I started trading equities (and equity derivatives) full time last year, without any prior training or experience, beyond some basic economics and finance courses that I took in college many years ago. I figured things out as I went by making a lot of mistakes, and listening to many podcasts.

My portfolio has gone up ~600%, counting from Jan 2020. (The US stock market went up ~50% during this time.) This was done using a variety of strategies across a large number of individual names, so it probably wasn’t just the result of luck. My AUM (assets under management) is currently about that of a small hedge fund. (I’d prefer to not talk about the dollar amount for privacy, but it is relevant because increasing AUM tends to make achieving high returns more difficult, so it gives some idea of what you can potentially do before diminishing returns set in. In other words, if it’s only possible to achieve this kind of return starting from a very low asset base, then maybe it’s not worth one’s time. As a compromise, I’m talking about it in a vague way and writing under a pseudonym.)

It took me about six months to a year to “get the hang of it” (develop a number of successful trading strategies and avoid making a lot of beginner mistakes), perhaps aided by the fact that the market was particularly inefficient last year due to a big influx of retail investors, which made the learning curve easier to climb. My trades are usually short to medium term (hours up to a year from entry to exit).

# Some Tips

1. Become an expert in some corner (industry or asset class) of the market (for example, REITs, mining, shipping, oil & gas, SPACs, distressed assets) so that you can reliably determine, without doing an unreasonable amount of work, whether any given asset in that sector is overvalued or undervalued (relative to where the market is likely to go, not necessarily relative to just “fundamental” or “intrinsic” value, see Addendum below).

2. Follow other sector experts (free or paid, SeekingAlpha seems to be a good resource). One problem with this is that while you can often rely on such experts for relative value within the sector that they cover, they have an incentive to overstate how undervalued their own sector is as a whole.

3. Follow some generalists who are good at calling out which sectors are currently undervalued, so you can rotate into them in a timely manner.

4. Try different strategies with small sizing and ramp up the ones that work. Put some deliberate thought into how quickly to ramp up an initially successful strategy. You can do it too fast and make big losses because the strategy only initially worked by luck, but you can also do it too slow and miss opportunities that are short lived.

5. Develop a portfolio of trading strategies familiar to you, that you can pick and choose from depending on current market conditions.

6. Manage your risks, keeping in mind potential correlations between different trades/​strategies.

7. When you buy or sell, try to get some sense of who is on the other side of the trade, and take the trade if it makes sense from this perspective. E.g., it may be a good idea to buy when a bond fund is selling equities they got in a bankruptcy because they’re not allow to hold equities.

8. Read analyst reports, SeekingAlpha articles, and the like for ideas, and develop and use your judgment of which ideas are likely to be valid and worth acting on.

9. One reason returns diminish with increasing AUM is that your trades have bigger impacts on the market, especially if you try to trade small-cap stocks or other illiquid instruments. But this can also be a source of opportunities, as the bigger funds tend to avoid these less liquid instruments as not being worth their time. So look into the least liquid instruments that you can trade without causing excessive market impact.

Note that these are just some of the things that I ended up doing, that I think contributed to my trading performance. I’m not really sure how much it will help someone else to explicitly try to follow these tips. I think the main thing I want to say is that if you’re substantially smarter and more rational than the average person, it may be worth checking if stock trading is one of your comparative advantages.

# Addendum: Types of value that the market may price into an instrument (now or in the future)

• intrinsic/​carry value—present value of expected income/​expenses generated by the underlying asset(s)

• liquidation value—value that can be obtained by liquidating the underlying assets (e.g., a company expected to make loses forever if it keeps in business, but can return positive value to shareholders in a liquidation)

• extrinsic/​option value—value that comes from offloading left tail risks to debt holders or society and capturing right tail risks (e.g., a stock heading for bankruptcy where shareholders are expected to be wiped out, but still trading at positive price)

• scarcity/​coordination value—value that comes from people using the scarcity of an asset for coordination (e.g., gold, Bitcoin)

• involuntary value—value that you involuntarily impute to an asset when you are forced to buy or sell it on the market (e.g., because of a margin call, stock loan recall, or “tap on the shoulder” from risk management)

• arbitrage value—value that comes from being expected to converge in price with another instrument

• lending value—expected income from borrow fees paid by others (i.e., when they short the instrument)

• collateral value—the value of being useful as a collateral (e.g., being more willing to buy/​hold an asset at a given price because it’s marginable)

• liquidity value—the value of being able to easily exchange the asset for something else

• diversification value—value that comes from price of an asset not being correlated with other assets

• psychological/​moral/​signaling value—psychic, moral, and/​or signaling costs/​benefits of owning an asset (e.g., for some, perhaps negative for the fossil fuels industry)

• I suspect you’re more optimistic than I am about how many LWers would make good traders.

