# Explain Efficient Frontier or Efficient set & Assumptions of Markowitz Model

Explain Efficient Frontier or Efficient set & Assumptions of Markowitz Model.

## Efficient Frontier

The efficient frontier represents the trade-off between risk and expected return faced by an investor when forming his portfolio. The efficient frontier was first defined by Harry Markowitz as part of his portfolio theory.

That theory considers a universe of risky investments and explores what might be an optimal portfolio based upon investments in these risky securities.

Assume a one year holding period for investment in these securities. (It can be any interval of time, but a one-year interval is typically assumed). Today’s values for all the risky investments in the universe are known.

The returns on these investments (reflecting price changes, coupon payments, dividends, stock splits, etc.) at the end of the holding period are random. As the return on securities is random, we can calculate expected returns and variances of returns for these securities.

The correlation of returns between each pair of securities may also be calculated. Using these inputs, we may then calculate the expected return and variance (and therefore standard deviation) of any portfolio that can be constructed using the instruments that comprise the universe.

#### Assumptions of Markowitz Model

Markowitz’s model identifies the trade-off facing the investor as the one between expected return (mean) and risk (variance). It makes the following assumptions concerning the investment market and investors’ behaviour within those markets.

• All investors have the same expected single period investment horizon. At the beginning of the period, the investor allocates his wealth among various assets, assigning a non-negative weight to each asset. During the period, each asset generates a random rate of return so that at the end of the period, his wealth has been changed by the weighted average of the returns.
• Investors are rational and behave in a manner so as to maximize their utility. They seek to maximize the expected return of total wealth.
• Investors base decisions on expected returns and risk (variance or standard deviation of these returns from the mean). They are risk-averse and try to minimize the risk and maximize return. They prefer higher returns to lower returns for a given level of risk.
• Investors have free access to fair and correct information on the returns and risk. All markets are perfectly efficient (e.g. no taxes and no transaction cost) and absorb the information quickly and efficiently.

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