Mean Variance Analysis

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Definition: Mean Variance Analysis

Mean Variance Analysis is the process of weighing risks against returns. According to modern portfolio theory, assuming rational investors make decisions for multiple risky assets – for higher risks, they expect high returns. The factors to be considered in this analysis are Variance (volatility in the returns of a security during a period of time) and Expected Return (Probability on return of stock).

Lower variance is considered to be a better indicator when choosing among two options having the same returns. By combining the stocks with different variances and expected returns in a portfolio, the diversification objective is fulfilled – the loss due to movement of a particular stock is countered by opposite movement of another stock. Thus for an optimal portfolio, an investor must consider the co-movement of individual securities.

Mean variance analysis makes the following assumptions:

• The investor can buy any amount of security. The negative weight is allowed, considering it as short-selling.

• The investor cannot affect the price of the security, i.e. a price-taker.

• Price for both long and short positions is the same.

• There are no transaction costs.

For Mean Variance Analysis,

Total expected return:

µR = ni=1 wiµi

Variance of total return:

Var[R] = ∑ni=1nj=1wiwjcov(i,j)

The risk averse investor chooses weights wi so that expected returns are high and the risk is low, while another risk-tolerant investor may choose a different value for the weights according to her risk capacity.

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