I started investing as a hobby in 1980, and alternated between trading and software jobs up through 1999 before getting good enough at trading to give low priority to seeking non-trading jobs. I averaged a bit over 15% per year over the 20 year period ending in 2018, and over 35% per year since then (pretax).

You seem to be implying that people can determine within a year or so of starting whether they’re good at trading. I think it’s complex enough that it’s hard to say how much time it takes.

Some people will do great for a few years, then go broke spectacularly (mostly people with ADHD? my intuition says you’re not going to fail this way, but maybe 13 of LWers who try trading might do so).

Your list of tips is mostly good.

Tip 7 seems close to being an important piece of advice, but my version of this advice focuses less on who, and more on why a person on the other side of a trade appears to disagree with me (keeping in mind Aumann-like reasons, plus the wisdom of crowds phenomenon).

I often ask my self questions like:

• could most traders be wrong here due to availability bias? (e.g. underestimating pandemic risks when the last 6 or so pandemic scares were false alarms; overestimating how much the pandemic would hurt profits during the worst times)

• Is the chart consistent with the hypothesis that traders are reacting to news that I haven’t noticed?

I expect that tip 2 downplays too much the difficulty of distinguishing competent experts. It’s been a long time since I put much thought into identifying expert commentators, but I expect that most LWers will make a fair number of mistakes here, and take a year or two to recognize those mistakes.

I recommend looking at commentators as a source of data, but doing your best to not believe anything that could reasonably be classified as an opinion rather than a fact. That includes opinions about what topics deserve attention.

I strongly advise would-be traders to balance that out by reading a lot of earnings reports (mostly the presentations that are publicized by the companies, with an occasional glance at SEC filings). These reports have a higher fact to opinion ratio, mainly because they run a higher risk of being sued if they say something misleading. But it’s still important to ignore their opinions about which facts deserve your attention.

Earnings reports are also important as a means of prompting you to learn enough about accounting.

Studying financial history seems important, as some important phenomena happen only a couple of times per century.

When I was getting started, Value Line was an important source of information, because it provided about 18 years of fundamental data on many stocks in a convenient format (a trial subscription should be all you need to get a better historical prespective than most investors).

I use Stock Investor Pro to download a large amount of fundamental data.

Some relevant books:

• I recommend looking at commentators as a source of data, but doing your best to not believe anything that could reasonably be classified as an opinion rather than a fact. That includes opinions about what topics deserve attention.

This must be the biggest disagreement between us. I think I couldn’t possibly have gotten the return that I did if I had followed this advice, especially the latter part about what deserves attention. Can you say more about why you think this?

ETA: Aside from the fact that it seems to have worked in practice, my theory is that it’s easier to detect good ideas than to generate them, especially when you read/​hear arguments/​comments from multiple perspectives, which is often possible (e.g., multiple SeekingAlpha articles plus their comments, and analyst reports about the same stock). (The same core premise makes AI Safety via Debate plausible.)

• I’m a bit unclear how to map your generate versus detect distinction onto my thoughts. Very little of what I do seems like generating ideas. I’d describe my process more as noticing possibilities /​ finding ideas, then evaluating them.

My experience says it’s harder to evaluate ideas than to find them. I doubt that I’m unusually good at finding ideas, so there’s something strange about our disagreement. I’ll guess it’s due to some combination of you being unusually good at evaluating ideas, and being overconfident about those evaluations.

I find new ideas mostly by looking at more companies than most other investors. That’s likely more time consuming than your approach, and sometimes feels like a mind-numbing search for a needle in a haystack. But I never exhaust the supply of new companies to look at (e.g. there are many non-US stock exchanges that I haven’t found time to look at).

My concerns with commentator opinions:

• Neglected topics /​ ideas tend to be more profitable than ones that get adequate attention, because getting attention tends to cause stocks to be efficiently priced.

