run average annual return on the S&P 500 stock market index (adjusted for dividends
and stock splits) has been 8.5%, with an annualized standard deviation of 15%. How-
ever, the consensus analyst forecast is that the standard deviation of the S&P 500
during the coming year will remain at an elevated rate of 25%, whereas the expected
return on the S&P 500 will decline from 8.5% to 7%.
(a) What are the odds of a positive stock market return during the coming year
(assuming that returns on the S&P 500 index are normally distributed)?
(b) Suppose that analysts revise their forecasts so that the consensus 2012 forecast
is that the S&P 500 will revert back to its long-run average return and standard
deviation of 8.5% and 15% respectively. Under this scenario, what are the odds
of a positive return on the S&P 500 stock market index during the coming year?