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Lies, Damned Lies and Statistics

Lies, Damned Lies and Statistics

Written by Tina Winter

If you are studying for CII R02, J10, J06 or AF4 exams then you need to get to grips with some statistical concepts. Our aim in this series of articles is to set out in hopefully simple fashion how the use of statistics can help us to understand the level of risk inherent in an investment and how that relates to investment return.

Measuring RiskRisk is traditionally understood to be measured by volatility – the rate at which the price of an investment moves up and down. High volatility = price moves up and down rapidly over short time periods. Low volatility = price changes very slowly over a long time period.

The most common statistical measure of risk / volatility is Standard Deviation (sigma /  σ ) – a standard statistical measure not only relevant to investments. It’s an acceptable measure of risk if the probability distribution of returns is a normal distribution – i.e. where the distribution of expected return is spread symmetrically around the mean (average) and the graph of the distribution is a bell shaped curve, and investment theory assumes that this is the case.

It’s very unlikely that you’ll be asked to calculate Standard Deviation in an exam but probable that you will come across a question where you are given the figures for the mean annual return of an investment or portfolio over a number of years, and the figure for standard deviation. The numbers that you do need to remember then are :

68 – roughly the % of returns that will fall between the mean return plus and minus one sigma

95 – roughly the % of returns that will fall between the mean return plus and minus two sigma

It’s not magic, it’s maths – believe you me, just remember those two numbers and you won’t go far wrong.

Looking at an example to show how this works:

A portfolio has a mean return of 8% and a standard deviation of 2.5%. You can expect:

–          68% of future returns to fall within the range 5.5% to 10.5%

–          95% of future returns to fall within the range 3% to 13%

–          Conversely you can expect future returns below 3% and over 13% to occur only 5% of the time

Investment theory assumes that investors are logical and risk averse, and where two investments have the same expected return but different standard deviations, the rational investor will choose the investment with the lower standard deviation hence the lower level of risk.

Standard Deviation is the key measure of risk and it’s used in the calculation of other useful numbers which help us to understand risk and return, particularly alpha and beta which we’ll look at next.  And remember those numbers!

68 – Mexico City Olympic Games took place, Hey Jude gets to No 1 in the charts

95 – Windows 95 introduced! Not a very good mnemonic but 1995 was a particularly boring year!


  1. Robert 5 years ago

    Just called the CII to get an update on when the J04/5 October 2012 papers (with examiners reports) were to come onto the revisionmate system. Last communication from EC2 on the matter was a dte of “middle of March”. A very helpful young man said that due to technical difficulties, it could be the first week in April (although it may be a bit sooner!) which is the week before the exams. So hey ho, there you go. Clearly the Qs are likely to be different although its still valid as we are in the same tax year. Just thought I would update the Brand FT posse that may be waiting on this coming through that there is likely to be a potential 2 week further wait. Good luck!


  2. Robert 5 years ago

    Well time does fly! It would appear that 2 weeks have flashed in a day as I looked on revsionmate just there and low and behold, both J04&5 are on there with the examiners reports!

    So take from that you will. Main thing is past-paper pop-pickers, the October 2012 J04/5s have been pre-released and are out there. Looks like they will be a smash!


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