• Framing effects: if I frame issues the same way as others, I’ll have some of the same biases they do.

• Social pressures: commentators have more goals than just making money for their followers. It’s hard for me to avoid being influenced by that.

Here are some more specific guesses as to why you might value commentators opinions more than I do:

• Your approach works a couple of years per decade, maybe when there’s a large influx of inexperienced investors, and underperforms the rest of the time. You might still be right in this case if the outperformance is high enough in the best years—I might have overweighted median years in evaluating my experience.

• Something has changed to make your approach usually work better (e.g. Seeking Alpha might have made it easier to distinguish good commentators). I haven’t thought much about these issues for over a decade.

• You’re unusually good at distinguishing good commentators.

• You’re unusually objective at evaluating ideas.

• I don’t know enough about the etiquette here, but I am having to fight the urge to post a bunch of memes along the lines of “It’s not the bull market, I really am a genius”.

I would strongly advise anyone who’s considering following this to consider doing this with considerably less than their whole portfolio and with much lower expectations than 7x’ing your money.

• A lot of people respond to things like this post by assuming that the author was lucky. This is usually correct, at least when applied to random claimants on the interwebs, but we can put some bounds on it: the higher the returns, the more luck required to achieve them, assuming an efficient market. The efficient markets model says that any strategy during this period had expected return of 50%. So, if the post author used a strategy with probability p of achieving 600% returns, and 1-p of losing everything, then efficient markets implies p*(100+600) + (1-p)*0 = (100+50), i.e. p = 0.21 (roughly). This is the highest probability any strategy could have of achieving 600% returns during this period, without exploiting any market inefficiency.

In other words: at most one-in-five people could achieve returns that high without exploiting market inefficiency. It should therefore probably update us nontrivially away from the possibility that the post author just got lucky. (Though depending on your priors, you might still think the post author got lucky.)

• Everyone else has already pointed out that you misunderstood what EMH states, so I wont bother adding to their chorus. (Except to say I agree with them).

I will also disagree with:

at most one-in-five people [...] It should therefore probably update us nontrivially away from the possibility that the post author just got lucky.

1 in 5 isn’t especially strong evidence. How many of the other 5 people would you expect to be publishing on the internet saying “You should trade stocks”.

• 1 in 5 isn’t especially strong evidence.

I agree this isn’t a very strong argument. I think theoretically we can probably get a much tighter probability bound than 20% by looking directly at the variance of my strategy, and concluding that given that variance, the probability of getting 600% return by chance (assuming expected return = market return) is <p for some smaller p. But in practice I’m not sure how to compute this variance. Intuitively I can point to the fact that my portfolios did not have very high leverage/​beta, nor did I put everything into a single or very few highly volatile stocks or sectors, which are probably the two most common high variance strategies people use. (Part of the reason for me writing this post is that while LW does have a number of people who achieved very high investment returns, they all AFAIK did it by using one of these two methods, which makes it hard to cite them as exemplifying the power of rationality.)

Assuming the above is still not very convincing, I wonder what kind of evidence would be...

• Without even checking, I can think of a bunch of assets which 7x’ed since Jan 2020. (BTC/​general crypto, TSLA, GME/​AMC etc). So yes, I agree this depends on the portfolio you ran.

Personally, I have seen enough people claiming to outperform, but then fail to do so out of sample. (I mean, out of sample for me, not for them) for me to doubt any claim on the internet without a trading record.

