Sizing for a Pegged Currency That Might Break

[Fairman]

Sizing for a Pegged Currency That Might Break

A currency is pegged at 10.00 per dollar. Forward markets hint at some stress. You see an opportunity: the peg has held for years, and the carry on holding the high-yielding currency is attractive. If the peg breaks, the currency could drop 30 percent.

Quantify the trade. You consider a 20,000-dollar position, earning carry of 8 percent a year. Over a year, that is 1,600 dollars, 8 percent of the position.

Compute the downside. A 30 percent devaluation costs 6,000 dollars on a 20,000-dollar position, which is 3.75 years of carry.

Now probabilities. If the chance of a break in any given year is 5 percent, the expected loss is 0.05 times 6,000, which is 300 dollars, against an expected carry of 1,600. The expected value looks positive, by 1,300 dollars.

Look at the shape. With probability 95 percent, you earn 1,600. With probability 5 percent, you lose about 4,400 net. A string of positive years teaches nothing about the tail. If the true probability is 15 percent, the expected loss is 900, and the margin shrinks. At 25 percent, expected loss of 1,500 roughly cancels the carry.

If you take the position, size it so that the 30 percent loss is tolerable. If the account is 20,000, a 6,000-dollar loss is 30 percent, which is far too much. Size to lose 2 percent: 400 dollars, which means a position of 1,333 dollars.

At that size, the carry is 107 dollars a year, hardly worth the effort, which tells you something.

Your turn: for a high-yield pegged currency, compute the break-even probability of a devaluation.