Scaling Currency Positions to Target Portfolio Volatility

Summary

The document considers how to size three long and short currency positions to target a specified annual portfolio volatility while allocating risk equally. The proposed procedure first scales each currency position separately so that each standalone position reaches the target volatility. It then combines the positions, measures the portfolio's realized volatility using historical returns, and adjusts all three leverage factors proportionately until the combined portfolio reaches the target.

The method accounts for diversification through an empirical portfolio check, rather than assuming that equal standalone volatility produces the same portfolio volatility. The answer does not define a return window, covariance estimator, rebalancing schedule, or treatment of transaction costs and changing correlations. Its example is a practical sizing sketch, so those implementation choices and leverage constraints need separate consideration.

Key ideas

• Estimate each currency trade's standalone volatility from historical returns.
• Scale each trade to the desired standalone volatility using its leverage factor.
• Combine the equally sized positions and calculate the resulting portfolio volatility.
• Adjust the leverage factors proportionately to bring portfolio volatility to the target.
• Diversification means equal standalone volatility does not ensure the same combined portfolio volatility.

Tags

# FX Portfolio Volatility Targeting


# FX Portfolio Volatility Targeting












If I have 3 different currency trades (ex short EURSEK, short NZDUSD, long USDJPY), how do I size each trade if I wish to allocate risk equally in order to target a 12% portfolio volatility (allowing for leverage and short selling)?

Any guidance would be greatly appreciated, along with R or python code examples.

## Answer by nbbo2 (score 1, accepted)

https://quant.stackexchange.com/a/18325

First, for each of the 3 currencies taken separately, find out the leverage $\lambda_i$ ($i=1,2,3$) that would be required to produce an annual standard deviation of $12\%$. [In my experience the std dev of currencies is about $8\%$ or $10\%$, so the three $\lambda$'s will be small, like $1.25$ or $1.2$].

Then find out what is the volatility that results when the three $12\%$ vol currency positions are combined equally into a portfolio. Because of diversification it will not be quite $12\%$, so adjust the three $\lambda$'s proportionately to bring it to the desired $12\%$.

I visualize this as a spreadsheet with separate columns for the historical returns of the different currencies, plus another column for the portfolio; but then I am an Exhell addict ;)

Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.