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So, the basic idea for an unleveraged investment is your geometric returns are lower than arithmetic returns because of volatility. E.g. if you have $100, gain 10% one period and lose 5% the next, the arithmetic average return is 2.5% per period, calculated as (10+(-5)/2 but you actually only have $104.5, a return of 2.25% per period, because you are losing 5% of a bigger number than you are gaining 10% on. Easy enough.

But let's say you leverage 2x. Assume no interest to keep it simple. Then this is 20% gain and 10% loss. You have $108. A bigger gain than in the above example, but not 2x as big. Or at least that's what I see articles online saying. But this doesn't make sense to me when I try to conceptualize it as actually holding an asset. Let's say I buy one share of the stock using my own money and one share using a loan. I hold exactly the two shares for the two periods regardless of what the price does, then sell them at the end and pay off the loan. My portfolio is 200, goes to 220 (10% gain), then goes to 209 (5% loss). Then I sell, pay off the loan, and I have $109, not $108. The problem comes if I am not allowed to have a loan too large compared to my assets and have to sell at a bad time. So if the 5% drop happens first, I have $190, of which 100 is borrowed. Have to sell $10 of stock to bring my loan to parity with my own investment. Then I have $180, of which 90 is borrowed, and can only make $18 when the market moves 10% up, instead of the 19 I'd have if I held on to everything. So then my return really is only 8% instead of 9%, because I was forced to maintain constant leverage ratio.

So among ETFs, investing on margin, and futures, which allows me to remain closest to the buy and hold strategy? Or do I face roughly the same constraint no matter what?

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[ Question ]

Best empirical evidence on better than SP500 investment returns?

by bluefalcon

25th Apr 2021

1 min read

5 23

12

I am not smart enough to be a real rationalist, and I am really lazy. But I am smart enough to understand and implement rationalist advice and I suspect y'all are a better source of advice than normal investors. What is the highest level of returns I can achieve with a buy and hold strategy of some kind, across any asset class, and what is the empirical evidence for this? Also, I am self-employed, in a field where the 99th percentile earners make 7 figures per year and I make only low six figures. So how should I assess investment in an asset vs trying to invest in my career? I am not quite risk-neutral but pretty close to it. My expenses are well below my income; I'm done saving for retirement; further investing is just a game at this point. But I don't know how to play it.

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PeterMcCluskey

Apr 25, 2021

100

The best answers to these questions that I've seen are in the book Expected Returns, which I reviewed here.

tryactions

Apr 25, 2021*

For buy-and-hold strategies: leverage (borrowing to invest) can be used to increase returns. The Sharpe ratio of a portfolio is a measure of it's risk/reward trade-off; there's a theorem that given a set of assets with fixed known distributions and ability to borrow at the risk-free rate, the Kelly optimal allocation is a leveraged version of the portfolio with highest Sharpe ratio. You can calculate that optimal leverage in various ways.

In practice, we don't know future Sharpe ratios (only the past), we don't have assets with fixed known distributions (to the extent there is a distribution, it likely changes over time), and there's other idiosyncratic risks to leverage.

Using past data, however, is highly suggestive that at least some leverage is a great idea. For instance, a 40/60 stock/bond portfolio has higher Sharpe ratio than a 100% stock portfolio in almost all historical models since bonds and stocks have low correlation. It's not unreasonable to assume that low correlation will hold going forward. If I leverage up a stock/bond portfolio to the same volatility as the corresponding 100% stock portfolio, I see a 2-4% increase in yearly returns depending on time period. This is easily achievable by buying leveraged ETFs.

Naive Kelly models will usually recommend more risk than the stock market, so if your risk tolerance is even higher the (potentially naive and misleading) math is on your side. Be careful if you might need the money soon: these models assume you're never withdrawing!

My opinion: ~1.5-2.5x leverage on stock/bond portfolios looks reasonable for long-term investors, although it really depends on the assets -- short term treasuries for example are so stable that even 10x leveraging isn't crazy.

In the real world, you can leverage by:

