Don’t discount bonds just because they have lower returns. They also have lower volatility. E.g. BND (Vanguard total bond market) has a Sharpe ratio of about 0.81, while VTI (Vangaurd total stock market) has a Sharpe ratio of about 0.56. That makes BND a better investment overall. If you had borrowed money to leverage BND up to the same volatility as VTI, you would have gotten a better return than from VTI alone.
Buying index funds is a much better plan than not buying assets, or using that money to buy liabilities. But I Can Beat the Index, and it’s not that hard.
The key concepts here are diversification and leverage. A portfolio containing both stocks and bonds tends to have lower volatility than either would alone. Both tend to go up over time, but they have a tendency to move in opposite directions (i.e. they are anticorrelated), so a lot of the noise cancels out. That means you can borrow money to buy more assets and get better returns than you could from either while targeting the same amount of volatility exposure as you would get from the portfolio of stocks alone.
And with further diversification of assets one can do even better. They don’t have to be anticorrelated. They’re helpful even if they’re uncorrelated.
Skimming that link, I think it shows backtesting; have you actually beaten the index yourself with real money? For what time period / amount of assets?
I mostly avoided leverage in this post because I don’t use it and kind of don’t trust it. But if I had to give a better defense of avoiding it, it would be because 1. it’s really easy to lose a bunch of money if you use it wrong and 2. I’m not sure there’s a reliable way to borrow money at low enough rates to get good results. Most of what I’ve read about leverage pretends the interest rate is 0, which it’s not—looks like Robinhood offers 2.5%? What’s the most reliable interest rate people can get, and does this rate kill results?
Definitely agree not to discount bonds though; without leverage, small amounts give you large risk reductions for small reductions in growth. I personally am 100% stocks because I’m preferring to maximize (unleveraged) growth, and have decided I can tolerate the increase volatility over 10-20 year time spans.
Skimming that link, I think it shows backtesting; have you actually beaten the index yourself with real money?
I am not rich yet. I haven’t been doing this long enough for my results to be meaningful. Ask me that again in five years. Or ten.
When the hypothesis at hand makes time valuable—when the proposition at hand, conditional on its being true, means there are certain things we should be doing NOW—then you’ve got to do your best to figure things out with the evidence that we have. — Eliezer Yudkowsky, You’re Entitled to Arguments, But Not (That Particular) Proof
[Not an argument from authority; Yudkowsky just explained it well.] In the meantime, to the best of my knowledge, we should be using leverage, and weighting the bonds more heavily than the stocks. I’m confident enough in this that the bulk of my portfolio is leveraged bonds balanced against about half as much in leveraged stocks, and most of my savings are invested in my portfolio.
I agree that it is wise to be skeptical of backtests (as a rule of thumb), but rejecting them categorically is a mistake.
So let’s back up a step. Why be skeptical of backtests? Because any monkey can overfit to noise and make a backtest look good, but such a strategy is useless going forward. The more parameters in a backtested strategy, the more suspicious you should be. Wait, that’s an oversimplification. There’s a one-parameter equation that can exactly fit any scatter plot, but it might take hundreds of thousands of digits to do so, and getting even one of them wrong gives you a completely different plot. That’s extreme compared to even a run-of-the-mill overfit backtest. (Occam’s razor as typically worded is wrong, but Solomonoff fixed it for us.) So let’s say the more fine-tuned the backtest has to be to look good, the less likely it works.
So, how fine-tuned is my strategy? Well, how much can we perturb it before it breaks? (For the one-parameter scatter equation, it’s a ridiculously tiny amount.) For a typical overfit backtest, it’s bigger, but usually still pretty small. So,
Does it matter what year it starts? Not really, for the period when we have data.
Does it work if we scramble the order of the years? Pretty much.
Does it have to be BND? No. Other long-term bond funds, e.g.TLT also work.
Does it have to be VTI? No. Other stock market funds, e.g. SPY, IWM, and QQQ also work.
Does it matter how often we rebalance? Not really. Once per quarter, once per month, or triggered at 10% absolute deviation all work.
