# Portfolio Theory

3048 Words Mar 19th, 2013 13 Pages
PORTFOLIO THEORY

Let us begin our discussion on Portfolio Theory with an example of two investments (assets or securities) – Ace and Bravo. Their return expectations are given in the table below. You will notice that both Ace and Bravo are risky investments because they do not offer a certain return. You can begin by comparing the expected return and risk of Ace and Bravo:

State of Probability Return
Economy of occurrence Ace Bravo

Boom 0.2 +20 -15
Growth 0.6 +5 +5
Recession 0.2 -10 +25

1. What kind of a correlation do you observe between the two securities? 2. Calculate the expected return and standard deviation of both Ace and Bravo. Interpret the results.

Expected Return = E(R) = ∑ ri.pi
Portfolio expected returns are a weighted average of the expected returns of the constituent investments. If the two investments are A and B, with a being invested in A and (1-a) in B, then

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Portfolio standard deviation is less than the weighted average of the standard deviation of the constituent investments (expect for perfectly +vely correlated investments where it is the weighted average). The risk of a portfolio is measured by its standard deviation and calculated as:

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Covariance means the extent to which the returns on two investments move together. It is related to correlation coefficient, but can take on any –ve or +ve value.

Let us learn the above concepts with the help of a solved example:

Let there be two shares A and B, with the following returns for alternative economic states:

|State of Economy |Probability |Returns on A |Returns on B |
|Boom |0.3 |20% |3% |
|Growth |0.4 |10% |35% |
|Recessions |0.3 |0% |-5%