Buying leveraged ETFs. These work just like buying stocks or regular non-leveraged ETFs. Vanguard doesn't allow these, so I use Fidelity. I might recommend SSO and TMF, along with international + extended market diversification. Since the leverage on these is set daily, they eliminate some of the tail risk of leveraging. Downsides: volatility decay in sideways markets and ETFs can simply fail to track their (leveraged) index.
Using margin accounts. This is where your broker lends you money, using your other investments as collateral. Rates are often really bad/not worth it -- be careful. Also they'll sell your other investments if you become overly leveraged due to a downturn (a "margin call") -- which means forced selling during a downturn, which can cause you to miss out on any recovery. I don't like this.
Directly taking on debt / counter-factually not paying off debt. If you take out a mortgage instead of paying cash for a house, the money you saved can be considered to be "on loan" at the mortgage rate. Investing it is then a form of leveraging. This is bad if the rate is too high, but mortgage rates are really low right now.
Futures. These allow higher leverage than ETFs and adoption of various strategies if you're willing to monitor them daily -- for instance, you can leverage/deleverage on a daily basis with no (additional) tax penalty. Great for getting really high leverage, e.g. for stable investments like treasuries. Downsides: your positions will be closed if you run out of margin -- which means you can be forced out of the market during a bad enough downturn, potentially missing the recovery. For high-leverage strategies, this means you probably need to monitor daily and de-lever as appropriate. Gains from futures are immediately taxed at 60% short-term 40% long-term capital gains, introducing tax drag that you wouldn't have with ETFs.
Options. I don't know much about these. Here's a book talking about passive indexing approaches using options, which I haven't read: https://www.amazon.com/Enhanced-Indexing-Strategies-Utilizing-Performance/dp/0470259256.
Other stuff (box spread financing?)

You can kind of backtest various strategies for yourself using e.g.:

https://www.portfoliovisualizer.com/backtest-portfolio#analysisResults. Entering a negative percent for CASHX until your portfolio adds up to 100% is an approximation for cost of borrowing at the risk-free rate. They also have ticker data for leveraged ETFs, although most have short histories.
https://www.bogleheads.org/wiki/Simba%27s_backtesting_spreadsheet. Entering a negative percent for 3-month T-bill rate under "Compare Portfolios" until your portfolio adds up to 100% approximates the cost of borrowing at the risk-free rate.

Keep in mind that the past doesn't predict the future, and naive back-testing might not track historical reality perfectly or may be missing some idiosyncratic risks of leveraging certain ways.

For your maximal laziness, here's an ~1.9x leveraged ETF allocation I made up just now that's around 40/60 world stock market/long-term bonds: 36% TMF, 16% SSO, 8% VXF, 40% VXUS. Full disclosure: Lots of people would think this is a terrible allocation since "everyone knows" the bond market is due to crash due to current low interest rates.

For increasing salary vs investing: do these really funge against each other? Why not both? Generically I'd think income should dominate before you have a lot invested, and then investment strategy becomes important once your yearly average investment returns become similar in scale to your yearly income.

[This comment is no longer endorsed by its author]

[-]bluefalcon4y20

Increasing labor income vs investing is not 100% fungible but there are some tradeoffs, especially being self-employed. Any time I spend to learn or manage finance stuff is time I could have spent working. And at least in principle there should be opportunities to spend money to increase my income, but it's a lot more unpredictable--I could advertise, in a non-pandemic environment I could join associations or go to events where I might meet lucrative clients, I could hire lower paid staff and take on clients who it is not worthwhile for me personally to pe... (read more)

waveman

Apr 25, 2021

Hmmm in order of certainty

1. Save and invest more = more total returns.
2. Diversification is the only free lunch in finance.
3. A cautious approach to tilting investments in favour of various factors has a lot of evidence around it. See e.g. this blog https://alphaarchitect.com/alpha-architect-white-papers/
4. Strict adherence to dollar cost averaging. Much harder to do than it looks.

Also all the personal finance rules apply - avoid unprofitable debt, take out insurance. avoid financial catastrophes like divorce, maximize marketable job skills, save hard.

In order of certainty, here are the bad ideas

1. Thinking that you can easily beat the market. Maybe with 70 hour weeks for many years... read hundreds of books and papers... otherwise assume you have negative skill to the tune of 4-6% per annum. Also going into the markets with psychological weaknesses unresolved and/or cognitive and emotional biases not dealt with - the markets have ways to find and exploit them all.
2. Investing in high cost funds based on recent outperformance.
3. Suddenly deciding to invest it all on stocks "for the long run" after a period of outperformance.

[-]bluefalcon4y10

The one advantage I do have over the market is more risk tolerance. I don't assume I can beat it on a risk-adjusted basis, but since I disvalue risk less than normal ppl do, beating it in absolute expected value terms is fine, and even EMH says there should be opportunity to get higher returns that way. Will take a look at the alpha architect paper.