Where’s the fine tuning? This strategy seems pretty robust. Is it the relative vol weighting? Targeting the same volatility as the stock portfolio alone? The easiest type of backtest would set this with the benefit of hindsight. But volatility is much more predictable than price. So I’m not very concerned. And indeed, a walk-forward backtest that dynamically weights based on a 1-month simple moving average of historical volatility to estimate future volatility also works. But 1-month is arbitrary, right? Maybe I fine-tuned that one. But 3 months works even better. And 2 months also works. And so does an exponential moving average. We can perturb that parameter quite a bit. A fixed 1:2 ratio of stocks to bonds the whole time also works. As does 1:3. No fine-tuning here.
Do we at least have a plausible explanation for why this strategy should work? Yes. Bonds are a “safe haven” asset. When stocks look scary, people look for “safer” investments. That explains the anticorrelation. And yet we expect both asset types to appreciate in value over time. Stocks pay dividends and companies get bought out at above-market prices. Bonds pay interest. They’re both pretty good investments in their own right.
Past results are no guarantee of the future, but I think it’s valid to use induction here. If we dynamically target vol, then if the anticorellation or relative ratio relationship breaks, we’ll still do OK.
it’s really easy to lose a bunch of money if you use it wrong
Very true, and important. Overbetting is the second-fastest way I know to lose money in the stock market (after overtrading). Don’t bet the farm. Don’t bet over Kelly. I explained this in my link. But with reasonable precautions, leverage is pretty safe. Not 100% safe. After all, you can die in a car accident before you have a chance to enjoy your early retirement. Big index funds have not historically dropped to zero overnight. You would have had time to make adjustments in a crash. And there are relatively inexpensive ways to hedge against the extreme tail, like far-OTM puts or VIX calls.
But what are the chances that the optimal Kelly bet is exactly 1x leverage? On priors, for the stock market, I’d start with 2x. But you can do better with dynamic vol targeting.
I’m not sure there’s a reliable way to borrow money at low enough rates to get good results. Most of what I’ve read about leverage pretends the interest rate is 0, which it’s not—looks like Robinhood offers 2.5%? What’s the most reliable interest rate people can get, and does this rate kill results?
Inflation is a drag. Taxes are a drag. And yes, interest rates are a drag when using leverage. Leveraging up is never going to improve your Sharpe ratio by itself, because leverage isn’t free. Some brokers are unreasonable here. You can buy a leveraged ETF and not bother with margin loans. These funds have the scale required to get the good rates. This even works in an IRA. It’s not as flexible as margin, but you don’t need it for this strategy.
For other strategies, you can finance with box spreads to get very good rates, even as a retail investor. These are more dangerous if you don’t know exactly what you are doing (and very safe if you do), but the more passive investors can just use the leveraged ETFs.
After reading around for half an hour, I think there’s a decent chance that some form of leveraged investing via e.g. ETFs might be a good idea. The basic idea makes sense to me.
This is currently completely out-weighed by my “being too clever in markets is a great way to lose all of your money” prior. But I’ll probably look into it more and see how convincing I find the numbers and historical evidence. If I’m pretty convinced I could see myself allocating 10-20% of my investments in a leveraged strategy at some point in the future.
A cursory look at box spreads makes me think it’s the kind of thing with so many caveats that I’d never feel certain I’d eliminated enough tail risk from it.
For posterity’s sake: I became convinced this is practically doable (using either treasury futures, leveraged ETFs like NTSX, or maybe options which I don’t understand as well) and probably a good idea/not very dangerous if done correctly. I think that fact is slightly info-hazardous for a couple reasons:
You shouldn’t trust most people to correctly advise you on financial products, to not be delusional, or to have your best interests at heart. So it’s hard to figure out exactly what to do. Index funds overcome this problem through the sheer size of their giant pile of empirical evidence and expert consensus; basically everyone agrees that they work as advertised, and no one reports getting accidentally burned using index funds—except when the whole market crashes, where they behave as expected.
If you learn that it’s probably a good idea when done correctly, you might feel obligated to go do it, and then you might do it incorrectly and foreseeably lose a bunch of money.
