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I've estimated a GARCH for S&P 500, Nikkei and DAX index.

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

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  • $\begingroup$ Are you saying that you're finding if German stocks do well, American stocks are less volatile? $\endgroup$ – heh Nov 6 '19 at 17:55
  • $\begingroup$ Yes. I also see that when the return of the German stocks go up, the volatily falls. $\endgroup$ – oxguru Nov 6 '19 at 18:48
  • $\begingroup$ So the expectation that "high volatility = high return" typically applies to the same asset or portfolio. These are different assets, in different portfolios. I would begin analyzing your issue by asking whether it makes sense to expect high volatility in one asset or portfolio to come with high returns in a different asset or portfolio. $\endgroup$ – heh Nov 6 '19 at 18:56
  • $\begingroup$ Yeah, but thats the thing. It does the same when you analyze the return of DAX and the volatility. There is a negative correlation there too.. Which I can't seem to explain why $\endgroup$ – oxguru Nov 6 '19 at 22:52
  • $\begingroup$ Well... yeah, correlations are bi-directional. That's not information. I guess what I'm saying is that just because the correlation you've found is statistically significant, does not mean it's theoretically important. It could be, but without a reason grounded in theory to inform your expectations, you have no way of making sense of things if those expectations are violated. And in general I would not have the expectation you have. Without a solid reason to do so, I would not expect the risk-return relationship to apply to two different portfolios. You dig? $\endgroup$ – heh Nov 6 '19 at 22:59
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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&P vs VIX below. Whenever the stock market plunges, volatility shoots up.

enter image description here

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.

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