2SimonM4y

The traditional finance theory way to acquire more risk would be to increase leverage in your portfolio (I explain more here and that thread is full of other ideas you might like)

1bluefalcon4y

My sense with leverage is it's more complicated than it looks. My naive intuition was you could match an underlying asset any time futures are available, by holding a total portfolio equal to the value of X shares of the asset, consisting of X futures on the asset and then the balance in cash. Which implies you could beat the asset without additional risk by investing that balance in treasuries. But there are a few things I don't understand here. 1. I assume treasury futures are more volatile than treasuries, to a sufficient extent that you could not use them to implement this and juice the returns even further. Is that correct? 2. I don't know how futures pricing works. If people know it's possible to do what I am suggesting, will futures prices already be bid up compared to the underlying, erasing the potential gains? 3. Futures don't pay dividends. Am I correct in assuming this is reflected in the price somehow, or is this just a net loss in carrying futures compared to the underlying? 4. I get the basic idea that volatility decay exists and I think I understand it for unleveraged investments but don't really understand how it works with leverage. Does it happen because people are rebalancing or is it inherent in the use of leverage? If you could let your leverage ratio float a bit instead of selling in response to margin calls, would you then have long run compound returns of (leverage ratio * compound returns of the underlying)? Why or why not? And does maintaining a balance in treasuries or treasury futures actually allow you to avoid margin calls in practice, or are there brokerage restrictions that would prevent it?

1SimonM4y

Leverage is not more complicated than it looks. "Borrow money to invest". (Or more usually in finance "borrow money using your investments as collateral to invest more"). Futures aren't the only way to invest with leverage. Probably the easiest way for a retail investor would be something along the lines of owning ETFs on margin. 1. Treasury futures and cash treasuries are pretty much exactly the same amount of volatile. Even when the cash/futures basis blows up, we are talking tiny amounts relative to the volatility of the underlying. You can absolutely leverage treasuries via treasury futures and assuming that treasuries outperform your cost of funding then you will "juice" your returns. 2. Futures prices are priced so there is no arbitrage - nothing more, nothing less 3. The price of the futures account for this. (Otherwise there would be an arbitrage, see 2.) 4. I don't really understand your question here? Yes, you definitely can let your leverage ratio float around a bit, in fact I would strongly recommend this. Just because someone will offer you X amount of leverage, doesn't mean you should take it all. In practice you should be able to avoid margin calls in a well managed position, although it is a risk you are taking with leverage, and you need to appreciate that before going down this path.

1bluefalcon4y

The concept of leverage is not complicated. How it affects volatility drag is, or at least seems so to me when I hear ppl explain it. There is a disconnect between how my bran conceptualizes the abstract percentages vs actually holding an asset. So, the basic idea for an unleveraged investment is your geometric returns are lower than arithmetic returns because of volatility. E.g. if you have $100, gain 10% one period and lose 5% the next, the arithmetic average return is 2.5% per period, calculated as (10+(-5)/2 but you actually only have $104.5, a return of 2.25% per period, because you are losing 5% of a bigger number than you are gaining 10% on. Easy enough. But let's say you leverage 2x. Assume no interest to keep it simple. Then this is 20% gain and 10% loss. You have $108. A bigger gain than in the above example, but not 2x as big. Or at least that's what I see articles online saying. But this doesn't make sense to me when I try to conceptualize it as actually holding an asset. Let's say I buy one share of the stock using my own money and one share using a loan. I hold exactly the two shares for the two periods regardless of what the price does, then sell them at the end and pay off the loan. My portfolio is 200, goes to 220 (10% gain), then goes to 209 (5% loss). Then I sell, pay off the loan, and I have $109, not $108. The problem comes if I am not allowed to have a loan too large compared to my assets and have to sell at a bad time. So if the 5% drop happens first, I have $190, of which 100 is borrowed. Have to sell $10 of stock to bring my loan to parity with my own investment. Then I have $180, of which 90 is borrowed, and can only make $18 when the market moves 10% up, instead of the 19 I'd have if I held on to everything. So then my return really is only 8% instead of 9%, because I was forced to maintain constant leverage ratio. So among ETFs, investing on margin, and futures, which allows me to remain closest to the buy and hold strategy? Or d

2SimonM4y

Right, so the back of the envelope calculation for what I think you are calling volatility drag is: geometric return = arithmetic return - volatility^2 / 2 If you have constant leverage (for example like most constant-leverage ETFs) then you effectively multiply your arithmetic return by a constant and your volatility by the same constant so your new geometric return is: leverage * arithmetic return - leverage^2 *volatility^2 / 2 Your example is correct. There is a sense in which all three (leveraged-ETFs, margin, futures) are all equivalent, the main difference is in how active you need to be to maintain you need to maintain your strategy. In terms of "closest to buy-and-hold" I think they go in this order: * Margin (buy less than your broker allows you too, maintain cash in your brokerage, periodically adjust) * Futures (make sure you hold significantly more cash than your brokerage, roll your futures appropriately) * Leveraged-ETFs (hold cash to rebalance, you will need to do so regularly) There is a sense in which they also go in the opposite order in terms of effort. (For example, if you do want to maintain constant leverage (which is of course the concrete recommendation for juicing returns) then leveraged ETFs are the way forward as tryactions explained)

Vladimir_Nesov

Apr 25, 2021*

Leverage can give arbitrarily high returns at arbitrarily high risk. With things easily available at a brokerage, this goes up to very high returns with insane risk. See St. Petersburg paradox for an illustration of what insane risk means. I like the variant where you continually bet everything on heads in an infinite series of fair coin tosses, doubling the bet if you win, so that for the originally invested $100 you get back the same $100 in expectation at each step (at first step, $200 with probability 1/2 and $0 with probability 1/2; by the third step, $800 with probability 1/8 and $0 with probability 7/8), yet you are guaranteed to eventually lose everything.

