Portfolio Theory & The Benefits of Diversification , Mean-Variance Analysis and Diversification

Portfolio Theory & The Benefits of Diversification

Chapter: 12 Portfolio Theory & The Benefits of Diversification

Section: 2 Mean-Variance Analysis and Diversification

In mean-variance analysis, we use the expected returns, variances, and co-variances of individual investment opportunity returns to analyzing the risk-return trade-off of combinations, or portfolios, of these individual investments. The assumptions of mean-variance analysis are:

All investors are risk averse

Asset expected returns, asset return variances, and covariance can be calculated.

Investors can create optimal portfolios by only knowing expected returns, variances, and covariances.

No frictions or trading costs exist.

I. Expected Return: The expected return on a portfolio of two assets is simply the weighted average of the returns on the individual assets, weighted by their portfolio weights:

E(R_p)	=	W1E(R1) + W2E(R2)
Where:
E(R_p)	=	Expected return on portfolio
E(R1)	=	Expected return on asset 1
E(R2)	=	Expected return on asset 2
W1	=	Percentage of total portfolio value invested in asset 1
W2	=	Percentage of total portfolio value invested in asset 2

II. Standard Deviation: The standard deviation of a portfolio of two assets is not a simple weighted average of the asset standard deviation; it is also a function of the correlation between the returns of the two assets:

σp	=	[W1² σ1² + W2² σ2² + 2W1W2_p 12 σ1 σ2]
Where:
σ1	=	Standard Deviation of the expected return on asset 1
σ2	=	Standard Deviation of the expected return on asset 2
ρ12	=	Correlation between the expected returns on assets 1&2

III. Correlation: Correlation can be defined as the percentage of variability in one variable (dependent variable) that is explained by another variable (independent variable). It is calculated as:

Corr (R_i, R_j)	=	Covariance (Ri, Rj)
		σ(Ri) σ(Rj)

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