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?
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.
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.
Futures prices are priced so there is no arbitrage—nothing more, nothing less
The price of the futures account for this. (Otherwise there would be an arbitrage, see 2.)
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.
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 do I face roughly the same constraint no matter what?
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:
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)
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)
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?
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.
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.
Futures prices are priced so there is no arbitrage—nothing more, nothing less
The price of the futures account for this. (Otherwise there would be an arbitrage, see 2.)
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.
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 do I face roughly the same constraint no matter what?
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)