Minimum-Variance Hedge Ratio and Basis Risk

On the morning of 1 August 2008, the remaining long holders of the Zimbabwe dollar were in for quite the shock. Overnight, the ZWD depreciated over 70% versus the USD. Hopefully those investors were hedged! But just hedging your currency risk isn't a set-it-and-forget-it approach. You need to monitor the currency risk exposure in relation to the hedge ratio. So what are you really focusing on when you evaluate currency risk versus the hedge?

That's right! You'd be concerned with the tracking error between the value of the hedged asset and the asset used to hedge the currency risk. This is where the __minimum-variance hedge ratio__ can come in. The minimum-variance hedge ratio is a mathematical approach that helps you determine the optimal cross hedging ratio. It uses regression analysis based on ordinary least squares to minimize the variance. Basically, it's mean–variance optimization for currency hedges, but not all hedges can be used for minimum-variance hedging.

Not quite. The hedge should reduce your maximum value at risk to low levels, unless it's not properly aligned.

No. The standard deviation of the currency pair isn't going to include the hedged exposure.

For example, you can hedge currency risk through forward contracts in the same currency pair. That's roughly a 100% hedge ratio that's not going to deviate much from the currency risk exposure, so it's not best for minimum-variance hedge analysis. Which type of hedge would be best for minimum-variance hedge analysis?

No. A direct hedge will roughly maintain its 100% hedge ratio to the currency risk at all times.

Not quite. Swaps with the same notional amount will provide 100% hedge ratios.

Right! A macro hedge is a great hedge to use for the minimum-variance hedge ratio analysis because it's not directly aligned with the currency risk. It's an indirect hedge, like shorting another currency with high correlation to your long currency risk. It's still a different currency exposure, and it can come in handy in building out a unique hedge structure.

For example, if there's only a single foreign-currency asset involved, you can perform a joint optimization over both the foreign-currency risks by regressing the changes in the domestic-currency return against the changes in the value of the hedging instrument. This joint regression can develop a better hedge ratio because it's focused on changes to both the domestic and foreign returns. What does this joint optimization take into consideration to improve the hedge ratio?

Yes! The joint regression is focused on the correlations between the foreign-currency risk exposure and the foreign-currency return because that will determine the joint level of risk that needs to be hedged. But remember that this only works for a single currency exposure, and it varies among different portfolio holdings. Research has shown that international bond portfolios usually have optimal hedge ratios close to 100%, but single-country foreign equity holdings will vary significantly depending on the domestic currency and the currency of the foreign investment.

Not quite. The risks associated with the domestic- and foreign-currency returns must be captured together, not in separate standard deviations.

No. Those are just two of the many factors that go into currency risk, but they're not going to fully capture the joint risk.

The hedge ratio for single foreign-currency exposures could also vary because of __basis risk__, or the risk that an indirect hedge's correlation between the currency exposure risk and the price moves in the hedge ratio aren't perfectly correlated. Essentially, the correlation breaks down over time as more data becomes available. For example, if you hedged long CNY/AUD exposure with a short CNY/NZD exposure, you would have an indirect hedge. But what currency pair would indicate basis risk?

No. That's your long currency exposure, not the cross exposure.

Not quite. That's your short currency exposure, not the cross exposure.

You got it! The NZD/AUD currency pair will capture the basis risk because movements in this exchange rate can alter the correlation between your hedge and your currency risk. So basis risk breaks the correlation of indirect hedges. This can also occur when using a derivative based on a currency basket, which can change the hedge ratio based on changing correlations inside of the basket. Clearly, it's important to monitor and rebalance hedges to account for the drift in correlations. Sometimes, hedges can actually turn into the same long exposure that was being hedged.

To sum it up: [[summary]]

Tracking error

Maximum value at risk

Standard deviation of the currency pair

Direct hedges

Swap hedges

Macro hedges

Correlation

Standard deviation

GDP and trade flows

CNY/AUD

CNY/NZD

NZD/AUD

Continue