They say blues legend Robert Johnson, considered by many to be the grandfather of rock and roll, sold his soul to the devil to be able to play the guitar. He is said to have “gone down to the crossroads” and given his guitar to the devil, who promptly tuned it for him and provided him with a mastery that made him the legend he is today.
It’s not clear when, or if, the devil ever returned to collect on his debts. But regardless, Johnson could be said to have sold an option to the devil. His success was simply the premium he earned on selling that option. Throughout his career, he should have kept that in mind.
To a great extent, the success enjoyed by hedge funds comes with similar strings attached. Investors and prime brokers hold an option to withdrawal their capital (equity and debt). In exchange, they allocate their capital to the fund, thereby enabling profits for the fund (and by extension, other investors in that fund and, of course, the manager).
As a result of this sword of Damocles hanging over them, hedge fund managers need to factor in the possibility of investors and/or prime brokers pulling the plug on their fund. This was quite apparent during the hedge fund deleveraging that occurred over the past year.
The trick for risk managers is to put a value on these options. If they do, then their leverage choices might be far different. This is the argument made in a recent paper called “Risk Management Framework for Hedge Funds: Role of Funding and Redemption Options on Leverage” by John Dai and Suresh Sundaresan of Capula Investment Management in London.
The duo refer to investors’ withdrawal option as the “redemption option” and the prime brokers’ option as a “funding option”. Since many hedge funds offering infrequent redemption dates, you could say that the redemption option has European option characteristics and the funding option has American option characteristics.
The costs of rapid, unplanned deleveraging resulting from the exercising of either option can be significant for bystanders in a fund. When bank investors yank their money, banks can dip into capital markets to shore up equity. But as Dai and Sunderesan point out hedge funds usually have no such luxury.
This can have a profound impact on leverage decisions. A manager has an incentive to lever up his alpha bets (assuming they are working). Assuming she is confident in her ideas, the more leverage the better. But with a tangible value on the (expected) costs of an untimely deleveraging, things look quite different. As leverage rises and unencumbered cash shrinks (i.e. cash not used as collateral), the potential cost of an exercised option increases.
So Dai and Sundaresan suggest there actually an “optimal” level of leverage. The math is somewhat dense, but this chart from their paper sums it up:
The red line shows a scenario where the costs of deleveraging are minimal. As you can see, adding more risk (i.e. leverage) increases the return commensurately. However, this increase is mitigated by the possibility that prime brokers and investors might freak out and running for the hills at any moment. When the costs of deleveraging are significant – as they are for most hedge funds (blue line) – then the cost of the redemption or funding option being exercised eventually trumps any gains from more leverage. The point where the cost of satisfying these (often concurrent) options equals the marginal alpha gain from more leverage marks the “optimal leverage”.
More than just a risk manager’s tool, this kind of analysis has implications for investors and policymakers say the authors. Investors should ask their managers for their management approach to these short option positions. Policy makers should track the aggregate costs of all of these options being exercised simultaneously (specifically, buy tracking each fund’s unencumbered cash level). And managers should institute an investor-level rolling lock-up, not one based on the fund as a whole.
Although this paper examines the effect of sudden withdrawals of equity and credit on the fund itself, you don’t need to be a hedge fund whiz to figure out that the manager herself faces the same calculus regarding her own compensation. However, if this approach is to be repurposed to explore the optimal leverage level for the manager, then the authors suggest that high water marks, hurdles, management and performance fees should be factored in.