A:
The ABC Global mutual fund exhibited the following rates of return over the last five years, starting with the most recent year: 15%, -7%, 6.5%, -11.3% and 32.7%. How much would the difference between the arithmetic mean and the geometric mean of this historical performance be?
a) Arithmetic mean is higher by 1.14%.
b) Both means would be the same, so the difference is zero.
c) Arithmetic mean is 1.14 times greater than geometric mean.
d) Arithmetic mean is lower by 1.14%.

The correct answer is: a)
Arithmetic Mean = (15 + -7 + 6.5 + -11.3 + 32.7)/5 = 7.18%
Geometric Mean =[(1.15 x 0.93 x 1.065 x 0.887 x 1.327)^(1/5)] - 1 = 6.04
Therefore, the arithmetic mean is higher than the geometric mean by 1.14% (7.18 - 6.04)




RELATED FAQS
  1. Can two numbers have the same arithmetic and geometric means?

    Learn about the often complicated relationship between the geometric mean and arithmetic mean for a set of numbers, and which ... Read Answer >>
  2. How do you calculate the geometric mean to assess portfolio performance?

    Learn how to calculate the geometric mean. Understand when the geometric mean should be used and how it differs from the ... Read Answer >>
  3. What is the difference between arithmetic and geometric averages?

    An arithmetic average is the sum of a series of numbers divided by the count of that series of numbers. If you were asked ... Read Answer >>
  4. What are some examples of applications of the geometric mean?

    Learn about applications of the geometric mean based on examples such as calculations of portfolio return, growth rates and ... Read Answer >>
  5. If a foreign currency dealer is quoting a bid-ask spread of $1.0500-35 ...

    The correct answer is: D) Percentage Spread = [(Ask Price - Bid Price)/Ask Price] x 100 = [(1.0535 - 1.0500)/1.0535] x 1 ... Read Answer >>
Related Articles
  1. Investing

    Explaining the Geometric Mean

    The average of a set of products, the calculation of which is commonly used to determine the performance results of an investment or portfolio.
  2. Financial Advisor

    Example of Applying Modern Portfolio Theory (MPS)

    Modern Portfolio Theory: brush up on key mathematical framework used in investment portfolio construction.
  3. Investing

    What Does Global X Purchase Mean for JP Morgan?

    Discover what JPMorgan Chase gets for its minority interest acquisition of ETF provider Global X, and learn about what it means for the company's ETF business.
  4. Trading

    Chart Summit 2017

    JC Parets discusses his top/down approach to markets, what we’re seeing in today’s environment, his approach to risk management and the arithmetic he uses for position sizing.
  5. Investing

    Calculating Annualized Total Return

    The annualized total return is the average return of an investment each year over a given time period.
  6. Managing Wealth

    Dissecting the Simple Interest Formula

    Simple interest ignores the effect of compounding: it's only calculated on the principal amount. This makes it easier to calculate than compound interest.
  7. Financial Advisor

    How to Win Gen X Clients

    Less numerous than the two generations they're sandwiched between, Gen X clients will still be a lucrative group for advisors. Here's how to snag them.
  8. Investing

    4 Cases to Buy If the Stock Market Is at an All-Time High

    Learn about why someone would invest in the stock market, even if it has reached an all-time high. This article will review four cases for doing just that.
  9. Investing

    GGGG: Pure Gold Miners ETF Performance Case Study

    Find out why the Global X Pure Gold Miners ETF barely made it off of the ground, closing before reaching its fourth full year of trading.
  10. Investing

    Calculating Future Value

    Future value is the value of an asset or cash at a specified date in the future that is equivalent in value to a specified sum today.
RELATED TERMS
  1. Arithmetic Mean

    A mathematical representation of the typical value of a series ...
  2. Mean

    The simple mathematical average of a set of two or more numbers. ...
  3. Unweighted Index

    A simple arithmetic or geometric average used to calculate stock ...
  4. Arithmetic Index

    An index of securities that uses an arithmetic sum to determine ...
  5. Time-Weighted Rate of Return

    A measure of the compound rate of growth in a portfolio. Because ...
  6. Covered Interest Arbitrage

    The practice of using favorable interest rate differentials to ...
Hot Definitions
  1. Price Elasticity Of Demand

    A measure of the relationship between a change in the quantity demanded of a particular good and a change in its price. Price ...
  2. Market Capitalization

    The total dollar market value of all of a company's outstanding shares. Market capitalization is calculated by multiplying ...
  3. Frexit

    Frexit – short for "French exit" – is a French spinoff of the term Brexit, which emerged when the United Kingdom voted to ...
  4. Stop-Limit Order

    An order placed with a broker that combines the features of stop order with those of a limit order. A stop-limit order will ...
  5. Down Round

    A round of financing where investors purchase stock from a company at a lower valuation than the valuation placed upon the ...
  6. Keynesian Economics

    An economic theory of total spending in the economy and its effects on output and inflation. Keynesian economics was developed ...
Trading Center