Because the pile of empirical evidence is less giant, it might not turn out to be such a good idea in retrospect, so it’s fundamentally riskier (even taking into account the risks people calculate). I’m sure someone would argue the pile is giant, but even if true that’s probably only the case if you’re sufficiently expert to judge more obscure evidence piles which most of us are not.
So I’d STILL recommend you not do this unless you’re extremely curious in this area, have no hang-ups, feel competent and trust your own judgment around things like intimidating financial products, have no track record of unwise gambling behavior, and have a stable enough life that if you fuck up you won’t be in a bad situation.
Here’s some resources. If you’re not interested enough to read and enjoy stuff like this, probably avoid doing this:
I’m a big fan of NTSX and have done a bunch of back tests to see how it would have performed in various conditions. In all reasonably long time periods that I simulated, something like NTSX had lower volatility and higher return compared to SPY. About a year ago I went ahead and replaced most of my US equity exposure with NTSX.
As a follow-up: I did this for a while, but I’ve become convinced there are a couple effects that make this not as good as it sounds:
Futures have taxes paid in the year gains are made, which significantly reduces returns in simulations I’ve run. In an ETF or mutual fund, you can instead let those gains ride.
Futures have an implicit financing cost, and portfolio performance is very sensitive to this cost if you’re using a lot of leverage (e.g. for intermediate term bonds).
Leveraged ETFs fluctuate a lot, and need to be rebalanced with the rest of your portfolio. This causes taxes like above. If you don’t rebalance, your leverage ratio changes which causes the portfolio to behave poorly as well.
With all of these effects accounted for, the gains from leveraging look very modest and depend a lot on what time period you look at. Given the risks, I’ve decided against it for myself.
Given those findings, is the strategy feasible in tax-sheltered retirement account? My backtests indicate that quarterly rebalancing is usually sufficient, even with leveraged ETFs, but it’s still worth intervening sooner when vol gets high.
In a taxable account, does tax-loss harvesting to offset your short-term capital gains help? You would rotate among leveraged ETFs. You can also indirectly reduce exposure by hedging with a different ticker rather than realizing short-term gains by selling immediately. You can either short-sell or buy an inverse ETF. LEAPS are also an option (heh), but you have to remember to roll them.
Don’t discount bonds just because they have lower returns. They also have lower volatility. E.g. BND (Vanguard total bond market) has a Sharpe ratio of about 0.81, while VTI (Vangaurd total stock market) has a Sharpe ratio of about 0.56. That makes BND a better investment overall. If you had borrowed money to leverage BND up to the same volatility as VTI, you would have gotten a better return than from VTI alone.
Buying index funds is a much better plan than not buying assets, or using that money to buy liabilities. But I Can Beat the Index, and it’s not that hard.
The key concepts here are diversification and leverage. A portfolio containing both stocks and bonds tends to have lower volatility than either would alone. Both tend to go up over time, but they have a tendency to move in opposite directions (i.e. they are anticorrelated), so a lot of the noise cancels out. That means you can borrow money to buy more assets and get better returns than you could from either while targeting the same amount of volatility exposure as you would get from the portfolio of stocks alone.
And with further diversification of assets one can do even better. They don’t have to be anticorrelated. They’re helpful even if they’re uncorrelated.
Skimming that link, I think it shows backtesting; have you actually beaten the index yourself with real money? For what time period / amount of assets?
I mostly avoided leverage in this post because I don’t use it and kind of don’t trust it. But if I had to give a better defense of avoiding it, it would be because 1. it’s really easy to lose a bunch of money if you use it wrong and 2. I’m not sure there’s a reliable way to borrow money at low enough rates to get good results. Most of what I’ve read about leverage pretends the interest rate is 0, which it’s not—looks like Robinhood offers 2.5%? What’s the most reliable interest rate people can get, and does this rate kill results?
Definitely agree not to discount bonds though; without leverage, small amounts give you large risk reductions for small reductions in growth. I personally am 100% stocks because I’m preferring to maximize (unleveraged) growth, and have decided I can tolerate the increase volatility over 10-20 year time spans.
