2022 was an excellent year for me. OK, I didn’t make as much from my investments as I did in 2020 or 2021—who did?—but I made more than I made in 2019. I ended up making a cool million dollars, up 22%.

But more important than how much I earned is how much I learned. Was this a better year than most? I don’t know. I learn a lot every year. But with every lesson I learn, I realize how stupid I was the year before.

So here are some things I learned in 2022, in no particular order at all. This article will discuss seven things; the other fifteen will be for Parts Two and Three.

**1. Put options are extraordinarily expensive.**

It’s not easy to tell whether an option is fairly priced, but there are some good formulas out there. One is the Black-Scholes formula; another is the binomial price formula. Personally, I like to buy options at a steep discount to prices determined by those formulas. But with puts, that is almost impossible in today’s market.

Let’s look at an example. On December 21, I wanted to buy some March out-of-the-money puts on Beyond Meat (BYND). The stock price was $13.26 and I was looking at an expiration date 86 days away. So I was looking at options with $12.50 and $10.00 strikes. The historical volatility of BYND was 97.3% and a 3-month T-bill yielded 4.25%. It wasn’t hard to do the math: the Black-Scholes price given those inputs was $1.98 for the $12.50 strike and $0.87 for the $10 strike; the binomial prices were $1.82 and $0.73. Yet the going prices for these puts (taking the midpoint between the bid and the ask) were $3.25 and $1.85! That’s extraordinarily expensive! I would never pay anywhere near that much! Compare those prices to the call options on the same stock. The Black-Scholes price for a $15.00 call was $2.03 and the binomial price was $2.21. And the call options were priced at only $1.23.

Finding a bargain in puts is really hard work. In 2022 I bought fewer than 4% of the puts that I wanted to buy. It worked: the few puts that I managed to buy gave me a return of over 100%. But it’s such hard work finding bargains that I’m tempted to give up.

**2. You don’t need to pass an exam in order to manage a hedge fund. **

I had always thought that in order to manage someone else’s money, you had to pass the FINRA Series 65 and/or Series 7 exams. But in fact, you can start your own hedge fund without taking any exams. There are limits as to what you can do:

- you can’t market your hedge fund;
- you can only invest money from accredited investors (people with liquid assets of more than $1 million or a salary of $200,000/year);
- you must have no more than 100 investors; and
- your assets under management have to be less than $150 million.

If you fulfill those conditions, you can claim Exempt Reporting Advisor status and you can establish a 3(C)(1) fund with a rule 506(B) exemption from Reg D.

Or something like that. I must confess I haven’t gotten this all totally straight yet. So if anyone reading this has actually tried to start their own hedge fund without passing any FINRA exams, please set me straight if I’m wrong.

And no, I’m not actually planning to start my own hedge fund. But it was interesting to learn that I could.

**3.** **Fidelity Is Full of S*** When It Comes to Foreign Investments in IRAs.**

Don’t get me wrong: I love Fidelity. They’ve been my broker from the word go and their customer service and order improvement is unparalleled. I like dealing with them so much better than dealing with Interactive Brokers.

But when it comes to holding foreign stocks in IRAs, their heads are on backwards.

Their international trading team patiently explained to me that the IRS forbids holding foreign currency in IRAs. This means that in order to hold foreign stocks in IRAs, they have to convert the currency on the fly and that one therefore cannot place orders for foreign stocks online. Instead, you have to call them to place the order. This is actually a very pleasant experience, but it costs $83 per trade, and then they charge you a 1% fee to convert the currency. Now currency conversion is actually very cheap—that 1% charge is extreme. Adding 2% round-trip transaction costs to every foreign stock I invest in is absurd.

No other broker places these limits on foreign stocks in IRAs. The IRS does *not* forbid holding foreign currency in an IRA: it forbids holding foreign *coins* (because they’re classified as collectibles). There’s a bit of a difference between currency and coins, isn’t there? Fidelity’s international trading team told me that they were lobbying congress to change the rules so that foreign currencies could be held in IRAs, and that they held meetings with congressmen about it. Why they would tell me such an elaborate lie is beyond me.

So I transferred a large part of my IRA assets to Interactive Brokers and am paying them a tiny fraction of what I’d be paying Fidelity in order to convert my currencies.

I will say that if Fidelity ever stops charging 1% for currency conversions, I’ll move my money right back to them, even if it means placing orders on the phone.

**4. Buy in Batches to Reduce Market Impact.**

I studied market impact a lot in 2022, and learned that the market impact cost of a trade is approximately

where *m *is a constant (approximately 0.8), *σ* is the daily volatility of the stock, *S* is the number of shares you want to trade, and *V* is the daily volume. Besides reading a lot on the subject, I also measured the market impact of my own trades, comparing the price of my fills to the price of the stock immediately before I placed the order. (I use VWAP orders a lot; if I used straight limit or market orders, *m *would likely be significantly higher.)

Before 2022, I had been placing my entire order for a stock on one day and paying the market impact cost accordingly because there’s a price you pay for delaying an order. But this year, I decided to do the math.

