1. Behavioral Finance The Critics April 21 Behavioral Finance Economics 437

2. Behavioral Finance The Critics April 21 How to calculate returns No one answer is always the right way Easiest situation is when there are no additions or withdrawals from the amount of money invested: Then “time-weighted” is the right way (1+ r(1)) times (1+ r(2)) times (1 + r(3))….. Where r(i) = (Price change in period i) divided by the price at the beginning of the period

3. Behavioral Finance The Critics April 21 But what if there are additions/substractions to the amount invested? Begin with $ 100 Six months later add another $ 100 Using time weighted, calculate return after one year: (1 + r(first six months)) times (1 + r)second six months)) Works fine if additions are relatively small compared to initial investment But, what if they aren’t?

4. Behavioral Finance The Critics April 21 If a huge amount is added or subtracted: Need to “weight” each period’s return by amount invested during the period: w(1) times (return in period 1) times w(2) times return in period 2) Where w(1) + w(2) = 1, both positive Each w(i) = initial inv in period i divided by sum of investments in each period Still, there are problems This is a big, big problem in evaluating the returns from private equity investments

5. Behavioral Finance The Critics April 21 Conrad and Kaul, 1993 Contrarian returns are upwardly biased because of using “cumulated average returns” as opposed to “time-weighting”, buy and hold returns For example, non-January returns were 12.2 % using “cum average” versus -1.7 % using time-weighted Also, re-weighting problem Plus upward bias on single period returns

6. Behavioral Finance The Critics April 21 Ball, Kothari, Shanken 1995 Contrarian results are “small stock” results which are mostly “January effect” results If you use June-end investment periods, it doesn’t work Beta higher in up markets, lower in down markets

7. Behavioral Finance The Critics April 21 The End