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I am trying to understand how currency hedged ETF returns work with a simple example, namely, that where a Swiss investor can choose between buying a S&P-500 index fund which either a) hedges the USD-exposure in CHF or b) doesn't hedge currency exposure.


Consider a two-period market with the following properties:

At the start, $t=0$, the exchange rate USD/CHF is equal to $1$ and the price of the S&P-500 in USD is $1$.

In the next period, $t=1$, the exchange rate USD/CHF is equal to $\frac{10}{11}$ and the price of the S&P-500 in USD is $1.1$ in the "up state" and $0.9$ in the "down state".

An investor buying an (unhedged) S&P-500 ETF will go from $1$ CHF at the start to $1$ CHF at $t=1$ in the "up state", and they will go from $1$ CHF at the start to $\frac{9}{11}$ CHF at the end in the "down state", leading to returns of $0\%$ and roughly $-18\%$, respectively.


How would the CHF-hedged ETF return look like in this case? As I see it, at $t=0$ the ETF manager would enter a futures contract to buy $1$ CHF for $1$ USD at $t=1$.

In the "up state", the investor would then go from $1$ CHF to $1$ share of S&P-500, which is then worth $1.1$ USD at $t=1$. The futures contract turns this into $1 \textrm{CHF}+0.1\textrm{USD}$, which then gets converted to $\frac{12}{11}$ CHF. Therefore, the return for the Swiss investor is about $9\%$ in the "up state".

In the "down state", the investor would go from $1$ CHF to $0.9$ USD, which then gets converted to $1\textrm{CHF}-0.1\textrm{USD}=\frac{10}{11} \textrm{CHF}$, so the return would be roughly $-9\%$.

Is my understanding of how these returns behave for currency hedged ETFs correct?


(Of course, the situation would be reversed if the USD/CHF rate had gone up instead of down.)

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    $\begingroup$ You have the right idea, although you did not take into account the difference in interest rates between CHF and USD, which causes the futures price of CHF to be about 2.7% a year higher that the spot price in USD. cmegroup.com/markets/fx/g10/swiss-franc.html#venue=globex $\endgroup$
    – nbbo2
    Feb 10 at 11:19
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    $\begingroup$ (Which means that if the S&P500 is unchanged and the exchange rate is also unchanged you make 2.7% a year simply from the fact that you invested abroad. Of course the year to year fluctuations of SP500 are much greater than 2.7%, more like 10 to 20%. And the inflation rate in US is higher than in CH). $\endgroup$
    – nbbo2
    Feb 10 at 12:31

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