CROSS HEDGE Explained
It is often the case that various assets in the portfolio and exposure to different currencies with imperfect correlation between them creates a natural hedge also known as the cross hedge or proxy hedge or macro hedge. A cross hedge is an indirect hedge as opposed to using forwards to hedge which is direct.
For example historically the Brazilian Real and the Russian Ruble have been closely correlated. A short position in the Real and a long in the Ruble can reduce overall portfolio risk (as measured by volatility). In this case derivatives and forward contracts are not needed and sometimes they are not available or illiquid.
It is important to note however that whenever a cross hedge is used to minimize portfolio risk, basis risk is incorporated into the portfolio which in a sense is produced by the fact that we are assuming that these correlations between currencies will hold in the future.
For example if we were to invest in Russian Ruble Bonds and Turkish Bonds on the premise that they have lower correlation and that the Russian economy is a net exporter of oil and gas while Turkey is a net importer. We would then use cross hedging to reduce portfolio risk by including both Russian and Turkish assets in the portfolio.
Then a crisis happens due to Turkish debts skyrocketing and investors becoming frightened, pulling out of emerging markets in general. This is called contagion. In this case the correlation between the currencies of the two countries can change significantly, now the currencies both fall and correlation increases towards positive 1 as investors sell their Liras and Rubles to purchase USD which is considered safer.
The risk that the correlations between the two currencies changes is the basis risk.
Basis risk is introduced by the cross hedge which is an indirect form of hedging while a direct hedge with a forward contract for example will not produce basis risk.
Minimum Variance Hedge Ratio (MVHR)
When using forward contracts to hedge, often an ideal hedge does not exist and hedging is also often expensive. Finding an optimal hedge that is less than 100% often known as the minimum variance hedge is often the best solution.
an ordinary least squares is typically used.
return in domestic currency = alpha + beta x (FX return) + resitual
the beta is given as correlaton of (Rfx, Rdc) x std (Rdc)/std (Rfx)
The beta is the minimum variance hedge ratio
in the case of basis risk, it is expressed in the instability of beta.
Note: If I am long USD/AUD, I am long the base currency, i.e. AUD
Example with Rubles and USD
I am a USD investor but am originally from Russia and like to have a little exposure to the local equity market in my portfolio (presumably because I think the Russian equity market is very cheap). I would like to hedge my Russian equity exposure however back to USD because I live in the US.
I note that the correlation between the returns of the Russian stock market in Rubles and the % change in USD/RUR is +0.6 i.e. when the Russian Stock Market goes up the Ruble tends to go up as well most of the time, so they to some extent move together but not perfectly.
I decide I want use forwards, so I would go short a USD/RUR forward but I need to know the nominal amount and I wish to use a minimum variance hedge ratio for this.
I regress Rdc = alpha + beta x Rfx + residual and find the beta of 1.35 fits.
If sport USD/RUR = 0.01666 and I invested $1m then I have 60m RUR invested in Russian stock market. I need to go short USD/RUR forward for the nominal amount 60m RUR x 1.35 = 81m RUR
Because the Ruble and the Ruble stock market is positively correlated, we need to hedge more than the Ruble exposure in order to account for the FX volatility.
It is often the case that various assets in the portfolio and exposure to different currencies with imperfect correlation between them creates a natural hedge also known as the cross hedge or proxy hedge or macro hedge. A cross hedge is an indirect hedge as opposed to using forwards to hedge which is direct.
For example historically the Brazilian Real and the Russian Ruble have been closely correlated. A short position in the Real and a long in the Ruble can reduce overall portfolio risk (as measured by volatility). In this case derivatives and forward contracts are not needed and sometimes they are not available or illiquid.
It is important to note however that whenever a cross hedge is used to minimize portfolio risk, basis risk is incorporated into the portfolio which in a sense is produced by the fact that we are assuming that these correlations between currencies will hold in the future.
For example if we were to invest in Russian Ruble Bonds and Turkish Bonds on the premise that they have lower correlation and that the Russian economy is a net exporter of oil and gas while Turkey is a net importer. We would then use cross hedging to reduce portfolio risk by including both Russian and Turkish assets in the portfolio.
Then a crisis happens due to Turkish debts skyrocketing and investors becoming frightened, pulling out of emerging markets in general. This is called contagion. In this case the correlation between the currencies of the two countries can change significantly, now the currencies both fall and correlation increases towards positive 1 as investors sell their Liras and Rubles to purchase USD which is considered safer.
The risk that the correlations between the two currencies changes is the basis risk.
Basis risk is introduced by the cross hedge which is an indirect form of hedging while a direct hedge with a forward contract for example will not produce basis risk.
Minimum Variance Hedge Ratio (MVHR)
When using forward contracts to hedge, often an ideal hedge does not exist and hedging is also often expensive. Finding an optimal hedge that is less than 100% often known as the minimum variance hedge is often the best solution.
an ordinary least squares is typically used.
return in domestic currency = alpha + beta x (FX return) + resitual
the beta is given as correlaton of (Rfx, Rdc) x std (Rdc)/std (Rfx)
The beta is the minimum variance hedge ratio
in the case of basis risk, it is expressed in the instability of beta.
Note: If I am long USD/AUD, I am long the base currency, i.e. AUD
Example with Rubles and USD
I am a USD investor but am originally from Russia and like to have a little exposure to the local equity market in my portfolio (presumably because I think the Russian equity market is very cheap). I would like to hedge my Russian equity exposure however back to USD because I live in the US.
I note that the correlation between the returns of the Russian stock market in Rubles and the % change in USD/RUR is +0.6 i.e. when the Russian Stock Market goes up the Ruble tends to go up as well most of the time, so they to some extent move together but not perfectly.
I decide I want use forwards, so I would go short a USD/RUR forward but I need to know the nominal amount and I wish to use a minimum variance hedge ratio for this.
I regress Rdc = alpha + beta x Rfx + residual and find the beta of 1.35 fits.
If sport USD/RUR = 0.01666 and I invested $1m then I have 60m RUR invested in Russian stock market. I need to go short USD/RUR forward for the nominal amount 60m RUR x 1.35 = 81m RUR
Because the Ruble and the Ruble stock market is positively correlated, we need to hedge more than the Ruble exposure in order to account for the FX volatility.
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