Page 83 - DMGT405_FINANCIAL%20MANAGEMENT

Unit 5: Risk and Return Analysis

Where Wx* is the proportion of investment in security X (since the variance in Security X is Notes
lower than Y). Investment in Y will be 1 – Wx*. In the above example, we find
-
-
58.2 ( 33) 91.2
Wx* = = = 0.578
58.2 33.6 2( 33) 157.6
+
-
-
Thus, the weight of Y will be 1 – 0.578 = 0.422
The portfolio variance (with 57.8 per cent of investment in X and 42.2 per cent in Y) is:
2
6p 2 = 33.6 (0.578) + 58.2 (0.422) + 2(0.578) (0.422) (5.80) × (7.63) (–746)
2
6p 2 = 11.23 + 10.36 – 16.11 = 5.48
Any other combination of X and Y will yield a higher variance.
(In the earlier example of 50% and 50% weights, we have seen the variance as 6.44)
Self Assessment

Fill in the blanks:
7. The return of a portfolio is equal to the ………………..of the returns of individual assets.
8. A portfolio that has the lowest level of risk is referred as the …………….portfolio.
9. The portfolio ……………is affected by the association of movement of returns of two
securities.

5.4 Portfolio Risk and Correlation
The risk of portfolio of X and Y has considerably reduced due to the negative correlation
between returns of securities X and Y. The above example shows that risk can be reduced by
investing in more than one security. However, the extent of benefits of portfolio diversification
depends on the correlation between returns of securities.
The correlation coefficient will always be between +1 and –1. Returns of securities vary perfectly
when the correlation coefficient is + 1.0 and is perfectly opposite direction when it is – 1.0. A zero
correlation coefficient implies that there is no relationship between the return of securities. In
practice, the correlation coefficients of returns of securities may vary between +1 and –1. How
the portfolio variance is affected by the Correlation Coefficient can be explained by an example.

Example: Securities M and N are equally risky but they have different expected returns:
2
Km = 0.16 6 m = 0.04 Kn = 0.24 6n = 0.20
Wm = 0.50 ám = 0.20 Wn = 0.50 6 n= 0.04
2
What is the portfolio variance if (a) Cormn = = +1.0, (b) Cormn = –1.0 (c) Cormn = +0.10 and
(d) Cormn – 0.10

Perfect Positive Correlation

When the returns of two securities M and N are perfectly positively correlated the portfolio
variance will be
2
2
6p 2 = 0.04 (0.5) + 0.04 (0.5) + 2 (0.5)(0.5) (1.0)(0.2)(0.2)
= 0.01 + 0.01 + 0.02 = 0.04
The portfolio variance is just equal to the variance of individual securities. Thus, the combination
of securities M and N is as risky as the individual securities.

LOVELY PROFESSIONAL UNIVERSITY 77