$1.$ If a portfolio has a positive weight for each asset, can the expected return on the portfolio be greater than the return on the asset in the portfolio that has the highest return? Can the expected return on the portfolio be less than the return on the asset in the portfolio with the lowest return? Explain. $2.$ Comment on the following quotation from a leading investment analyst.

Stocks that move perfectly with the market have a beta of $1.$ Betas get higher as volatility goes up and lower as it goes down. Thus, Southern Co$,$ a utility whose share have traded close to $$12$ for most of the past three years, has a low beta At the other extreme, there is True North Networks, which has been as $$150$ and as low as its current $$15.$

$3.$ Given the following situations, determine in each case whether or not the hypothesis of an efficient capital market $($semistrong form$)$ is contradicted

a$)$ Through the introduction of a complex computer program into the analysis of past stock price changes, a brokerage firm is able to predict price imovements well enough to earn a consistent $3\%$ profit, adjusted for risk, above normal market returns.

b$)$ On the average, investors in the stock market this year are expected to earn a positive return $($profit$)$ on their investment. Some investors will earn considerably more than others. c$)$ You have discovered that the square root of any given stock price multiplied by the day of the month

provides an indication of the direction in price movement of that particular stock with a probability of $0\mathrm{.}7.4.$ What sort of investor rationally views the variance $($or standard deviation$)$ of an individual security$\text{'}$s return as the security$\text{'}$s proper measure of risk? What sort of investor rationally views the beta of a security as the security$\text{'}$s proper measure of risk?