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 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)