Statistics: Arithmetic and Geometric Mean

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What is the formula for calculating the arithmetic mean?

$\frac{x_1 + x_2 + ... + x_n}{n}$ (correct)

$\frac{x_1 × x_2 × ... × x_n}{n}$

$\sqrt[n]{x_1 × x_2 × ... × x_n}$

$\frac{x_1 - x_2 + ... + x_n}{n}$

When should the geometric mean be used?

When the observations are not independent (correct)

When the observations are independent

When the observations are normally distributed

When the observations are positively correlated

What happens to the capital invested in the second period if the portfolio declines by 50% in the first period?

It becomes zero

It decreases significantly (correct)

It remains the same

It increases significantly

Why does the geometric mean take account of the effect of a 50% decline in portfolio value?

Because it takes into account the compounding effect Signup and view all the answers

What is the main difference between the arithmetic and geometric means of periodic returns?

The geometric mean takes into account the compounding effect Signup and view all the answers

What was the mean return of the portfolio in the example?

3.2% Signup and view all the answers

What is the primary benefit of combining assets with low or negative correlation in a portfolio?

Reduced volatility of the portfolio without impacting expected return Signup and view all the answers

How is the mean return of a portfolio calculated?

It is the sum of the individual asset returns, weighted based on beginning-of-period value Signup and view all the answers

What is the definition of a period in the context of portfolio return calculation?

The time between the inflow or outflow of any cash Signup and view all the answers

What is the return of the portfolio in the given example?

3.2% Signup and view all the answers

What is the difference between arithmetic mean and geometric mean in the context of asset returns?

Arithmetic mean is used for long-term returns, while geometric mean is used for short-term returns Signup and view all the answers

What is the beginning-of-period value of asset ABC?

$800 Signup and view all the answers

What is the change in capital value of asset DEF?

$75 Signup and view all the answers

What is the end-of-period value of the portfolio?

$2,580 Signup and view all the answers

What is the geometric mean return for the given period?

-4.98% Signup and view all the answers

What is the main difference between using arithmetic mean and geometric mean for return calculation?

Geometric mean accounts for compounding over multiple periods Signup and view all the answers

What is the future value when the arithmetic mean return is used?

$2188.88 Signup and view all the answers

How is the volatility of a two-asset portfolio impacted by the correlation between the assets?

Higher correlation leads to higher volatility Signup and view all the answers

Which value was calculated using Excel without rounding errors?

$2188.88 for arithmetic mean Signup and view all the answers

What impact does the correlation between two assets have in a two-asset portfolio?

It affects the portfolio's volatility Signup and view all the answers

Which formula represents the future value using the arithmetic mean return?

$2500 (1 + (-4.33%))^3$ Signup and view all the answers

Which rate of return calculates the most accurate ending value of the portfolio?

Geometric mean return Signup and view all the answers