Most people estimate that an index will rise 10% per year on average, going by past performance. Does this apply to all indexes?
No. All indexes are different and have different
expected rates of return (as well as expected risks). Furthermore, "most people" don't estimate a 10% return for equities, especially not after inflation is factored in. Think 5% as a real return, and that would be great.
The history of the S+P 500 is long enough to average out, but can we assume a long term 10% growth in European and emerging market equities also?
No. We can't assume anything.
Being a cautious risk taker, I’ve looked at bank accounts that pay high interest on hard currencies and also have a deposit insurance scheme in place. On the USD, Azerbaijan pays 9.8% on a 1 year deposit and has a $40k ish usd cap to the insurance scheme per bank. Mongolia pays 7% and has a $10k cap per bank for the insurance scheme. The negative point here is that the insurance scheme pays out in local currency which will likely be devalued at that point. Which investment is safer?
Neither of those investments are "safe" and neither of them are going to return that amount after currency fluctuations, exchange rates, and fees and commissions. "Being a cautious risk taker" means assessing your risk tolerance for your portfolio as a whole and allocating your assets accordingly.