**Introduction**

In the first part of this series of blog entries we looked at the definitions of risk and return and how they interconnect in the investment arena. In this blog entry, we expand on this by extending our analysis to include an introduction to basic portfolio theory. There is some maths involved but we have tried to keep it as simple as possible.

**Revisiting the definition of risk**

The definition of risk that is commonly found in finance textbooks is based on statistical analysis designed to measure the variability of the actual return from the expected return. The statistical measure of variability most commonly found in textbooks is the variance from expected return and the standard deviation (the square root of the variance).

We will explain this by looking at two possible investments.

**Worked example – risk and return with a slice of statistical analysis**

Errol is considering an investment in either Aston Limited or Zetec Limited.

An investment in Aston Limited has the following range of expected returns and associated probabilities of those returns occurring:

Probability |
Return (%) |

0.1 | 30 |

0.8 | 20 |

0.1 | 10 |

An investment in Zetec Limited has the following range of expected returns and associated probabilities of those returns occurring:

Probability |
Return (%) |

0.1 | 33 |

0.7 | 21 |

0.2 | 10 |

Errol wants to know what the expected return on each of the investments is and which of the investments exposes him to the greatest amount of risk.

**Solution Step One – Work out the Expected Return**

The first step is to work out the expected returns for the Aston Limited and Zetec Limited investments. The expected returns of each of the investments is calculated by multiplying the probability of each of the possible returns by the return expected and summing the results.

For Aston Limited the expected return is:

(0.1 x 30%) + (0.8 x 20%) + (0.1 x 10%) = 20%

For Zetec Limited the expected return is:

- x 33%) + (0.7 x 21%) + (0.2 x 10%) = 20%

We can see that despite having a different range of expected outcomes and probabilities the return on Aston Limited and Zetec Limited are equal. If we considered expected return only Errol would be indifferent between making an investment in Aston Limited or Zetec Limited.

**Solution Step Two – Work out the Variance of Returns**

Risk is measured by the variance of the expected returns of both Aston Limited and Zetec Limited.

The variance of return is calculated as the weighted sum of the squared deviations from the expected return. These are added and the square root of the sum gives us a measure of how risky each of the investment is.

*The variance of the returns in Aston Limited can be calculated as follows:*

- x (30 – 20)
^{2}) + (0.8 x (20 – 20)^{2}) + (01 x (10 – 20)^{2}) = 20

*To find the risk of Aston Limited we simply take the square root of its variance of returns.*

= 4.47%

*The variance of the returns in Zetec Limited can be calculated as follows:*

- x (33 – 20)
^{2}) + (0.7 x (21 – 20)^{2}) + (0.2 x (10 – 20)^{2}) = 37.6

*To find the risk of Zetec Limited we simply take the square root of its variance of returns.*

= 6.13%

**The results in summary**

In summary form the results of our analysis of Aston Limited and Zetec Limited is as follows:

Potential Investment |
Expected Return |
Standard Deviation (Risk) |

Aston Limited | 20% | 4.47% |

Zetec Limited | 20% | 6.13% |

Given that the expected return is the same for both Aston Limited and Zetec Limited, Errol should opt for an investment in Aston Limited because it has the lowest risk and the same level of return as Zetec Limited.

**Taking this a step further**

In real-life we are seldom faced with a decision to invest in one of two different stocks as is the case with Errol. Usually we are considering a multitude of investments in the context of adding those investments to a portfolio of assets that we already own.

When we start to look at portfolios with more than one investment the maths gets more complicated because we should consider how each of the individual investment relates to the existing investments we already own. When exposed to the same external factors some investments in our portfolio go up while others will go down. This is the realm of advanced portfolio theory.

When we add portfolio theory into the mix we should consider how the individual returns of the investments in our portfolio co-relate or co-vary. If two or more investments move in the same direction (for example they both go up) when exposed to the same factors they are said to be positively correlated, while if they move in different directions they are negatively correlated.

It follows from this that it is possible to add a new investment into an existing portfolio and reduce the overall risk of the overall portfolio of investments. Portfolio theory is a subject we will return to in a future blog entry.

If you feel comfortable managing your portfolio we congratulate you. If you feel you need help please contact us. We have a whole team dedicated to the area of wealth management. This team can look at your portfolio, assess the risk you are exposed to, and make recommendations with a view to maximising you return and reducing your risk.

**Closing thoughts – a time to chill and a time to invest?**

Firstline Securities Limited offers comprehensive coverage of local and international markets with a bias for the energy sector. Firstline offers many unique opportunities to put surplus cash to work either as your asset manager or investment advisor. Please contact us for more details at **info@firstlinesecurities.com** or at **868.628.1175**, we can discuss your investment needs in detail and craft a portfolio that makes sense for you. We look forward to hearing from you.