Either way, I think it’s very hard to convince me with just ~1.5 years of evidence that you have edge. I think if you showed me ~1k trades with some sensible risk parameters at all times, then I could be convinced. (Or if in another year and a half you have $300mm because you’ve managed to 7x your small HF AUM, I will be convinced). • Without even checking, I can think of a bunch of assets which 7x’ed since Jan 2020. (BTC/​general crypto, TSLA, GME/​AMC etc). I figured that’s the first thing someone would think of upon hearing “7x” which is why I mentioned “This was done using a variety of strategies across a large number of individual names” in the OP. Just to further clarify, I have some exposure to crypto but I’m not counting it for this post, I bought some TSLA puts (forgot whether I made a profit overall), and didn’t touch AMC. I had a 0.1% exposure to some GME calls which went to 1% of my portfolio and that’s the only involvement there. Personally, I have seen enough people claiming to outperform, but then fail to do so out of sample. Can you please give some examples of such people? I wonder if there are any updates or lessons there for me. Either way, I think it’s very hard to convince me with just ~1.5 years of evidence that you have edge. I think if you showed me ~1k trades with some sensible risk parameters at all times, then I could be convinced. I don’t think I’ve done that many trades (depending on how you define a trade, e.g., presumably accumulating a position across different days doesn’t count as separate trades). Maybe in the low hundreds? But why would you need ~1k trades to verify that I was not doing particularly high variance strategies? I guess this is mostly academic though, as it would take a lot of labor to parse my trade logs and understand the underlying market mechanics to figure out what I was doing and how much risk I was taking (e.g., some pair/​arbitrage trades were spread across several brokers depending on where I could find borrow). I don’t supposed you’d actually want to do this? (I also have some privacy concerns on my end, but maybe could be persuaded if the “value added” in doing this seems really high.) Or if in another year and a half you have$300mm because you’ve managed to 7x your small HF AUM, I will be convinced

I’m definitely not expecting such high returns going forward. (“600% return” was meant to be Bayesian evidence to update on, not used to directly set expectations. I thought that went without saying around here...) Obviously there was a significant amount of luck involved, for example as I mentioned the market was particularly inefficient last year. One of the hedge fund managers I follow had returns similar to mine this year and last year, but not in the years before that. I’d guess 20-50% above market returns is a realistic expectation if market conditions stay similar to today’s, and I hope I can still outperform if market conditions go more “out of sample” but I currently have no basis to say by how much.

Also, I’m already starting to feel diminishing returns (is there a more technical term for this in the investing world?) kick in at my AUM level, as I now have to spend multiple days accumulating some positions to the sizes that I want (and they sometimes take off before I finish), or ignore some particularly illiquid instruments that I would have traded in the past.

• I figured that’s the first thing someone would think of upon hearing “7x” which is why I mentioned “This was done using a variety of strategies across a large number of individual names” in the OP.

Right, I wasn’t disagreeing with you, just explaining why 7x isn’t strong evidence in my own words.

Can you please give some examples of such people? I wonder if there are any updates or lessons there for me.

Yes, but I don’t think there’s a huge amount of value in doing that. If you spend any time following stock touts on twitter /​ stock picking forums etc you will see these people quickly.

To be clear, I have no interest in dissuading you from trading. You’ve smashed it—you have confidence in your edge—go wild. I’m more cautioning people from following you thinking this is easy. Financial markets are extremely competitive and hard. It’s easy to mistake luck for skill and I don’t want other people losing money they can’t afford. I generally find posts like this are net-negative EV.

But why would you need ~1k trades to verify that I was not doing particularly high variance strategies?

I wouldn’t with something like that. However, assuming 250 trades each done on 5% of your capital, you’d need to be returning >15% on every single trade to return 7x. My experience say that’s unlikely, but ymmv. If that is the case then yes, you have serious edge and please take my money. (Especially if those are after tax returns!).

I don’t supposed you’d actually want to do this? (I also have some privacy concerns on my end, but maybe could be persuaded if the “value added” in doing this seems really high.)

I’m not sure what the value would be for me doing it? I’m not sure adding my word saying “I think this guy is legit because I saw a track record” would bring much value to either of us. I guess if I worked for a fund which might have interest in hiring people then I guess I might. But at the times when I have been in those roles, if someone turns up and makes implausible claims about returns, I politely show them the door.

I’d guess 20-50% above market returns is a realistic expectation if market conditions stay similar to today’s, and I hope I can still outperform if market conditions go more “out of sample” but I currently have no basis to say by how much.

I wish you the best of luck. I have never achieved anything close to those levels of returns, but would sorely love to do so.

• If you spend any time following stock touts on twitter /​ stock picking forums etc you will see these people quickly.

The people I follow generally don’t advertise their track record? For the hedge fund manager I mentioned, I had to certify that I’m an accredited investor and sign up for his fund letters to get his past returns. For the ones that do, e.g., paid services on SeekingAlpha that advertise past returns, it has not been my experience that they “then fail to do so out of sample” (at least the ones that passed my filter of being worth subscribing to).

