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Portfolio Risk

In: Business and Management

Submitted By hatuma8
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Applied Microeconomics Coursework 1


To derive and describe the effect of stock 2 and that of correlation between stock 1 and 2 prices on the overall portfolio risk.


Standard deviation (SD) is used to measure risk by determining the volatility of a stock. It is a statistical term that measures the amount of variability around an average mean price.

Correlation measures the relationship between two variables. Coefficient of Correlation can range between -1 and +1 depending on the degree and direction of the relationship. Positive correlation denotes that both stocks will follow similar movement whereas negative correlation denotes the opposite relationship.

Portfolio risk is used to measure risk when investing in more than one security, where it can be reduced but never eliminated.


1. I chose two companies from the FTSE 100: BP (Stock 1) and HSBC (Stock 2) keeping in mind the dependency between them. I made sure I used companies from different industries to minimize the unsystematic risk.

2. I obtained prices of each stock and correspondingly calculated the SD of each and the correlation between them. The prices of each stock are from 1-10-2007 to 1-10-2012.

3. I created portfolios with different weights of each stock on current day prices (1-10-2012).

4. Calculated portfolio risk for each possible combination of the two stocks.

5. Changed the SD and correlation coefficient to measure the impact of each on the portfolio risk.


Changes in Standard Deviation of Stock 2

Figure 1.

Originally, stock 2 is relatively less risky than stock 1( SD2=38.06 vs SD1=57.09 ) and hence every additional unit of stock 2 reduces the total portfolio risk.

For the purpose of analysis, I used two higher values of SD (80, 150) and two lower values (7, 20) from the original value (38.1). Firstly, I found that the lower the SD the quicker the risk fell.

As you can see from Figure 1, the opposite occurs when higher SD values are used. Every additional unit of Stock 2 would actually increase the portfolio risk result in an upward sloping curve.

Initially with an increase in proportion of stock 2 the SD of the portfolio was decreasing. However after a certain portfolio, the proportion of Stock 2 became so high that each additional unit of Stock 2 was adding to the portfolio risk, as the effect of diversification with stock 1 was wearing out.

Hence with a SD of 80 of stock 2 an ideal portfolio would be 9 units of Stock 1 and 81 units of Stock 2. This portfolio will have the lowest risk.

|QA |QB |Portfolio Risk AB |
|10 |80 |10924652.53 |
|9 |81 |10919149.82 |
|8 |82 |10919319.38 |

Table 1.

Changes in Coefficient of Correlation

Portfolio Risk = a2(sd1)2 + b2(sd2)2 + 2ab(sd1)(sd2)(r)

Where ‘a’ and ‘b’ represents the number of Stock 1 and 2 shares respectively and

‘r’ is the correlation between the two stocks.

Figure 2.

In this part of the analysis, all figures are kept constant while changing the correlation values. For the purpose of analysis, I used higher correlations (.65, 0.9) and negative correlations of (-0.1, -0.8). The results are shown in Figure 2.

A noticeable point is that with a decrease in correlation, for a fixed portfolio, the risk of the portfolio kept on decreasing. The reason for this is that the third term(2ab(sd1)(sd2)(r) would be lower with a lower level of correlation.

A negative correlation would reduce the risk of the portfolio lower than combined risk of the two stocks held individually.


The key to efficient diversification involves combining securities with negative or low correlation among them to reduce risk without sacrificing return.

A highly volatile security should be combined with a less volatile security to reduce the overall risk.

Also, from the above analysis, we can conclude that portfolio risk depends upon the proportion invested in each security, their individual risk and their correlation.


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