Statistics: Arithmetic and Geometric Mean

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Questions and Answers

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?

<p>Because it takes into account the compounding effect (D)</p> Signup and view all the answers

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

<p>The geometric mean takes into account the compounding effect (D)</p> Signup and view all the answers

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

<p>3.2% (A)</p> Signup and view all the answers

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

<p>Reduced volatility of the portfolio without impacting expected return (D)</p> Signup and view all the answers

How is the mean return of a portfolio calculated?

<p>It is the sum of the individual asset returns, weighted based on beginning-of-period value (A)</p> Signup and view all the answers

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

<p>The time between the inflow or outflow of any cash (D)</p> Signup and view all the answers

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

<p>3.2% (A)</p> Signup and view all the answers

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

<p>Arithmetic mean is used for long-term returns, while geometric mean is used for short-term returns (A)</p> Signup and view all the answers

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

<p>$800 (C)</p> Signup and view all the answers

What is the change in capital value of asset DEF?

<p>$75 (D)</p> Signup and view all the answers

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

<p>$2,580 (A)</p> Signup and view all the answers

What is the geometric mean return for the given period?

<p>-4.98% (B)</p> Signup and view all the answers

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

<p>Geometric mean accounts for compounding over multiple periods (B)</p> Signup and view all the answers

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

<p>$2188.88 (A)</p> Signup and view all the answers

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

<p>Higher correlation leads to higher volatility (A)</p> Signup and view all the answers

Which value was calculated using Excel without rounding errors?

<p>$2188.88 for arithmetic mean (D)</p> Signup and view all the answers

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

<p>It affects the portfolio's volatility (C)</p> Signup and view all the answers

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

<p>$2500 (1 + (-4.33%))^3$ (B)</p> Signup and view all the answers

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

<p>Geometric mean return (D)</p> Signup and view all the answers

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