Efficient portfolio calls for an optimal investor to adopt an efficient combination of investment that minimizes the level of risk subject to returns on that investment. A major limitation is that the decisions on capital expenditure are based on the expectation, and no facts are available at the time of decision-making. Although information is the basis for decision-making, efficient portfolio creates another element of risk because it is not always true that the expected returns will actualize (Reilly 52). The investor, therefore, may undertake an investment with a higher expected return but in the end it yield unfavorable outcome. The concept of optimal portfolio does not take into account transaction cost and investors may not yearn to change their portfolio as often as the model suggests.

Derivatives are instruments in finance whose characteristic and value depends upon the value and characteristic of an underlie such as a commodity, equity, bond or currency. These financial instruments include security derived from a debt instrument share, risk instrument, loan or contract for differences of any other type of security (Reilly 131). Derivative derives its value from the index of price of underlying securities. If the value of the underlying changes, the price of the derivative also changes. In nature, derivatives are not a product or commodity. The price of gold futures contract is obtained from the price of the underlying asset such as gold.

The future outcome of all investable assets including derivatives is at stake and is based on so many uncertainties. The expected value of derivatives is faced with the risk and therefore there is a need to adjust these returns for risk giving rise to risk-neutral probabilities. The concept of risk neutrality pricing of derivatives generally means taking both long and short position in the derivatives market (Weaver 89). It does not depend on risk disposition of the investor. It takes into account the