Bias, Equity Index and Equity Risk Premium

Question

Hi, I just have a quick question. A required return usually entails adding additional premium on top of a risk-free asset like a gov bond or bill. The additional premium is to compensate the higher risk an investor bears for investing. In the case of equity index, we knew about survivorship bias because dead companies are not included in the index. In other words, only companies which are still operating and raising capital from the equity market present in the said index. My question is if these companies have survived compared to those dead companies, why is it the bias is upward orientated instead of downward? shouldn't these companies then supposedly have lower risks compared to these dead companies? Also, if a particular period is turbulent (war, economic uncertainties, etc), shouldn't the index will be upward bias instead of downward bias because investors need to bear more risk?

ec_test · Answer

Hi! @wannabe1988, The reason is that if you were counting the dead companies, you would add a zero and divide by such company. For example, Stock Company #1 Return - 5%Stock Company #2 Return - 7%Stock Company #3 Return - 9%Stock Company #4 Return - 0% (dead company)Average return with dead company (5+7+9+0)/4=5.25%Average return without dead company (5+7+9)/3=7.00% - This one is biased upward. Hope it helps!  :D