I generally find posts like this are net-negative EV.

Personally, I wish I had seen a post like this 10 years ago. My guess is that there’s at least 2 or 3 people on LW who could become good traders if they tried. Even if 10 times that many people try and don’t succeed, that seems overall a win from my perspective, as the social/​cultural/​signaling and monetary gains from the winners more than offset the losses. In part I want LW to become a bigger cultural force, and clear success stories that can’t be dismissed as “luck” seem very helpful for that.

Especially if those are after tax returns!

Pre-tax.

I have never achieved anything close to those levels of returns, but would sorely love to do so.

Maybe try some of my tips, if you haven’t already? :)

• 1 in 5 isn’t especially strong evidence.

(You’re not wrong, but I wanted to flag: the way I read John’s comment, the word “nontrivially” already admitted this. If he thought it was strong evidence I’d expect him to have used a stronger word. Nothing wrong with adding clarification, but I don’t particularly think you’re disagreeing with him on this point.)

• The efficient markets model says that any strategy during this period had expected return of 50%.

Wait, I think this is wrong. It actually says that any beta 1 strategy had the same expected return as the market as a whole. If my portfolio had a beta of 2, for example, either by using leverage or by buying only high beta stocks, then my expected return would be double that of the market.

I wish I could say that I kept my portfolio’s beta at or below 1 at all times, which would make the reasoning easier, but I did sometimes trade derivatives that arguably had high beta. It would be pretty cumbersome to calculate the exact overall beta, but I’d guess that the average over time probably wasn’t more than 1.5, so you could perhaps redo your reasoning using that.

• See my answer to Paul below. Same thing applies for the CAPM: it’s an approximation, and the expected value formula is the efficiency condition which correctly accounts for how much margin one should actually expect to be able to get, as well as the effect of margin calls.

(In the expected value formula, beta is wrapped into the discount factor; the CAPM approximation pulls it out.)

• As at_the_zoo said, this isn’t quite right. Under EMH there is a frontier of efficient portfolios that trade off risk and return in different ways. E.g. if the market has an expected return of 6% and an expected variance of 2%, then the 3x leveraged policy has expected return 18% and expected variance of 18% (for expected log-return of 9% vs 5% for the unlevered portfolio). And then when you condition on ex post returns it gets even messier.

I think you could get returns this high without being wise and you are basically trusting at_the_zoo that they didn’t implicitly use a bunch of leverage. Though 600% is high enough that it would require a reasonably large amount of leverage and even then a fair amount of luck, even buying UPRO (=3x levered SPY) at market bottom is only 430% returns.

(More generally, I assume “EMH” here is basically captured by the two mutual funds theorem, and “beta” is the correlation of your portfolio with the risky fund.)

• The most fundamental market efficiency theorem is V_t = E[e^{-r dt} V_{t+dt}]; that one can be derived directly from expected utility maximization and rational expectations. Mean-variance efficient portfolios require applying an approximation to that formula, and that approximation assumes that the portfolio value doesn’t change too much. So it breaks down when leverage is very high, which is exactly what we should expect.

What that math translates to concretely is we either won’t be able to get leverage that high, or it will come with very tight margin call conditions so that even a small drop in asset prices would trigger the call.

• I think the two mutual funds theorem roughly holds as long as asset prices change continuously. I agree that if asset prices can make large jumps (or if you are a large fraction of the market) such that you aren’t able to liquidate positions at intermediate prices, then the statement is only true approximately.

I think leveraged portfolios have a higher EV according to every theoretical account of finance, and they have had much higher average returns in practice during any reasonably long stretch. I’m not sure what your theorem statement is saying exactly but it shouldn’t end up contradicting that.

