Standard deviation steps in where average failed. It gives you an idea about the rating of the quality for the average. It can be defined as the difference between the numbers used in calculating the average and the actual average. It is an indication of how accurately the average represents its parent numbers.
Imagine you have invested in a fund that has given a return of 12%, -5% and 48% over the period of 3 years. The question is how to decide the average performance over the period of 3 years. Here we can take an average of these 3 numbers and consider it as the average performance of the fund. However this is not accurate.
Defects in using average
Though important, average does not give us the complete picture of the situation. It is highly subjective. E.g. saying the average temperature in India is 38 degrees is quite inaccurate. It can range from below 20 degree Celcius to as high as 40+ degree Celcius. Due to this inaccuracy, average does not give us the accurate picture, but standard deviation does.
Welcome to standard deviation
Standard deviation steps in where average failed. It gives you an idea about the rating of the quality for the average. It can be defined as the difference between the numbers used in calculating the average and the actual average. It is an indication of how accurately the average represents its parent numbers. So in the above example, the standard deviation can be defined as difference between the average of the fund’s performance for the 3 years and the actual performance. It denotes the amount of risk involved in investing in the fund.
Calculation of standard deviation of fund
To find out how safe or risky the fund is, you need to calculate its standard deviation. This can be done as follows:
– Computing the performance of the fund for each month over a long period of time.
– Compute the average of the performances of the fund for this period.
– If there is a significant difference between each monthly performance and the average performance of the fund, you can say the fund is very risky. If there is not significant difference between both these figures, you can say the fund is safe.
If the monthly performance of the fund is more or less same as its average performance over a period of time, it is a low risk fund. But if the difference is quite high, then the fund is said to be very risky. Once you get the differences between the fund’s monthly performance and its average, take the average of these differences. The figure that you get is called as standard deviation.
Limitations of standard deviation
Don’t consider standard deviation as the ultimate indicator of fund’s volatility. Though high standard deviation does indicate high degree of volatility, it doesn’t mean it is worse than the fund having a low standard deviation. If the fund with high standard deviation is a better performer than the one with low standard deviation, the deviation is quite immaterial, as you as an investor should focus on the performance. If you understand this very clearly, standard deviation should not bother you if you can withstand the volatility of the fund.
Note of caution
Standard deviation is an important statistical measure that gives you an idea of the variation in the fund’s performance from its average performance. High deviation means the fund is highly volatile and low deviation means the fund is low risk. But don’t make the mistake of thinking that volatile funds are poorer than safer funds. If the fund has consistently managed to give strong performance, standard deviation does not matter.