I am not rich yet. I haven’t been doing this long enough for my results to be meaningful. Ask me that again in five years. Or ten.
[Not an argument from authority; Yudkowsky just explained it well.] In the meantime, to the best of my knowledge, we should be using leverage, and weighting the bonds more heavily than the stocks. I’m confident enough in this that the bulk of my portfolio is leveraged bonds balanced against about half as much in leveraged stocks, and most of my savings are invested in my portfolio.
I agree that it is wise to be skeptical of backtests (as a rule of thumb), but rejecting them categorically is a mistake.
So let’s back up a step. Why be skeptical of backtests? Because any monkey can overfit to noise and make a backtest look good, but such a strategy is useless going forward. The more parameters in a backtested strategy, the more suspicious you should be. Wait, that’s an oversimplification. There’s a one-parameter equation that can exactly fit any scatter plot, but it might take hundreds of thousands of digits to do so, and getting even one of them wrong gives you a completely different plot. That’s extreme compared to even a run-of-the-mill overfit backtest. (Occam’s razor as typically worded is wrong, but Solomonoff fixed it for us.) So let’s say the more fine-tuned the backtest has to be to look good, the less likely it works.
So, how fine-tuned is my strategy? Well, how much can we perturb it before it breaks? (For the one-parameter scatter equation, it’s a ridiculously tiny amount.) For a typical overfit backtest, it’s bigger, but usually still pretty small. So,
Does it matter what year it starts? Not really, for the period when we have data.
Does it work if we scramble the order of the years? Pretty much.
Does it have to be
BND? No. Other long-term bond funds, e.g.TLTalso work.Does it have to be
VTI? No. Other stock market funds, e.g.SPY,IWM, andQQQalso work.Does it matter how often we rebalance? Not really. Once per quarter, once per month, or triggered at 10% absolute deviation all work.
Where’s the fine tuning? This strategy seems pretty robust. Is it the relative vol weighting? Targeting the same volatility as the stock portfolio alone? The easiest type of backtest would set this with the benefit of hindsight. But volatility is much more predictable than price. So I’m not very concerned. And indeed, a walk-forward backtest that dynamically weights based on a 1-month simple moving average of historical volatility to estimate future volatility also works. But 1-month is arbitrary, right? Maybe I fine-tuned that one. But 3 months works even better. And 2 months also works. And so does an exponential moving average. We can perturb that parameter quite a bit. A fixed 1:2 ratio of stocks to bonds the whole time also works. As does 1:3. No fine-tuning here.
Do we at least have a plausible explanation for why this strategy should work? Yes. Bonds are a “safe haven” asset. When stocks look scary, people look for “safer” investments. That explains the anticorrelation. And yet we expect both asset types to appreciate in value over time. Stocks pay dividends and companies get bought out at above-market prices. Bonds pay interest. They’re both pretty good investments in their own right.
Past results are no guarantee of the future, but I think it’s valid to use induction here. If we dynamically target vol, then if the anticorellation or relative ratio relationship breaks, we’ll still do OK.
Very true, and important. Overbetting is the second-fastest way I know to lose money in the stock market (after overtrading). Don’t bet the farm. Don’t bet over Kelly. I explained this in my link. But with reasonable precautions, leverage is pretty safe. Not 100% safe. After all, you can die in a car accident before you have a chance to enjoy your early retirement. Big index funds have not historically dropped to zero overnight. You would have had time to make adjustments in a crash. And there are relatively inexpensive ways to hedge against the extreme tail, like far-OTM puts or VIX calls.
But what are the chances that the optimal Kelly bet is exactly 1x leverage? On priors, for the stock market, I’d start with 2x. But you can do better with dynamic vol targeting.
Inflation is a drag. Taxes are a drag. And yes, interest rates are a drag when using leverage. Leveraging up is never going to improve your Sharpe ratio by itself, because leverage isn’t free. Some brokers are unreasonable here. You can buy a leveraged ETF and not bother with margin loans. These funds have the scale required to get the good rates. This even works in an IRA. It’s not as flexible as margin, but you don’t need it for this strategy.
