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# Modern Portfolio Theory (MPT) - PowerPoint PPT Presentation

Modern Portfolio Theory (MPT). Introduction. Portfolio theory is about finding the balance between maximizing your return and minimizing your risk .  The objective is to select your investments in such as way as to diversify your risks while not reducing your expected return.

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### Modern Portfolio Theory (MPT)

• The objective is to select your investments in such as way as to diversify your risks while not reducing your expected return.

• Emphasizes statistical measures to develop a portfolio plan

• Focus is on:

• Expected returns

• Standard deviation of returns

• Correlation between returns

A

B

B

Expected Returns

Investment A is the obvious choice…

… but add risk, is the choice still obvious?

B would die out through lack of takers

• Correlations can range from -1 (perfectly negatively correlated) through to +1 (perfectly positively correlated).

• If asset B tends to move in the opposite direction to asset A then these two assets are said to have “negative correlation”, and they can be highly effective at cancelling out each other’s volatility.

• If the assets both trend upwards over the longer term a combination of them will have a return equal to the average of the two assets’ returns but with substantially reduced volatility.

Negatively correlated assets cancel the greatest amount of each other’s volatility.

• Positive Correlation

• Perfect Positive Correlation

• Zero Correlation

• Negative Correlation

• Perfect Negative Correlation

• Portfolio Expected Return

where

E[Rp] = the expected return on the portfolio,

N = the number of stocks in the portfolio,

wi = the proportion of the portfolio invested in stock i, and

E[Ri] = the expected return on stock i.

Ex - A portfolio consists of two securities 1 and 2 , in the proportions 0.6 and 0.4. The standard deviations of the returns on securities 1 and 2 are 10 and 16 respectively. The coefficient of correlation between the returns on securities 1 and 2 is 0.5. What is the standard deviation of portfolio return?

• where

• r12 = the correlation coefficient between the returns on stocks 1 and 2,

• s12 = the covariance between the returns on stocks 1 and 2,

• s1 = the standard deviation on stock 1, and

• s2 = the standard deviation on stock 2.

Ex - The standard deviations of the returns on asset 1 and 2 are 4% and 7.27% respectively. The covariance between the returns on assets 1 and 2 is 29. What is the coefficient of correlation between the returns on assets 1 and 2?

Efficient portfolios on or near the efficient frontier

Risk

Inefficient portfolios below efficient frontier

Efficient Frontier

• The “efficient frontier” is the name of the line that joins all portfolios that have achieved a maximum return for a given level of risk (portfolios that are “efficient”).

• The top of the curve and anything actually on the curve, or close to it, is an “efficient” frontier or portfolio, anything below that curve is an “inefficient” portfolio.

• The optimal portfolio is found at the point of tangency between the efficient frontier and a utility indifference curve.

• The point represents the highest level of utility the investor can reach.