Risk of Two Cash Positions

You now have two assets: JPY 1 billion + THB 4 billion. What is the risk over a 1-day period?

Solution

Step	Calculation	Comment
1. Measure value in USD	$200 million	140 JPY/USD and 40 THB/USD
2. 1-month volatility	JPY/USD 1.78% THB/USD 1.96%
3. What are risks?/$	On JPY $ 1.78 million On THB $ 1.96 million	Data Set
4. What is total risk?	$ 1.78 + $ 1.96 m = $ 3.74 million	This is incorrect you cannot just add the risks!

Simply adding risks together is incorrect: This would assume that both JPY and THB would move together in perfect lockstep. To calculate the total risk of two or more positions, we need to know correlations between all variables.

We will now show you how it is actually calculated.

Risk of Two Cash Position (With Correlation)

The data set shows a correlation of 55% between JPY/USD and THB/USD.

Because the correlation is less than 1, we expect the total risk of our JPY and THB positions to be less than $3.74 million.

Undiversified risk	$3.74. million
Diversification benefit	-$0.45 million
Net risk	$3.29 million

The diversification shows the difference between net portfolio risk and gross risk assuming perfect correlation (i.e., net portfolio risk minus gross risk). We can calculate the risk of two linear positions using the following formula:

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Risk of Two Cash Positions

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Risk of a Single Cash Position

Time Scaling of Volatility

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