Understanding Portfolio Mathematics

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Concept of Expected Return of Portfolio

• Assume that you form a portfolio consisting two securities A and B.

• E(RA) and E(RB) are the expected return on the security A and B.

• There are two steps in computation of Expected Return of Portfolio

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Example• You have a portfolio consisting two securities. Reliance

Industries and Wipro Ltd. Assume that your investment in Reliance is Rs 12000 and in Wipro is Rs 18000. You estimate the expected return on these two stocks to be 10% and 15% respectively. Find the Expected Return of the portfolio Portfolio Value : Rs 30,000

W(Reliance) = 40%W(Wipro) = 60%Expected Return on Portfolio =

.40 (10%) + 0.60 (15%) = 13%

Note : The portfolio weights are usually calculated on the basis of market value of securities at the time the expected return of the portfolio is computed.

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Expected Return on portfolio consisting three securities

• Example• Lets imagine a portfolio consisting three securities. Tech

Mahindra, NHPC and Kotak Bank. The total Investment is Rs 25000, Rs 30000 and Rs 45000 respectively. The expected return on each securities are 12.5%, 15% and 18% respectively. Find the Expected return on the portfolio.

Ans : 15.725%

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Concept of Coefficient of Correlation

• Its a statistical concept that captures the extent of co-movement between pair of variables.

• The relation between pair of variable can be– Positive : Two variable move together in same

direction.– Negative : Two variable move in opp direction– None : No patternIts value always lies between - 1 and + 1

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Positive Correlation

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Perfect Positive Correlation

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Negative Correlation

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Perfect Negative Correlation

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ZERO Correlation

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Why Correlation?• Modern finance is based on the concept of diversification.• When two investments move in the same direction, there is no

reduction in risk.• If two investments have a negative correlation, downward

movement of one can be offset by upward movement in another, thus creating a lower risk portfolio.

• Coefficient of Correlation is foundation of portfolio diversification.

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Concept of Covariance Its related with Correlation..

• Historical Data

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Its positive Correlation…. LEARNINGMade Simple

Lets calculate Covariance

Step ONEFind MEAN of Stock PriceFind MEAN of Earning

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Lets calculate Covariance

Step TWOFind the Difference betweenObservation and Mean for Stock PriceAndEarning

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Lets calculate Covariance

Step 3 : Multiply 2a and 2bStep 4 : Add them

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Lets calculate Covariance

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Correlation

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Example Probability Distribution

Ans.Covariance : 1.02700Correlation : 0.30SD (stock price) = 2.40260, SD (Earning) : 0.10735

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