Given a leverage portfolio, what does the term volatility drag mean? And how does it affect the value of the portfolio?
In the general case, volatility drag is about how an "average" return over several years may be wildly different than the real return. An example: If your portfolio doubled in value one year, and then halved in value the next year, your real return is 0%. However, if you were being sufficiently careless, you could also say that the average annual return was
(-50% + 100%)/2 = 25%. The difference between that 25% and that 0% is volatility drag.
Volatility drag in a sense isn't a real "force" most of the time. There's just a bunch of people out there buying and selling stocks at different prices, and at the end of your investment it only matters what you can sell your holdings at, not where they were in between and how wildly the price swung (+). Any "drag" you experience is a mathematical artifact of being mislead and using the wrong set of numbers (though it's worth thinking about how you may be looking at the wrong set of numbers even now).
With regards to leveraged portfolios, things get trickier, especially when you turn the math into returns.
There's a couple of ways of leveraging your portfolio. A standard way is to borrow on margin: you put $1000 in an ETF, and then take out a loan against your holdings in that ETF for another $1000 and buy more of that ETF. (You don't actually need to do it in multiple steps like that, but conceptually that's what happens. Also, in practice you probably don't want to borrow every single dollar you can, but whatever, this is an example.)
Another way is to invest in a leveraged ETF. You place $1000 in a fund whose prospectus says something like "This fund seeks to provide 2 times the daily return of [index]."
Now suppose that the index the ETFs are trying to replicate goes crazy and doubles in value one day (+100%). Then the next day everyone comes to their senses and it returns to its original value (-50%). In the first case, you still own the same number of shares in that ETF, and you're essentially back where you started, minus two days' worth of interest on the $1000 you're borrowing.
In the second case, you gained 200% of your original investment the first day, but then lost 100% of your portfolio's value on the second day. Game over; you lose.
(+) Price swings do make a difference if you were adding additional funds in the middle of the process - for instance, by reinvesting dividends - but that's another kettle of fish.
See the answers for the question Investing in a leveraged index ETF for retirement. Risky? .
Whether an ETF is the investment or you create your own leverage, it's the same phenomenon.
Say the market (or whatever 'basket' you invest in) is up 10% one day, down 10% the next. .9 * 1.1 is .99 of course and that basket is off 1%. But. If you are leveraged 2X, You will be up 20%, then down 20%, and .8 * 1.2 is .96 or down 4% vs the basket down just 1%.