Thanks for the link. It sounds like Brian is saying that margin works in a way like taking out a loan. If you had $100,000 to start with and took out a loan for $200,000 and invested all $300,000, and the value went to 50%, your net worth would be $-50,000. My understanding of these leveraged funds is that you cannot go negative. You can rebalance yourself to avoid this, but that is a lot of work.
Check out http://āāfinance.yahoo.com/āāecharts?s=TECL+Interactive#symbol=TECL;range=my . This is the 3X investment that produced 15 times as much money, and we got that the underlying asset had a growth ratio of roughly the cube root of 15. So basically leverage is not multiplying the returns by three, but raising to the third power. You can see this with a simple case of underlying investment return of 10% per year over 20 years give 6.7 times as much money. However, if you double the annual return to 20%, after 20 years you get 38 times your money (and really doubling your daily return would mean 21% annual). It is does not quite achieve this I believe because of the impact of volatility (Brian says alternating days of gains and losses hurt) and of course the fees and interest on the implicit loan.
If thatās true then it sounds like the way ETFs implement leverage is completely different from how margin works. I donāt really know how ETFs implement leverage though.
If you use margin, you can rebalance at different intervals. ETFs are roughly the same as using margin, but rebalancing daily.
Rebalancing daily doesnāt really āeat up your returnsā in any meaningful way. It replaces a smaller probability of losing a larger amount of money with a larger probability of losing a smaller amount of money.
Doesnāt it reduce your returns though? It increases transaction costs, and it increases variance drag. If a highly-leveraged stock is more volatile then it will perform worse under daily rebalancing than a stock with equal returns but less volatility.
Under the assumption that each dayās expected return is a constant that doesnāt depend on the previous days, the average growth rate of your investment is basically the same whether you rebalance daily or weekly or monthly. It decreases slightly as you go to longer time scales (e.g. at 2x leverage annually you will get wiped out pretty often, so your average growth rate is negative).
(Of course if days are correlated with each other, then different rebalancing periods will have different values. E.g. if there is short-term momentum then rebalancing frequently will be good and if there is short-term reversal then it will be bad.)
If you care about expected returns rather than growth rates, then rebalancing daily is a good idea iff you are using >1x leverage. Well, hard to say what it means for it to be a āgood idea,ā since your optimal strategy is infinitely much leverage, which yields infinite expected returns. But having Nx leverage rebalanced daily will lead to higher expected returns than rebalancing monthly.
Yes, more volatile stocks with the same expected (i.e. arithmetic average) returns have lower growth rates. Thatās true whether or not you use leverage though. More volatile stocks with the same growth rate will have lower growth rates when leveraged, whether you rebalance daily or annually.
Thanks, Paul. To further address Michaelās question, I think the reason why leverage gives returns raised to a power, rather than multiplying by a constant factor is the rebalancing. Letās say we have $100 and we take out a $100 loan and invest those $200. This is 2x leverage. However, if the fund increases 10%, we would have $220 and still a $100 loan, which is less than 2x leverage. In order to maintain the leverage, you should take out $20 more in loan and then have $120 in loan and $240 in the market. Then you can see why as the stock goes up, a given percent increase will give you a greater dollar increase if you rebalance. The converse is true if the stock goes down. And this is how you protect yourself from going to zero (a given percent decrease in the market means a smaller dollar value loss if you reduce your loan).
The problem comes if gains and losses alternate each rebalancing period. One day it goes down and you sell some, and the next day goes up and you buy some. Since you donāt want to sell low and buy high, I believe this is the volatility drag.
In the case of 3X Russia, it uses derivatives (typically swaps or futures) to implement much of the leverage. Also, it reserves the right to intervene on very large daily movements, which I interpret to mean that it would not let the fund go to zero if there were a 34% daily drop.
Thanks for the link. It sounds like Brian is saying that margin works in a way like taking out a loan. If you had $100,000 to start with and took out a loan for $200,000 and invested all $300,000, and the value went to 50%, your net worth would be $-50,000. My understanding of these leveraged funds is that you cannot go negative. You can rebalance yourself to avoid this, but that is a lot of work.
Check out http://āāfinance.yahoo.com/āāecharts?s=TECL+Interactive#symbol=TECL;range=my . This is the 3X investment that produced 15 times as much money, and we got that the underlying asset had a growth ratio of roughly the cube root of 15. So basically leverage is not multiplying the returns by three, but raising to the third power. You can see this with a simple case of underlying investment return of 10% per year over 20 years give 6.7 times as much money. However, if you double the annual return to 20%, after 20 years you get 38 times your money (and really doubling your daily return would mean 21% annual). It is does not quite achieve this I believe because of the impact of volatility (Brian says alternating days of gains and losses hurt) and of course the fees and interest on the implicit loan.
If thatās true then it sounds like the way ETFs implement leverage is completely different from how margin works. I donāt really know how ETFs implement leverage though.
If you use margin, you can rebalance at different intervals. ETFs are roughly the same as using margin, but rebalancing daily.
Rebalancing daily doesnāt really āeat up your returnsā in any meaningful way. It replaces a smaller probability of losing a larger amount of money with a larger probability of losing a smaller amount of money.
Doesnāt it reduce your returns though? It increases transaction costs, and it increases variance drag. If a highly-leveraged stock is more volatile then it will perform worse under daily rebalancing than a stock with equal returns but less volatility.
Under the assumption that each dayās expected return is a constant that doesnāt depend on the previous days, the average growth rate of your investment is basically the same whether you rebalance daily or weekly or monthly. It decreases slightly as you go to longer time scales (e.g. at 2x leverage annually you will get wiped out pretty often, so your average growth rate is negative).
(Of course if days are correlated with each other, then different rebalancing periods will have different values. E.g. if there is short-term momentum then rebalancing frequently will be good and if there is short-term reversal then it will be bad.)
If you care about expected returns rather than growth rates, then rebalancing daily is a good idea iff you are using >1x leverage. Well, hard to say what it means for it to be a āgood idea,ā since your optimal strategy is infinitely much leverage, which yields infinite expected returns. But having Nx leverage rebalanced daily will lead to higher expected returns than rebalancing monthly.
Yes, more volatile stocks with the same expected (i.e. arithmetic average) returns have lower growth rates. Thatās true whether or not you use leverage though. More volatile stocks with the same growth rate will have lower growth rates when leveraged, whether you rebalance daily or annually.
Transaction costs are not zero. If you assume they are you can make an easier model but you fail to capture the reality of how RUSS/āRUSL act.
Thanks, Paul. To further address Michaelās question, I think the reason why leverage gives returns raised to a power, rather than multiplying by a constant factor is the rebalancing. Letās say we have $100 and we take out a $100 loan and invest those $200. This is 2x leverage. However, if the fund increases 10%, we would have $220 and still a $100 loan, which is less than 2x leverage. In order to maintain the leverage, you should take out $20 more in loan and then have $120 in loan and $240 in the market. Then you can see why as the stock goes up, a given percent increase will give you a greater dollar increase if you rebalance. The converse is true if the stock goes down. And this is how you protect yourself from going to zero (a given percent decrease in the market means a smaller dollar value loss if you reduce your loan). The problem comes if gains and losses alternate each rebalancing period. One day it goes down and you sell some, and the next day goes up and you buy some. Since you donāt want to sell low and buy high, I believe this is the volatility drag.
In the case of 3X Russia, it uses derivatives (typically swaps or futures) to implement much of the leverage. Also, it reserves the right to intervene on very large daily movements, which I interpret to mean that it would not let the fund go to zero if there were a 34% daily drop.