Let’s say I have two portfolios. Both have diffr mean, diffr std devn and one is positively skewed other is negatively skewed. What is the order of prefr that I need to give while selecting assuming that I am a risk averse investor? Assume suitable data like return on A is greater than return on portfolio B. Std devn On A is greater than std devn on B. Which portfolio will I choose? What are the measures that I need to look at?
There is no universal answer. Mean return is important (choose higher over lower), standard deviation of returns is important (generally choose lower over higher), skewness of returns is important (choose positive skewness over negative skewness), kurtosis of returns is important (generally choose platykurtic over leptokurtic), and so on.
Different investors have different views on how to measure risk. (In truth, most investors have no idea how to measure risk; they take a stab.) One investor may base it on standard deviation of returns, another on skewness of returns.
You pays your money and you takes your chances.