Tonight I want to introduce an advance lesson in financial theory: Probability of Return.

1) So far we have been talking about return per se and we have seen how volatility affects our mood and mental well-being.

2) I wish now to talk about this concept called probability of return which is based on statistic z-score methodology.

3) Suppose hypothetical you have a portfolio of various assets or UT and you calculated it to have a return of 3 year annual 14% p.a with a standard deviation 10%. Just take it that a very stable money market fund gives 4% p.a. rate of return. The Sharpe ratio is then a nice hypothetical (14 - 4)/10 = 1 

4) Suppose that the return are spaced in a normal distribution curve (aka bell shaped curve).

5) Suppose you are happy with just 10% and wondered what is the probability or chance of getting a 10% hit.

6) Using the formula Z-score = (ROI - Avr ROI)/Std-Dev = (10 - 14) / 10 = -0.4. Now with a Z-score of -0.4, look up a standard text book Z-table you will get 0.3446.

7) This 0.3446 tells you that the chance or probability of your portfolio achieving a 10% or more is 1 - 0.3446 = 0.6554 i.e., 65.54% within a one year period.

8) 34.46% chance you will get a return of 10% or less. So, is this a good hedge? Anything more than 50% is the good already!

9) Suppose you now want only a 5% ROI; then the Z-score becomes 0.1841; which means now you have a 1 - 0.1841 = 0.8159 or 81.59% chance in one year to get a 5% ROI.

10) Conversely, should you desire a say 20% ROI based on your portfolio.... using the same formula; Z-score becomes 0.7257; i.e. 1 - 0.7257 = 0.2743 or only 27.43% chance of getting a 20% ROI within a one year period.