Thanks, Paul. To further address Michael’s question, I think the reason why leverage gives returns raised to a power, rather than multiplying by a constant factor is the rebalancing. Let’s 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 don’t want to sell low and buy high, I believe this is the volatility drag.
Thanks, Paul. To further address Michael’s question, I think the reason why leverage gives returns raised to a power, rather than multiplying by a constant factor is the rebalancing. Let’s 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 don’t want to sell low and buy high, I believe this is the volatility drag.