How would you read these two formulas? The 1/4 and 1/6 are throwing me off. These are example problems from what I need to do.
Variance=1/4[(0.03 – 0.1)2 + (–0.14 – 0.1)2 + (0.27 – 0.1)2 + (0.22 – 0.1)2 + (0.12 – 0.1)2]
Geometric average return =[(1 + (0.17))(1 + (0.19))(1 + (0.18))(1 + (-0.09))(1 + (0.18))(1 + (0.11))](1/6) – 1
To read these two formulas, it's important to understand the mathematical operations being used:
1. Variance:
The formula for variance is used to measure how spread out a set of numbers is. In this case, we have the following formula:
Variance = 1/4[(0.03 – 0.1)2 + (–0.14 – 0.1)2 + (0.27 – 0.1)2 + (0.22 – 0.1)2 + (0.12 – 0.1)2]
Let's break it down step by step:
- The term 1/4 indicates that the sum of squared differences will be divided by 4. This is because the average of squared differences gives us the variance.
- The squared difference is calculated for each number in the set: (actual value - expected value)^2. In this case, the expected value is 0.1.
- Each calculated squared difference is summed up, giving the total variance.
2. Geometric Average Return:
The formula for geometric average return is used to calculate the average growth rate over a series of periods. In this case, we have the following formula:
Geometric average return = [(1 + (0.17))(1 + (0.19))(1 + (0.18))(1 + (-0.09))(1 + (0.18))(1 + (0.11))](1/6) – 1
Let's break it down step by step:
- The terms (1 + x) represent the growth rate for each period, where x is the return for that period. For example, (1 + 0.17) represents a growth rate of 1.17.
- Each growth rate is multiplied together for all the periods being considered.
- The resulting product is then raised to the power of 1/6. This is because there are 6 periods in the example.
- Finally, subtracting 1 gives the average growth rate over the 6 periods.