Xiaohau Hu, chief research officer and co-chair of Campbell & Co., a Baltimore-based investment firm, gave a talk entitled “Two Envelopes, Siegel’s FX Paradox, and Currency Hedging.”
In his Tuesday presentation in Whitehead Hall, Hu explained the similarity between a theoretical paradox and the real-world phenomena that occur in the financial sector. The room was packed with both graduate students and professors.
“It’s very interesting,” graduate student Aoqiang Wang said. “It’s not so hard that we can’t get most of the things he said. It kind of gave us some reference that, if we’re interested, we could go further in this topic.”
In the first part of the lecture, Hu outlined a classic mathematical problem that has many applications in real life. He asked the audience to imagine a scenario in which they had access to two envelopes, one of which contains twice the amount of money as the other. If someone picks an envelope at random, and is given the option to switch the envelope they chose with the second envelope, they have to decide whether to do so.
Hu first explained that one approach to solving this problem consists of finding the expected value of the second envelope. This approach assumes that the other envelope is 50 percent likely to contain twice the amount of money in the selected one, and 50 percent likely to contain half the amount of money that the selected envelope contains.
Using these values, switching envelopes would yield 1.25 times the amount of money on average in the envelope that one chose.
“If you’re risk neutral, you should switch. That’s the conclusion based on this argument,” Hu said.
However, Hu noted, this argument contains logical flaws. If switching is truly better than keeping the envelope one has, then one would be better off continuing to switch envelopes forever.
Hu explained that the result reached previously was based on an assumption that the unchosen envelope is equally likely to contain double the money and half of the money as the envelope that was chosen.
Hu concluded that, if one is not allowed to peek into the envelope that one chose, the expected value of switching envelopes would be zero and one should be indifferent between both envelopes. However, if someone can peek, he or she can attempt to resolve the paradox by making assumptions about the algorithm that was used to fill the envelopes. Hu has worked on computer programs that create algorithms for filling such envelopes.
“This problem appears to be quite trivial, but there are a lot of interesting things that can come out of it,” Hu said. “If you make no assumptions, indeed this problem becomes very rich.”
Hu then proceeded to explain Siegel’s FX paradox, which relates to foreign exchange. He displayed a table of exchange rates between the Japanese yen and the U.S. dollar over a two-year period that extended from March 2012 to June 2014.
Over this time period, the dollar gained about 22.24 percent in value over the Japanese yen, while the yen fell about 18.31 percent relative to the dollar. In this apparent paradox, the gain in one country’s currency relative to another can end up being greater than the loss in the second country’s currency relative to the first.
“If you look deeper, it’s actually true every quarter,” Hu said. “Can changing a currency back and forth really create that kind of an economic benefit?”
Hu compared this paradox in foreign exchange rates to the paradox involving two envelopes. If one assumes that another currency has as much of a chance of rising as it does of falling, an expected value could be calculated.
However, unlike in the paradox between the envelopes, one does not know the ratio in the values of both foreign currencies.
Hu referred to this method of gaining profits from trading currencies as the Siegel’s effect. If this phenomenon really does occur, then it would be detrimental to combine many individual currencies into one, because currency trading is so profitable.
“If Siegel’s effect were real, then the Euro experiment would have been a mistake,” Hu said.
Depending on what drives exchange rates, he explained, Siegel’s paradox could be possible in the real world. A commodity that is sold in two different countries, but that is rarely traded between these two countries, might keep its original price even if the exchange rates between those two countries change. As Hu explained, this could allow someone to extract a profit from the change in the foreign exchange rates.
Hu concluded his lecture with some notes on currency hedging, which is a strategy that is used to reduce the risks that arise from trading foreign currencies. He explained that although currency hedging can lower the risks associated with a portfolio, few traders are 100 percent engaged in currency hedging. He presented a mathematical formula that is helpful in someone’s decision of whether to engage in currency hedging.
Hu joined Campbell & Co. in 1994 as a systems analyst, and he has worked there ever since. Campbell & Co., which was founded in 1972, is the country’s oldest managed futures hedge fund.
According to Hu, foreign exchange is just one of the areas in which Campbell & Co. has investments; the company’s other investments include stocks, bonds, and commodities.
“It’s extremely hard to trade currencies and make money,” Hu said. “Risk management is very much a coherent part of our portfolio construction.”