Conference nyoss1::market_investing

423.0. "Arithmetic vs Geometric Returns" by NOVA::FINNERTY (Sell high, buy low) Mon Mar 22 1993 11:40

    
    Here's something you may never have thought about concerning rates of
    return.  I think it's pretty interesting.
    
    Case 1:
    
        You have an investment that has a 50% chance of doubling and a 50%
        chance of halving.  What is its expected *future* return?
    
    	Ans:  (-50% + 100%)/2 = 25%
    
        This is because the expected gains are larger in magnitude than the
        expected losses.
    
    Case 1A:
    
        What is the best estimate of its *past* performance?
    
    	Ans:  (.5 * 2.0) ** 1/2   -   1.0 = 0%
    
        This is because the median of all return scenarios is 0%.
    
    Case 2:
    
        You have an investment that has a 1/3 chance of losing 100% and
        a 2/3 chance of gaining 100%.  What are its expected returns, past
        and future?
    
    
     	Ans:  Future: (-100 + 100 + 100)/3       =   33%
    	      Past:   (0 * 2 * 2) ** 1/3   - 1.0 = -100%
    
        Here seems to be an illustration of what appears to be a fallacy
        in the way expected future returns are calculated...  you're 
        essentially guaranteed to lose all your investment eventually
        because of the 1/3 chance of losing 100%, and yet the expected
        return, even after n >> 0 rounds, is 33%.