Page 79 - DMGT405_FINANCIAL%20MANAGEMENT

Unit 5: Risk and Return Analysis

that investors hold well diversified portfolio instead of investing in a single asset or security. A Notes
portfolio as the name signifies, is a bundle or a combination of individual assets or securities.
Hence individuals concern should be on the expected return and risk of the portfolio rather than
on individual assets or securities. The second assumption of the portfolio theory is that the
returns of securities are normally distributed. This means that the expected value (mean) and
variance (or standard deviation) analysis is the foundation of the portfolio decisions.

5.3.1 Portfolio Return and Standard Deviation
The return of a portfolio is equal to the weightage average of the returns of individual assets or
securities in the portfolio with weights being equal to the proportion of investment in each
asset.

Example: Suppose you have the opportunity of investing your wealth either in asset X
or asset Y. The possible outcomes of the two assets indifferent states of economy are given
below:

The expected rate of return of an individual asset:

K =  (already seen earlier)

The expected rate of return of X is
k = (–8 × 0.1) + (10 × .2) + (8 × 0.4) + (5 × 0.2) + (– 4 × 0.1) = 5%
x
and of Y =

k y = (14 × 0.1) + (– 4 × 0.2) + (6 × 0.4) + (15 × 0.2) + (20 × 0.1) =
8%
Suppose you decide to invest 50% on X and 50% in Y.
Since we know the expected rate of return of X (5 per cent) and Y (8%) and their weights (50%
each) we can calculate the expected rate of return on the portfolio as the weighted average of the
expected rates of return of X and Y.
i.e. 0.5 × 5 + 0.5 × 8 = 6.5%
Thus, we can conclude the return on a portfolio is a weightage average of the returns on the
individual assets from which it is formed. The portfolio return
n
K = W × k + W k + …….. W k =  W 1  k i
p 1 1 2 2 n n
 i 1
Where W = proportion of the portfolio rupee value represented by asset;
i
k = return on asset
i

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