Maybe the weirdness is that you are assuming all investors have linear utility? (I don’t know what the symbol V_t means, and generally don’t quite understand the theorem statement.) Or maybe in your theorem “E” is an expectation that weights worlds based on the marginal value of $in those worlds, whereas in other places we are using “probability” to refer to the fraction of worlds in which an event occurs? • NOTE: Don’t believe everything I said in this comment! I elaborate on some of the problems with it in the responses, but I’m leaving this original comment up because I think it’s instructive even though it’s not correct. There is a theoretical account for why portfolios leveraged beyond a certain point would have poor returns even if prices follow a random process with (almost surely) continuous sample paths: leverage decay. If you could continuously rebalance a leveraged portfolio this would not be an issue, but if you can’t do that then leverage exhibits discontinuous behavior as the frequency of rebalancing goes to infinity. A simple way to see this is that if the underlying follows Brownian motion and the risk-free return is zero, a portfolio of the underlying leveraged k-fold and rebalanced with a period of T (which has to be small enough for these approximations to be valid) will get a return On the other hand, the ideal leveraged portfolio that’s continuously rebalanced would get If we assume the period T is small enough that a second order Taylor approximation is valid, the difference between these two is approximately In particular, the difference in expected return scales linearly with the period in this regime, which means if we look at returns over the same time interval changing T has no effect on the amount of leverage decay. In particular, we can have a rule of thumb that to find the optimal (from the point of view of maximizing long-term expected return alone) leverage in a market we should maximize an expression of the form with respect to k, which would have us choose something like . Picking the leverage factor to be any larger than that is not optimal. You can see this effect in practice if you look at how well leveraged ETFs tracking the S&P 500 perform in times of high volatility. • I didn’t follow the math (calculus with stochastic processes is pretty confusing) but something seems obviously wrong here. I think probably your calculation of is wrong? Maybe I’m confused, but in addition to common sense and having done the calculation in other ways, the following argument seems pretty solid: • Regardless of , if you consider a short enough period of time, then with overwhelming probability at all times your total assets will be between 0.999 and 1.001. • So no matter how I choose to rebalance, at all times my total exposure will be between and . • And if my exposure is between and , then my expected returns over any time period are between and . (Where is the expected return of the underlying, maybe that’s different from your but it’s definitely just some number.) • So regardless of how I rebalance, doubling approximately doubles my expected returns. • So clearly for short enough time periods your equation for the optimum can’t be right. • But actually maximizing EV over a long time period is equivalent to maximizing it over each short time period (since final wealth is just linear in your wealth at the end of the initial short period) so the optimum over arbitrary time periods is also to max leverage. • Thanks for the comment—I’m glad people don’t take what I said at face value, since it’s often not correct... What I actually maximized is (something like, though not quite) the expected value of the logarithm of the return, i.e. what you’d do if you used the Kelly criterion. This is the correct way to maximize long-run expected returns, but it’s not the same thing as maximizing expected returns over any given time horizon. My computation of is correct, but the problem comes in elsewhere. Obviously if your goal is to just maximize expected return then we have and to maximize this we would just want to push as high as possible as long as , regardless of the horizon at which we would be rebalancing. However, it turns out that this is perfectly consistent with where is the ideal leveraged portfolio in my comment and is the actual one, both with k-fold leverage. So the leverage decay term is actually correct, the problem is that we actually have and the leverage decay term is just the second term in the sum multiplying . The actual leveraged portfolio we can achieve follows which is still good enough for the expected return to be increasing in . On the other hand, if we look at the logarithm of this, we get so now it would be optimal to choose something like if we were interested in maximizing the expected value of the logarithm of the return, i.e. in using Kelly. The fundamental problem is that is not the good definition of the ideally leveraged portfolio, so trying to minimize the gap between and is not the same thing as maximizing the expected return of . I’m leaving the original comment up anyway because I think it’s instructive and the computation is still useful for other purposes. • I think the two mutual funds theorem roughly holds as long as asset prices change continuously. I agree that if asset prices can make large jumps (or if you are a large fraction of the market) such that you aren’t able to liquidate positions at intermediate prices, then the statement is only true approximately. That’s not the key assumption for purposes of this discussion. The key assumption is that you can short arbitrary amounts of either fund, and hold those short positions even if the portfolio value dips close to zero or even negative from time to time. Leveraged portfolios will of course have a higher EV if they don’t get margin called. But in an efficient market, the probability of a margin call (and the loss taken when the call hits) offsets the higher EV—otherwise the lender would have a below-market expected return on their loan. Unfortunately most theoretical accounts assume you can get arbitrary amounts of leverage without ever having to worry about margin calls—a lesson I learned the hard way, back in the day. In general, if leveraged portfolios have higher EV, then we need to have some explanation of why someone is making the loan. Maybe the weirdness is that you are assuming all investors have linear utility? (I don’t know what the symbol V_t means, and generally don’t quite understand the theorem statement.) Or maybe in your theorem “E” is an expectation that weights worlds based on the marginal value of$ in those worlds, whereas in other places we are using “probability” to refer to the fraction of worlds in which an event occurs?

