To dollar-weight or share-weight a dislocation in a highly correlated pair?

[Talking about the HSBC share class arb in the 90s]
  • What is the cost of this dollar-for-dollar trading? What is the downside? Maybe you make less money on the convergence than otherwise. But this is not true! In our example, the share-for-share profit would have always been $5, regardless of when or how the convergence occurred. But because you traded dollar-for-dollar and the market went up, you actually made more money! Could dollar-for-dollar be a superior way of trading the discrepancy? Not necessarily. Had the market gone down by 10 percent, and then the two share classes converged, you would have made a 10 percent smaller profit. In fact, you can think of the dollar-for-dollar trade as being exactly the same as the share-for-share trade, plus an additional long amount in the expensive share equal to the amount of the dollar discrepancy. Specifically, with A costing $100 and B costing $105, the dollar-for-dollar position is the share-for-share position of long one share of A and short one share of B, plus a long position in 5/105 shares of B. The difference in the profit between share-for-share and dollar-for-dollar comes precisely from this net long position. So why be long? Because of the market risk.
  • If you know the convergence will happen within a few months, you are probably better off just trading it share-for-share, and taking the short-term mark-to-market risk of your portfolio moving against you in the meantime because of broad market movements. But if you think the convergence may take years, you may be better off with the smaller daily mark-to-market profit variation, at the cost of greater terminal profit variation. With share-for-share, you know for sure what your profit will be when the two share classes merge. With dollar-for-dollar, your profit depends on the level of the market when the convergence happens. If the convergence happens when the market is low, your profit will be low.
  • There is one other wrinkle to the dollar-for-dollar way of trading, and that's the fact that you have to rebalance if you want to maintain your dollar-for-dollar exposure. A share-for-share trade never needs to be rebalanced, but in dollar-for-dollar, if the discrepancy widens to say $10 from $5, you need to either buy more of the A share or buy back some of the B shares to maintain an equal dollar exposure. This additional trading can bring with it its own profit profile, one that depends neither on the overall direction of the market or the discrepancy, but on their correlation and on whether you are willing to increase your bet!
  • Say you always want to maintain a $100 exposure in each share class. Then if the discrepancy tends to widen when the market rises, you would be buying back the B shares at a high price, and selling more of them at a low price. That would hurt you over the long run. But let's say you are willing to increase your position size. Then if the market is up and the discrepancy is wider, you can buy more of the A shares instead of the B shares. And when the market and the discrepancy come down, you can sell more of the B shares. The result will be that your overall position size is larger, but you haven't necessarily lost money yet. There is no easy straightforward answer. There are only issues and considerations for you to weigh. That's what makes it fun!