Page 84 - DMGT405_FINANCIAL%20MANAGEMENT

Financial Management

Notes Perfect Negative Correlation

If the returns of securities M and N are perfectly negative correlative the portfolio variance will be:
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
The portfolio variance is zero. The combination of securities M and N completely reduces the
risk.
Weak Positive Correlation: The portfolio variance under weak positive correlation (+0.10) is
given below:
2
6p 2 = 0.04 (0.5) + 0.04 (0.5) + 2 (0.5)(0.5) (0.1)(0.2)(0.2)
2
= 0.01 + 0.01 + 0.002 = 0.022
The portfolio variance is less than the variance of individual securities.

Weak Negative Correlation

The portfolio variance under weak negative correlation (–0.10) is given below:
6p 2 = 0.04 (0.5) + 0.04 (0.5) + 2 (0.5)(0.5) (–1.0)(0.2)(0.2)
2
2
= 0.01 + 0.01 –0.002 = 0.018
The portfolio variance has reduced more than when the returns were weak positive correlated.

5.4.1 Portfolio Risk N-Security Case
We have so far discussed the computation of risk when a two security portfolio is formed. The
calculations of risk becomes quite involved when a large number of securities are combined to
form a portfolio.

Based on the logic of the portfolio risk in a two security case, the portfolio risk (measured as
variance) in N security can be calculated as follows:
2
2
2
6p 2 = n(1/n) × average variance (+n – n) (1/n) × average covariance
= (1/n) × average variance + (1 – 1/n) × average covariance
It may be noted that the first term on the right hand side (1/n) will become insignificant when
n is very large and thus the positive variance will become approximately equal to average
covariance.

5.4.2 Systematic and Unsystematic Risk
Risk has two parts. A part of the risk arises from the uncertainties which are unique to individual
securities and which is diversifiable if large number of securities are combined to form well
diversified portfolios. The unique risk of individual securities in a portfolio cancel out each
other. This part of the risk can be totally reduced through diversification and is called
unsystematic or unique risk. The examples of unsystematic risk are:
1. The company loses a big contract in a bid.

2. The company makes a breakthrough in process innovation.
3. The R&D expert of the company leaves.
4. Workers declare strike in a company.

5. A formidable competitor enters the market.

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