Negative correlation conditional variance and return I've estimated a GARCH for S&amp;P 500, Nikkei and DAX index. 

The model for the return of S&amp;P 500, the results indicate the return of DAX has an negative effect on the S&amp;P 500 conditional variance? 

This is not in line with what I expected, given that high volatily must give a higher return. 

Can anyone help with this?
This is simply saying that the falling returns are usually correlated with high variance (i.e. sharp movement in prices). This is not very surprising... you can see from the graph of S&amp;P vs VIX below. Whenever the stock market plunges, volatility shoots up.



What @heh said was right. You need to compare assets that are more or less substitutable. For example, for what you said to hold true, it must be that investors in the US could say, returns in the US relative to the volatility is pretty low, so I'll move my money to Germany (where returns relative to volatility is higher) and invest there instead. In reality, such investors would have to face with interest rate differentials, FX risks, etc.

The "high volatility -> high return" applies to assets that are in the same "portfolio" (for me, this means in the same country at least). For example, you could say that a stock of a small company offers very high return but is very risky. You then have another asset, of a large company, that offers low return but is more stable. You also have the "risk-free" treasury bill that offers the lowest return and no risk at all.