Nope, not linear utility, unless we’re using the risk-free rate for r, which is not the case in general. The symbol V_t is a lazy shorthand for the price of the asset, plus the value of any dividends paid up to time t. The weighting by marginal value of \$ in different worlds comes from the discount rate r; E is just a plain old expectation.

• Leveraged portfolios will of course have a higher EV if they don’t get margin called. But in an efficient market, the probability of a margin call (and the loss taken when the call hits) offsets the higher EV—otherwise the lender would have a below-market expected return on their loan. Unfortunately most theoretical accounts assume you can get arbitrary amounts of leverage without ever having to worry about margin calls—a lesson I learned the hard way, back in the day.

In general, if leveraged portfolios have higher EV, then we need to have some explanation of why someone is making the loan.

Imagine someone who is extremely risk-averse. They aren’t willing to invest much in equities, but they are willing to make a margin loan with ~0 risk. They will get lower return than if they had invested in equities, and they’ll have less risk. I don’t see what’s contradictory about this.

I was being a bit lazy earlier—when I said “EV”, I was using that as a shorthand for “expected discounted value”, which in hindsight I probably should have made explicit. The discount factor is crucial, because it’s the discount factor which makes risk aversion a thing: marginal dollars are worth more to me in worlds where I have fewer dollars, therefore my discount factor is smaller in those worlds.

The person making the margin loan does accept a lower expected return in exchange for lower risk, but their expected discounted return should be the same as equities—otherwise they’d invest in equities.

(In practice the Volker rule and similar rules can break this argument: if banks aren’t allowed to hold stock, then in-principle there can be arbitrage opportunities which involve borrowing margin from a bank to buy stock. But that is itself an exploitation of an inefficiency, insofar as there aren’t enough people already doing it to wipe out the excess expected discounted returns.)

• Well, think about it, one-in-five is an extremely high probability! We only need 5 people to try what the OP tried, for one of them to be this successful and to write this post, and we won’t hear about most of those who failed.

• Thanks for the post, you mentioned SeekingAlpha as a ressource, would you mind making a top 5 (or top 10?) of ressources that were important to you? From podcasts, books, or research websites.

• How much time did you invest for this activity?

• If you are willing, how did that 600% distribute across your trading—individual stocks, equity funds/​etfs and derivatives (options? futures? both?).

• Can we get a snapshot of your portfolio?

I am interested in seeing what you hold /​ held to assess your risk adjusted return.

You started investing at a time where virtually all real assets beat their mean averages substantially. It was quite difficult to lose money investing in capital markets if you bought in January 2020 and held until today.

• I currently have ~100 positions spread across: uranium, copper, lithium, oil, fertilizer, shipping, Nvidia Google Microsoft Baidu (hedge against short AI timeline), a basket of SPAC/​deSPAC commons&warrants (which I bought after the SPAC sector became severely depressed), individual “value stocks” and “special situations” in various other sectors. Most of these were entered within the last few months, and my portfolio looked pretty different before that, but I can’t really talk about what I was doing before without risking de-anonymizing myself.

• Thank you.

I am inferring that your investing portfolio is 100% in equities and equity derivatives, and it seems that quite a bit of it is in high beta stuff.

So you combine high beta with derivatives (leverage), and you get a great combination of risk that in the 22 months that you’ve invested paid off quite handsomely.

Congratulations, your ability /​ willingness to bear risk combined with timing has worked. I hope we get to see future updates on your strategy.

• “uranium, copper, lithium, oil”
These are commodities, not equities (unless OP meant invested in companies in those industries?)

• Sorry for being unclear. I meant producers of those commodities, except for uranium for which I also have some exposure to the commodity itself.

• I assumed that, or derivatives of those commodities.

• Congratulations on your success! A few questions that came to mind (I don’t expect you to answer all of them):

• What did you give up to pursue trading full time?

• How much capital did you start with? (6x is not enough to get to the size of a small hedge-fund if you start out with 50k...)

• Do you use leverage?

• Do you manage other investors’ assets or only your own?