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A simulation gives a portfolio view for the future with some given probabilities. The investor must be aware of the probability to be below a given return in the next x years. The simulation below shows that the portfolio has 50% probability to be higher than 20.9% in 2 years.

Why is it important to visualize a portfolio in the future?
For example, an investor will be able to known of that he has 5% probability to be below his initial investment of USD 10mio, in 3 years.  He will then decide whether 5% is too high.  If it is too high he will have two possibilities, in a normally distributed world:
- Decrease the portfolio volatility
- Increase the portfolio expected return

What is a shortfall risk?
The shortfall risk is the portfolio probability to be below its target return at the end of the investment horizon.

What is the portfolio probability to beat the market index?
The portfolio manager should compute this probability when he builds a portfolio. Otherwise, the investor is better of to invest in a fund tracking the index  and he will be sure not to be beaten by  the index. The portfolio manager who is selecting sectors, equities, bonds, mutual funds, hedge funds or  currency has a vision of these markets, in term of expected returns. It is important to group these visions and simulate them, by accounting for market  skewness and kurtosis in order to see the effect of extreme events on the portfolio.

Does correlation increase during  turbulent markets?
Yes, on average.  If the investor is risk averse, this is an important concept. In order to choose the assets with a low correlation during market turmoil, a  bear correlation must be used. This is the correlation during the market negative returns. For more on bear correlation, read Chambers&Hastie,  Statistical models in S, 1992, Chapter 8, Wadsworth & Brooks.

Is the portfolio maximum loss relevant to the investor?
Yes, if he is risk averse.  For example, assume the investor can not bear a monthly loss lower than -8%.  Consequently, you have to simulate the investor portfolio and see how many times the historical portfolio returns were lower than -8%.

Is the probability of losing more than -3% per month useful to the investor?
Yes, it he is risk averse.  If the investor does not care about volatility, negative skewness, and positive kurtosis, you do not need to simulate the portfolio although for a marketing point of view, it could be useful.  If the investor knows, for example, that over the next year he has a probability to lose 3 times more than -3%, he will know exactly whether the portfolio fits his needs.

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