March Mathness

It was one of the most dramatic moments of the NCAA tournament’s opening act. With 17 seconds left in their first-round game against Northwestern, Vanderbilt seized a one-point lead. With the rest of his team hurrying back to defend their basket, Vandy’s Matthew Fisher-Davis inexplicably fouled Northwestern’s Bryant McIntosh, an 86% free-throw shooter. McIntosh hit both free throws, Northwestern won the game, and Fisher-Davis was left to say afterwards: “My dumb mistake is why we lost.”

Rebukes swiftly poured in from astonished sports fans and commentators. Some called it bone-headed, others a career-defining mistake. Still others ranked it among the most foolish moments in NCAA tournament history, like Chris Webber’s calling a timeout he didn’t have in 1993, or Georgetown’s Fred Brown passing directly to an opponent, both of which happened with less than fifteen seconds to go in those years’ final games. So even as Vanderbilt rallied around Fisher-Davis, outsiders largely dubbed his foul a mistake for the ages.

But was it? As Andrew Beaton of the Wall Street Journal points out, whereas U.S. college teams with a small lead essentially never foul, international basketball teams are more comfortable doing so. After all, why not have the ball in your hands with the chance to make the final game-defining play, rather than cede that to your opponent?

Beaton goes on to note that Northwestern made 49% of their two-point shots over both that game and their season, implying that Vanderbilt roughly had a 51% chance of winning had they not fouled and Northwestern missed as time expired. But a case could be made that they had an even higher chance of winning by fouling:
(a) If McIntosh made both free throws, with probability 74%, Vanderbilt could take their typical two-point shot and make it (winning the game) with probability 48%, contributing a 36% chance of victory.
(b) If McIntosh made one free throw, with probability 24%, Vanderbilt could take their typical shot and make it with probability 48%, or miss with probability 52% and go to overtime. Assuming overtime was a coin toss, this scenario would contribute a 17% chance of victory.
(c) If McIntosh missed both free throws, with probability 2%, Vanderbilt could close out the game and win more than 90% of the time, so this scenario would contribute a 2% chance of victory.

Hence, the strategy of fouling immediately would yield a 55% total chance of victory, slightly better than the non-fouling approach. Of course, such analyses are necessarily simplified, and small changes to probabilities can alter the outcomes, but they roughly cut evenly against both teams. So Beaton’s conclusion is that – far from making a blunder worthy of lasting memory — Fisher-Davis may have acted optimally, even if “conventional wisdom” suggested otherwise.

Beyond March Madness outcomes, “conventional wisdom” can be equally misleading in risk management topics. Here are a few examples:

“I can rely on economic forecasts to make sure I hedge my interest rate exposure on time.” Forecasts generally lack predictive power. For instance, as we’ve demonstrated in the pages of this newsletter, unemployment rate forecasts for next month are only accurate when they predict little or no change from the current month. With positive or negative spikes (i.e. more than 0.2%), we found only one correct call out of three hundred and eighteen attempts! Successful forecasting is directly tied to the rate’s not moving from one month to the next. This is like a weatherman who forever predicts that tomorrow’s weather will mirror today’s; he always gets it right, except on days when a new front blows in and changes atmospheric conditions. This is precisely when you want a weatherman to warn you about changing weather. Those who rely on economic forecasts can never be sure that they will have time to take risk off the table before markets move.

“I’ve hedged my top foreign currency exposures by notional, so I have definitively reduced my risk.” Consider a Euro functional company with significant manufacturing operations in China, Malaysia, Brazil, Poland, and Romania. Putting on forward contracts to sell Euros and buy each of those currencies can increase hedging costs unnecessarily. Since the EUR’s movements against CNY have been strongly correlated to MYR, weakly correlated to BRL, weakly inversely correlated to RON, and strongly inversely correlated to PLN, hedging each of these currencies in entirety may negate significant natural offsets. If cross-correlation is not taken into account, the company’s hedges may reflect far higher notional amounts than actually required to produce a given risk reduction. And if any exposures suddenly go away, the hedge unwind costs will be larger than they needed to be, magnifying currency risk.

“Hedge accounting criteria constrain me from hedging my full consolidated currency exposures.” It is certainly true that hedge accounting rules impose certain constraints: the specific entity with the currency exposure is usually required to be party to the hedging instrument, and the hedged transaction must be denominated in a different currency from the hedging unit’s functional currency. While this caps the notional amount of currency exposure that can be directly designated, firms can also benefit from indirect designation (level two) or split designation (level three) to increase their hedge accounting capacity. Higher-level hedge designation does require additional setup and analysis to implement correctly, but firms that do so can achieve their risk reduction objectives more comprehensively.

In risk management, as in NCAA basketball, the conventional wisdom often isn’t really wisdom. If you have questions about how to separate myth from reality regarding market timing, hedge structuring, or accounting for derivatives, please don’t hesitate to give us a call. And enjoy March Mathness!

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