap:

  • If you want to know how the manager is doing over time (particularly with investments that have different volatilities), you want the geometric return without any cash flows.
  • If you want to know how the client is doing over time you want the geometric return with cash flows.
  • If you want to know the shape of the annual distribution of returns (the bell curve) as input to an MCS, or to know what to expect in a single year, it is best described as the arithmetic mean and a standard deviation (not getting into higher moments here, but the skewness and kurtosis also matter for investments such as hedge funds).

Over time, the arithmetic return compounds into the geometric return as I demonstrated here: Converting Arithmetic to Geometric Averages Spreadsheet

See the second tab for actual historical data, the market’s arithmetic average from 1926-2023, 98 years, was 12.16% but the geometric average was 10.28%. If you invested $X in 1926 you would have $X*(1.1028^98) at the end. But, assuming the distribution of future returns is expected to be like the past (which is probably erroneous), your expectation of next year (or any single year) would be a bell curve with a mean of 12.16% and a standard deviation of 19.72%.

Finally, given a high enough volatility, a positive arithmetic return can be a negative geometric return. This is the problem with extremely levered investments like the 2x, 3x, and -2x, -3x funds (and, again, some “hedge” funds).

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“Adulting” Milestones

I had a conversation recently with a young adult who was focused on buying a home. It got me thinking about priorities, and while it was on my mind I wrote some general advice for young people:

While individual situations will vary, as a young adult there are some basic financial milestones that I think you should strive to achieve. These are listed in roughly the order I think they should ideally occur:

  1. Complete your education.
  1. Have the ability to pay your own living expenses from your earned income. For most people this means having a spending plan (aka a budget). This doesn’t mean you actually have to be paying your own expenses, but if you aren’t, then you should be saving the amount that you are being subsidized. In other words, if you are on someone else’s insurance/Netflix account/cell phone plan/etc., that’s fine, but you should be saving that amount then, not spending it.
  1. Have appropriate amounts of the crucial types of insurance: health insurance, disability insurance, and liability insurance. (If you have people who are financially dependent on you then add life insurance to this list.)
  1. Save in your employer’s retirement plan, such as a 401(k), each year to the extent of any match.
  1. Have no consumer debt (i.e., credit cards, car loans, etc.).
  1. Accumulate three to six months of expenses in an emergency fund.
  1. Get estate planning done. This may move up (or down) the list depending on your individual situation, but at some point, you should get a:
    • Will (this is important if you have a minor child or assets that would pass through probate)
    • Durable power of attorney (specifies who handles your finances if you can’t)
    • Living will (specifies what life-prolonging actions you want taken, if any)
    • Durable power of attorney for healthcare (specifies who makes medical decisions if you can’t).

(In some states, such as Georgia, those last two are combined into one document called an Advance Medical Directive.)

  1. Save to the maximum limit of retirement plans such as a 401(k) or IRA/Roth. This will be a financial stretch (or perhaps impossible) if your income isn’t high. For a younger person in 2024 the 401(k) limit is $23,000 and the IRA/Roth limit is $7,000 so this is $30,000 combined before you move to the next level.
  1. Accumulate a 20% down payment for a home. There are two reasons for the 20% number. First, and most obviously, that is the level that saves you the private mortgage insurance (PMI) premium. Second, and more importantly, if you can save that then you probably have the financial habits and ability to handle the ongoing responsibility (and irregular expenses) of homeownership.
  1. Buy a home. This is optional, but this is the spot on the list where it would go.

As a young person, that list undoubtedly seems daunting, but that’s why I put it in priority order, you just have to work your way down. The further you get down the list the brighter your financial future will be. (See also Four Rules for Guaranteed Financial Success.)

Happy adulting!

I want to expand a little on buying a home. Many young people have no idea how much home they can afford, and lenders will encourage borrowing more than I think is prudent. There are two rules of thumb for this:

  1. Regular homeownership expenses should not exceed 28% of gross income. Those expenses are PITI (Principle, Interest, Taxes, and Insurance) plus any HOA/COA/POA fees. This ratio is frequently used by banks and other lenders.
  1. The value of the home should not exceed 2-3 times gross income. This is my rule of thumb and is usually more conservative than the banks’ rule.

People tend to get excited about buying after real estate prices have risen quickly (they do the same with other assets too). Prices may continue to rise or they may not, but the long-term expected appreciation on real estate is roughly the rate of inflation. Total return on real estate is higher because of rental income, or imputed rent (the rent you don’t pay on your own residence), but of course there are expenses as well.

Furthermore, for a young person, flexibility is important. In the early years of employment, moving (even across town) to take a better job frequently changes the trajectory of lifetime earnings, and renters are much more willing and able to do that than homeowners are.

Finally, people often “stretch” to buy their first home and then are in a precarious situation if they lose a job or the HVAC system needs to be replaced. Waiting to buy until more financial resources are firmly in place is more prudent in many cases.

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Investment Rules

A while back the topic of “Investment Rules” came up in an email exchange, and I wrote a quick list of mine. These are just my simple, and perhaps arbitrary, rules. I’m mostly trying, as Charlie Munger said, to not be stupid: “It is remarkable how much long-term advantage people like us have gotten by trying to be consistently not stupid, instead of trying to be intelligent.”

  1. No sector investing – I generally don’t have enough sector expertise to have a better opinion than the market.
  2. No zero-sum asset classes (derivatives) – I don’t want to be reliant on someone else losing for me to win. They undoubtedly think they are smarter than me, and there is no obvious reason for me to disagree.
  3. No investments where a negative opinion (shorts) can’t be expressed (IPOs, PE) – When only bullish opinions can be reflected it would be hard for prices to be attractive, or even reasonable.
  4. Don’t buy things with high expense ratios – expensive is, of course, relative, but why have headwinds?
  5. Don’t buy things that are illiquid – I am unconvinced that an illiquidity premium reliably exists. (And Cliff concurs.)
  6. Don’t buy things where the counter-party can change the rules against you in the middle of the game (many insurance products).
  7. Don’t buy things that are expensive (even if it might seem justified) – mean reversion is a real thing (even if folks are confused about what it means).
  8. Don’t buy things that have no possibility of cash flows (i.e. zero-dividend stocks are fine, but no NFTs, art, gold, cryptocurrencies, etc.) – there is no way to value such a thing that doesn’t end up being a mere psychological exercise – “People seem to like it/have always liked it so it must be worth something.”