The main purpose of this study is the development of a model for evaluating the performance of portfolios of risky assets taking into account the effects of differential risk on required returns. The portfolio evaluation model developed here incorporates these risk aspects explicitly by utilizing and extending recent theoretical results by Sharpe (1964) and Lintner (1965) on the pricing of capital assets under uncertainty. Given these results, a measure of portfolio performance (which measures only a manager's ability to forecast security prices) is defined as the difference between the actual returns on a portfolio in any particular holding period and the expected returns on that portfolio conditional on the riskless rate, its level of systematic risk, and the actual returns on the market portfolio. Criteria for judging a portfolio's performance to be neutral, superior, or inferior are established. A measure of a portfolio's efficiency is also derived, and the criteria for judging a portfolio to be efficient, superefficient, or inefficient are defined. I also show that it is strictly impossible to define a measure of efficiency solely in terms of ex post observable variables. I define two forms of the efficient market hypothesis, the weak form and the strong form (following terminology introduced by Harry Roberts, who used these terms in an unpublished speech entitled Clinical vs. Statistical Forecasts of Security Prices, given at the Seminar on the Analysis of Security Prices sponsored by the Center for Research in Security Prices at the Univ. of Chicago, May 1967. One can define a weakly efficient market in the following sense: Consider the arrival in the market of a new piece of information concerning the value of a security. A weakly efficient market is a market in which it may take time to evaluate this information with regard to its implications for the value of the security. Once this evaluation is complete, however, the price of the security immediately adjusts (in an unbiased fashion) to the new value implied by the information. In such a weakly efficient market, the past price series of a security will contain no information not already impounded in the current price. In such a market, forecasting techniques which use only the sequence of past prices to forecast future prices are doomed to failure. The best forecast of future price is merely the present price plus the normal expected return over the period. The available evidence suggests that it is highly unlikely that an investor or portfolio manager will be able to use the past history of stock prices alone (and hence mechanical trading rules based on these prices) to increase his profits. However, the conclusion that stock prices follow the weak form of the efficient market hypothesis allows for an investor to increase his profits by improving his ability to predict and evaluate the consequences of future events affecting stock prices. This brings us to the strong form definition of an efficient market, that is, one in which all past information available up to time t is impounded in the current price. If security prices conform to the strong form of the hypothesis, no analyst will be able to earn above-average returns by attempting to predict future prices on the basis of past information. The only individual able to earn superior returns will be that person who occasionally is the first to acquire a new piece of information not generally available to others in the market. But as Roll (1968) argues, in attempting to act immediately on this information, this individual will insure that the effects of this new information are quickly impounded in the security's price. Furthermore, if new information of this type arises randomly, no individual will be able to assure himself of systematic receipt of such information. Therefore, while an individual may occasionally realize such windfall returns, he will be unable to earn them systematically through time. While the weak form of the hypothesis is well substantiated by empirical evidence, the strong form of the hypothesis has not as yet been subjected to extensive empirical tests. The model developed in this paper allows us to submit the strong form of the hypothesis to such an empirical test - at least to the extent that its implications are manifested in the success or failure of one particular class of extremely well-endowed security analysts. I use the portfolio evaluation model developed here to examine the results achieved by the managers of 115 open end mutual funds. The main conclusions are: 1) The observed historical patterns of systematic risk and return for the mutual funds in the sample are consistent with the joint hypothesis that the capital asset pricing model is valid and that the mutual fund managers on average are unable to forecast future security prices. 2) If we assume that the capital asset pricing model is valid, then the empirical estimates of fund performance indicate that the fund portfolios were inferior after deduction of all management expenses and brokerage commissions generated in trading activity. When all management expenses and brokerage commissions are added back to the fund returns and the average cash balances of the funds are assumed to earn the riskless rate, the fund portfolios appeared to be just neutral. Thus, on the average the resources spent by the funds in to forecast security prices do not yield higher portfolio returns than those which could have been earned by equivalent risk portfolios selected (a) by random selection policies or (b) by combined investments in a market portfolio and government bonds. 3) I conclude that as far as these 115 mutual funds are concerned, prices of securities seem to behave according to the strong form of the efficient market hypothesis. That is, it appears that the current prices of securities completely capture the effects of all information available to these 115 mutual funds. Although these results certainly do not imply that the strong form of the hypothesis holds for all investors and for all time, they provide strong evidence in support of that hypothesis. 4) The evidence also indicates that, while the portfolios of the funds on the average are inferior and inefficient, this is due mainly to the generation of excessive expenses.