Let’s talk about the daily cost of delaying an order, which I signify as *y *in the equations below. I’m assuming that it has a linear relationship to the daily volatility of the stock.

If you place 100% of your order today, there’s no delay cost, and if you place none of it today and all of it tomorrow, the delay cost is *y*. If you place half today and half tomorrow, your delay cost is 0.5*y*. If you place a third today, a third tomorrow, and a third the next day, your delay cost is *y* (0 today, a third *y *tomorrow, and two-thirds *y *the next day). If you place a quarter today, a quarter tomorrow, a quarter the next day, and a quarter the day after that, your delay cost is 1.5*y*. So the delay cost can be expressed as

where *S* is the total number of shares you want to trade and *a *is the actual order size.

Now let’s let *c *be the total cost of the trade. We want to minimize our cost and figure out what the best order size is to do so. In mathematical language, our object is to minimize *c* as a function of *a*. And the best way to do that is to use differential calculus.

So here’s the equation for the total cost of a trade, assuming that placing an order one day has no effect on the price the next day (a tenuous assumption, yes, but we have to simplify this somehow):

Since *y *and *σ* have a linear relationship, we can substitute *nσ *for *y *above, where *n*, like *m*,is another constant.

To minimize *c *we take the derivative of the right side and set it equal to zero, treating all variables as constants except *a*.

After some simplification, we come to

If I use a new constant, *k = *(*n*/*m*)^{2/3},then

From my calculations, based on the returns I’m getting, *k *≈ 0.42. It would be significantly smaller if my alpha were lower, because my delay cost would be lower.

So let’s say I want to buy $66,000 worth of IBEX (IBEX), which trades $500,000 a day. Can I buy the whole amount in one day? Well, let’s do the math.

0.42*66,000^{2/3}*500,000^{1/3}=54,442. So I should buy only about $54,000 the first day and the rest on the second.

**5. Free Cash Flow Yield Is the Best Value Ratio**

This was the subject of a recent article I wrote. I’m not going to repeat it here. I’ve been using free cash flow yield in the form of unlevered free cash flow to enterprise value ever since 2016. But it was only in 2022 that I realized that it beats all other value ratios, and that net free cash flow to market cap can be an equally productive factor.

## 6. **The Ins and Outs of VWAP Orders with Fidelity.**

2022 was the year I started using VWAP orders, and it has not only improved my life no end, it has made a huge impact on my trading practices. I’ll discuss this some more in a future article, but for now, I want to share what I’ve learned about placing VWAP orders with Fidelity and Interactive Brokers.

In order to place a VWAP order with Fidelity, you use an application called Fidelity Active Trader Pro. From the main menu choose “Trade & Orders,” then “Directed Trade & Extended Hours.” If the market is open, you can then place a VWAP order by selecting “VWAP” in the “Route” box. If the market is not open yet, you’re out of luck. There are two other very important restrictions on VWAP orders with Fidelity: you have to order at least 1,000 shares, and the stock has to be listed on a major exchange. Because a lot of my daily trades are for fewer than 1,000 shares or are for Canadian F shares, I use limit orders for those and crudely simulate a VWAP order by breaking up the trades into four or five equal amounts and placing them throughout the trading day.

The way Fidelity actually trades its VWAP orders is pretty commonsensical. Orders are broken into small chunks and submitted throughout the day, but the chunks are larger and more frequent when trading is heaviest (the end of the day). By the end of the day, as long as your limit hasn’t been exceeded, your order will have been completely filled.

**7. The Ins and Outs of VWAP Orders with Interactive Brokers.**

The major advantages of placing VWAP orders with Interactive Brokers rather than with Fidelity is that you don’t have to worry about the above restrictions. VWAP orders can be placed prior to market open, can be placed for practically any stock (though not on all exchanges—for trades on the Warsaw and Stockholm exchanges, for instance, you can’t use VWAP), and can be used with orders of less than 1,000 shares. The major disadvantage is that VWAP orders for thinly traded shares are executed haphazardly if at all. I can’t count the number of times I’ve placed a VWAP order and watched in vain for a trade to actually occur, even when other people are trading the stock. Moreover, there’s no guarantee of a complete fill even if the stock is trading under your limit. Interactive Brokers’ algorithms seem to be trying to get *good prices *for all their tiny orders, so if there’s a wide spread and no hidden orders in the book, a trade simply won’t be placed. Or perhaps their algorithm places small trades between the bid and the ask and when they go unfilled they don’t submit the trades at the bid or ask—they don’t “take liquidity,” as the jargon has it. But these are just guesses. All I know is that VWAP orders on Interactive Brokers for thinly traded stocks are about as dependable as a 1967 Volkswagen that hasn’t had a tune-up in twenty years. Sometimes they work extremely well, and sometimes they don’t.

In a week or two or three or four, I’ll tell you some of the *other *things I learned in 2022. It was a great year for learning, even if it wasn’t a great year for index funds.

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