Question

1. Describe the term Standard Deviation:

2. Describe the term Sharpe Ratio:

Please answer in your own words and make sure it's correct 100%

Answer 1

a) Standard deviation is a method of dispersion which indicates how much spread out a set of numbers are from the mean. So if a set of numbers for example, say a set of returns of an investment, has high standard deviation ,then it means that the volatility of returns is high meaning it is a risky investment which can give high as well as low returns. Whereas a low standard deviation indicates more stable returns around the mean.

Standard deviation is calculated as the square root of the variance. Variance is calculated as the average of the squared difference of each number from a set of numbers from the mean.

For example let us consider four returns -- 4%,6%,10% and 12%

The mean is 8%

Variance is [ (4-8)^2 + (6-8)^2 + (10-8)^2 + (12-8)^2]/4

=10

Standard deviation = sqrt(10) = 3.16

B) The Sharpe ratio measures the excess return of an investment compared to the risk free return, for every unit of total risk taken by that particular investment. The total risk is also called volatility and is measured by the standard deviation of the portfolio (represented by sigma). The basic formula for Sharpe ratio is,

Sharpe ratio =( portfolio return - Risk free return) /Standard deviation of portfolio