Diversification, if done correctly, reduces risk at the expense of some reduction in returns. At which point increasing leverage to move the risk back up to where it was originally increases returns to a level above what they were originally. Diversification without leverage can make things worse, because it reduces returns.

Not making use of leverage is an arbitrary choice, it's unlikely to be optimal. For any given situation, there's almost certainly some level of leverage that's better than 1 (it might be higher or lower than 1). There are various heuristics for figuring out what to do, like Sharpe ratios and Kelly betting. As an outsider to finance, it was initially hard for me to make sense of this, as discussion of the heuristics is usually fairly unprincipled and relies on fluency with many finance-specific concepts. A math-heavy finance-agnostic path to this is to work out something along the lines of Black–Scholes model starting from expected utility maximization and geometric Brownian motion. For actual decisions, calculation through Monte Carlo simulations rather than analytical solutions lets utility functions, taxes, and other details be formulated more flexibly/straightforwardly.

Teerth Aloke

Apr 25, 2021

-30

Investing some money in Bitcoin would not be a bad idea. Bitcoin is both high-risk and high-potential.

[-]bluefalcon4y40

I'm interested in the possibility but it doesn't have enough of a history for me to be able to think about it usefully. What is the broader reference class I should be looking at, and what is the evidence on historical returns for that class?

1[anonymous]4y

If you believe the doubters, like buying tulips at the peak of the bubble. If you believe the boosters, like buying gold before it was used as a currency. The issue is that there simply isn't past evidence. Bitcoin's only past evidence is itself, which seems to be periods of extreme rises and extreme crashes but so far a hugely upward trend.

[-]Dentin4y20

I still have some remaining bitcoin, from the olden days when mortal man could mine it themselves. My advice to everyone I've ever talked to regarding bitcoin is to avoid it. I have been slowly divesting my holdings.

My rationale is that while both the dollar and bitcoin are fiat currencies, bitcoin is far, far less anchored to reality than most 'normal' currencies. The dollar and the euro at least have people trying to keep monetary levels somewhat tied to physical economic value. The value of bitcoin, meanwhile is largely driven by... (read more)

2Teerth Aloke4y

I don't hold Bitcoin, friends.

1Jozdien4y

What would your advice be on other cryptocurrencies, like Ethereum or minor coins that aren't as fad-prone and presumably cheaper to mine?

2ChristianKl4y

Given that there's a competive mining market these days there's nothing that's cheap to mine unless you have access to very cheaper electricity then the average miner.

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[-]Vladimir_Nesov4y40

My expenses are well below my income; I'm done saving for retirement

Note that a simple FIRE heuristic giving about 3% chance of running out of money at some point is to have 30x yearly expenses in 100% stock index with no leverage, which is a lot more than the usual impression along the lines of "my expenses are well below my income" and is still not something that can be reasonably described as safe.

[-]bluefalcon4y20

I am far away from retirement so not at 30x yet. But assuming 7% real returns, my projected nest egg is about 108x my current living expenses around the age I want to retire. If something goes wrong before then I can always put more in. Compounding is fucking magic if you start it in your early 20s.

[-]Vladimir_Nesov4y*30

(This feels more like a dragon hoard than retirement savings, something that should only form as an incidental byproduct of doing what you actually value, or else under an expectation of an increase in yearly expenses.)

[-]bluefalcon4y10

Haha. I didn't really know what was a reasonable amount to save when I started because I had just gotten my first real job and really had no idea how expensive a lifestyle I might want in the future. But I knew I didn't want to be poor ever again. So I set a fairly arbitrary goal, spent a few more years living on the poverty-level income I had had before getting a good job so that I could save while it still had lots and lots of time to grow, and now it's done.

And from a stress/flexibility standpoint I think it was the right decision. I probably don't have to think about saving ever again, except for fun, so if I want to take a job that is funner but pays less, I have absolute freedom to do that.

And it turns out even having money I can live pretty cheap. There were only a few material things I hated about being poor. The constant stress over money was the real problem most of the time. I don't enjoy cooking and the food was boring when I couldn't afford restaurants, so I eat more takeout. And walking 5 miles bc the bus doesn't go where you want kinda sucks, so I take more cabs/ubers/lyfts.