For other strategies, you can finance with box spreads to get very good rates, even as a retail investor. These are more dangerous if you don’t know exactly what you are doing (and very safe if you do), but the more passive investors can just use the leveraged ETFs.
After reading around for half an hour, I think there’s a decent chance that some form of leveraged investing via e.g. ETFs might be a good idea. The basic idea makes sense to me.
This is currently completely out-weighed by my “being too clever in markets is a great way to lose all of your money” prior. But I’ll probably look into it more and see how convincing I find the numbers and historical evidence. If I’m pretty convinced I could see myself allocating 10-20% of my investments in a leveraged strategy at some point in the future.
A cursory look at box spreads makes me think it’s the kind of thing with so many caveats that I’d never feel certain I’d eliminated enough tail risk from it.
For posterity’s sake: I became convinced this is practically doable (using either treasury futures, leveraged ETFs like NTSX, or maybe options which I don’t understand as well) and probably a good idea/not very dangerous if done correctly. I think that fact is slightly info-hazardous for a couple reasons:
You shouldn’t trust most people to correctly advise you on financial products, to not be delusional, or to have your best interests at heart. So it’s hard to figure out exactly what to do. Index funds overcome this problem through the sheer size of their giant pile of empirical evidence and expert consensus; basically everyone agrees that they work as advertised, and no one reports getting accidentally burned using index funds—except when the whole market crashes, where they behave as expected.
If you learn that it’s probably a good idea when done correctly, you might feel obligated to go do it, and then you might do it incorrectly and foreseeably lose a bunch of money.
Because the pile of empirical evidence is less giant, it might not turn out to be such a good idea in retrospect, so it’s fundamentally riskier (even taking into account the risks people calculate). I’m sure someone would argue the pile is giant, but even if true that’s probably only the case if you’re sufficiently expert to judge more obscure evidence piles which most of us are not.
So I’d STILL recommend you not do this unless you’re extremely curious in this area, have no hang-ups, feel competent and trust your own judgment around things like intimidating financial products, have no track record of unwise gambling behavior, and have a stable enough life that if you fuck up you won’t be in a bad situation.
Here’s some resources. If you’re not interested enough to read and enjoy stuff like this, probably avoid doing this:
https://www.aqr.com/Insights/Research/Journal-Article/Why-Not—Equities
https://www.amazon.com/Enhanced-Indexing-Strategies-Utilizing-Performance/dp/0470259256
https://www.bogleheads.org/forum/viewtopic.php?t=143037
But I’ll probably do it myself and might write a blog post about it.
I’m a big fan of NTSX and have done a bunch of back tests to see how it would have performed in various conditions. In all reasonably long time periods that I simulated, something like NTSX had lower volatility and higher return compared to SPY. About a year ago I went ahead and replaced most of my US equity exposure with NTSX.
As a follow-up: I did this for a while, but I’ve become convinced there are a couple effects that make this not as good as it sounds:
Futures have taxes paid in the year gains are made, which significantly reduces returns in simulations I’ve run. In an ETF or mutual fund, you can instead let those gains ride.
Futures have an implicit financing cost, and portfolio performance is very sensitive to this cost if you’re using a lot of leverage (e.g. for intermediate term bonds).
Leveraged ETFs fluctuate a lot, and need to be rebalanced with the rest of your portfolio. This causes taxes like above. If you don’t rebalance, your leverage ratio changes which causes the portfolio to behave poorly as well.
With all of these effects accounted for, the gains from leveraging look very modest and depend a lot on what time period you look at. Given the risks, I’ve decided against it for myself.
Given those findings, is the strategy feasible in tax-sheltered retirement account? My backtests indicate that quarterly rebalancing is usually sufficient, even with leveraged ETFs, but it’s still worth intervening sooner when vol gets high.
In a taxable account, does tax-loss harvesting to offset your short-term capital gains help? You would rotate among leveraged ETFs. You can also indirectly reduce exposure by hedging with a different ticker rather than realizing short-term gains by selling immediately. You can either short-sell or buy an inverse ETF. LEAPS are also an option (heh), but you have to remember to roll them.