Hedging against stock indices

Correlation coefficients against the Nikkei average

We examined the correlation coefficients against the Nikkei average. We found that the correlation with USD/JPY has tended to strengthen since around the middle of 2007, and that about half of the fluctuations can be explained by movements in the exchange rate. On the other hand, while the correlation with the S&P 500 also tends to strengthen, there has been a consistent correlation for a long time.

Figure 1: Correlation coefficients against the Nikkei average
(each point is the correlation coefficient of the 3- to 10-day log differences over the past 200 days)

Slope of the linear regression against the Nikkei average

To hedge the Nikkei average with other factors, we examined how much leverage should be applied. We can see that in recent years, hedging with USD/JPY requires a USD/JPY hedge of more than an equal amount.

Figure 2: Slope of the linear regression against the Nikkei average
(each point is the correlation coefficient of the 3- to 10-day log differences over the past 200 days)

Hedge simulation for the Nikkei average

We can see that hedging the Nikkei average with USD/JPY reduces the range of fluctuations slightly, but this does not seem to bring it to a level where one could invest in the Nikkei average.

Figure 3: Hedge simulation for the Nikkei average

Hedge simulation for the S&P 500

The S&P 500 is an index that has risen steadily over the past several decades, but problems such as the Lehman shock have still occurred. We can see that hedging the S&P 500 with the Nikkei average allows one to invest in the S&P while preventing crashes in the stock price.

Figure 4: Hedge simulation for the S&P 500

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