An investors buys 2 shares of a stock at $85 at t=0, and at the end of the year (t=1), he buys 1 additional share for $72. At the end of year (t=2), he sells both shares for $97 each. At the end of first year (t=1), the stock paid a $2.50 dividend per share and $3.00 dividend at the end of the second year (t=2).
Compute the dollar-weighted and the time-weighted rate of return.
a. On each trading day, a portfolio manager has 25% chance of earning a return that is equal to or greater than the market. What is the probability that the portfolio manager will underperform (earn a return that is lower than) the market in 4 out of 5 weekly trading days. (This is a binomial probability distribution problem).
b. The portfolio manager of open-end mutual fund estimates on the average that 5,000 investors will redeem shares from the fund in a month. The average total redemption per investor is $20,000. What is the probability that at least 1 investor will make a redemption on a given trading day.