Question

Bank of Bentley has determined that its inventory of yen (¥)-and Swiss franc (SFr)-denominated securities is subject to market risk. The spot exchange rates are ¥120.00/$ and SFr0.9500/$, respectively. The σ’s of the spot exchange rates of the ¥ and SFr, based on the daily changes of spot rates over the past six months, are 75 bp and 55 bp, respectively. Using adverse rate changes in the 99th percentile, the 10-day VARs for the two currencies, ¥ and SFr, are $350,000 and $500,000, respectively. Calculate the yen and Swiss franc-denominated value positions for Bank of Bentley.

Answer 1

Answer: N day VAR = 1 day VAR * Square Root(N)

10 Day VAR of Yen = 1 day VAR * Square root(10)

350,000 = 1 Day VAR * 3.162

1 Day VAR YEN = 110680

Similarly for swiss franc 1 day VAR is = 10 Day VAR / square root(10)

On putting values this will come out to 500,000/3.162 = 158114

FX Volatility = 2.335 * Daily changes of spot rates over the past six months

FX volatility yen = 2.33 * 75 bp = 1.7475%

FX volatility Swiss franc = 2.33 * 55bp = 1.2815%

1-day VAR = $ value of position * price Volatility

Yen 1 day VAR = $ value of position * price Volatility

110680 = $value of position * 0.0174

$value of position YEN= $6,333,619

Similarly for Swiss Franc, $value of position= 158114/0.012815 = 12,338,197

FX position in YEN = YEN position/ 120

YEN Position = 120* 6,333,,619 = 760034280 in YEN

FX position in Swiss Franc = SF Position/ 0.95

SF Position = 12,338,197 * 0.95 = 11721287 in Swiss Franc

These are the value positions for the Bentley