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Portfolio Theory

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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 for each state of the economy
Standard Deviation = σ = √ [∑(ri – E(R))2 .pi]

Thus calculated, we have the following results:

|Security |Expected Return |Expected Risk |
| | |(measured by σ) |
|Ace |5% |±9.49% |
|Bravo |5% |±12.65% |

Ace is better than Bravo when viewed in the risk-return framework, because it offers the same level of return as Bravo, while exposing its investor to a lower level of risk. However, is it possible to combine Ace and Bravo into a portfolio to achieve a combination that is better than its constituent securities?

Let us now understand how these two assets can be combined into a portfolio such that the expected return from the portfolio is higher than that of its component

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