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Portfolio Management – Standard Deviation

Two concepts are important to hedge funds as they manage risk and portfolio allocation:

Standard deviation

Standard deviation is used to measure the risk of an investment. Looking at historical performance and calculating standard deviation will tell how much variation an investment has around a mean return. The bigger the standard deviation, the bigger the difference between the various individual returns and the mean return – making it more volatile and risky.
To calculate:
Calculate the average of an investment’s monthly returns for a period of time (i.e. 1 year)
Calculate the difference between each monthly return and mean
Square all those numbers and add them up
Calculate average of those squares
Take square root of that number
Example:
Monthly returns:
Jan: 2%
Feb: 5%
Mar: 1%
Apr: 0%
May: 9%
Jun: 5%
July: 4%
Aug: 3%
Sept: 9%
Oct: 8%
Nov: 2%
Dec: 2%

1. Calculate average of monthly returns: 4.2%

2. Calculate the difference between each monthly return and mean

Jan: 2% – 4.2% = -2.2
Feb: 5% – 4.2% = 1.2%
Mar: 1% – 4.2% = -3.2%
Apr: 0% – 4.2% = -4.2%
May: 9% – 4.2% = 5.2%
Jun: 5% – 4.2% = 1.2%
July: 4% – 4.2% = -0.2%
Aug: 3% – 4.2% = -1.2%
Sept: 9% – 4.2% = 5.2%
Oct: 8% – 4.2% = 4.2%
Nov: 2% – 4.2% = -2.2%
Dec: 2% – 4.2% = -2.2%

3.Square all those numbers and add them up

Jan: 2% – 4.2% = -2.22 = 4.84
Feb: 5% – 4.2% = 1.2%2 = 1.44
Mar: 1% – 4.2% = -3.2%2 = 10.24
Apr: 0% – 4.2% = -4.2%2 = 17.64
May: 9% – 4.2% = 5.2%2 = 27.04
Jun: 5% – 4.2% = 1.2%2 = 1.44
July: 4% – 4.2% = -0.2%2 = .04
Aug: 3% – 4.2% = -1.2%2 = 1.44
Sept: 9% – 4.2% = 5.2%2 = 27.04
Oct: 8% – 4.2% = 4.2%2 = 17.64
Nov: 2% – 4.2% = -2.2%2 = 4.84
Dec: 2% – 4.2% = -2.2%2 = 4.84

Sum = 118.48

4. Calculate the average of those squares

118.48 / 12 = 9.87

5. Take the square root of that number
= sqrt(9.87) = 3.14

This investment is riskier than one with a standard deviation of 2.