Suppose there are N E N assets that compose a portfolio P. Assume that n; shares of asset i (i = 1,..., N) are purchased and the price of asset i in time period t is denoted by Pit. Let Vi be the value of the portfolio in time period t and wit Pribe the share of the investment on asset i in period t. Show that net return and gross returns of holding the portfolio for one time period can be written as a weighted average of net returns and gross returns of the component assets of the portfolio. Show that the same is not true for log-returns