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Investments and Returns Quiz
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Investments and Returns Quiz

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Questions and Answers

What is the formula for calculating variance from the time series of returns?

  • $Var(rt) = \frac{1}{n-1} \sum (rt - rt)^2$ (correct)
  • $Var(rt) = \frac{1}{n} \sum (rt - \bar{r})^2$
  • $Var(rt) = \sum (rt - \bar{r})^2$
  • $Var(rt) = \frac{1}{n} \sum (rt - rt)^2$

    • How is standard deviation related to variance?

  • Standard deviation is the square of variance.
  • Standard deviation is calculated only for investment returns.
  • Standard deviation and variance are unrelated metrics.
  • Standard deviation is the square root of variance. (correct)

    • Which index represents U.S. large stocks?

  • Standard & Poor's 500 (correct)
  • Russell 2000
  • NASDAQ Composite
  • Dow Jones Industrial Average

    • What does the term 'U.S. small stocks' refer to?

    <p>The smallest 20% of stocks on the NYSE, Nasdaq, and Amex.</p> Signup and view all the answers

    Which countries are included in the 'World Large stocks' portfolio?

    <p>24 developed countries.</p> Signup and view all the answers

    What is the Barclay's Long-Term Treasury Bond Index used to represent?

    <p>U.S. Treasury bonds performance.</p> Signup and view all the answers

    What years does the frequency distribution of annual returns for United States Treasury Bills cover?

    <p>1927-2022</p> Signup and view all the answers

    Which of the following does NOT describe the World bonds portfolio?

    <p>Comprises only government-issued debts.</p> Signup and view all the answers

    What does the Holding-Period Return (HPR) formula consist of?

    <p>Ending price minus beginning price plus dividends divided by beginning price</p> Signup and view all the answers

    Given an HPR of 13%, what is the cumulative performance of the investment?

    <p>The investment returns 13% in total over the period.</p> Signup and view all the answers

    Which average is used to give the same cumulative performance as a sequence of actual returns?

    <p>Geometric average</p> Signup and view all the answers

    How is the arithmetic average of returns calculated?

    <p>Sum of returns in each period divided by number of periods</p> Signup and view all the answers

    What part of the HPR contributes to total investment return?

    <p>Both dividend yield and capital gains yield</p> Signup and view all the answers

    Which return measurement is defined as the internal rate of return on investment?

    <p>Dollar/SAR-weighted average return</p> Signup and view all the answers

    If a stock was bought for $25, sold for $27, and paid $1.25 in dividends, what is the formula applied to find the HPR?

    <p>$27.00 - $25.00 + $1.25 / $27.00</p> Signup and view all the answers

    In a financial context, what does cash flow refer to?

    <p>The net cash going in and out of a business or investment</p> Signup and view all the answers

    What is the primary purpose of calculating the geometric average of returns?

    <p>To determine a single period return that matches cumulative performance.</p> Signup and view all the answers

    Which return calculation ignores compounding effects?

    <p>Annual percentage rate.</p> Signup and view all the answers

    How is the arithmetic average of returns calculated?

    <p>By summing the returns and dividing by the number of years.</p> Signup and view all the answers

    What formula represents the geometric average return?

    <p>$[(1 + r_1) imes (1 + r_2) imes ... imes (1 + r_n)]^{ rac{1}{n}} - 1$</p> Signup and view all the answers

    What is the effective annual rate (EAR) used for?

    <p>To show how an investment grows without ignoring compounding.</p> Signup and view all the answers

    In the formula for arithmetic average, if the returns are 10%, 25%, -20%, and 20%, what is the average return?

    <p>8.75%</p> Signup and view all the answers

    Which of the following best describes the dollar-weighted average return?

    <p>The internal rate of return on an investment.</p> Signup and view all the answers

    What does the formula for calculating EAR specifically take into consideration?

    <p>The compounding effects of interest.</p> Signup and view all the answers

    What is meant by asset allocation in investment portfolios?

    <p>Portfolio choice among various broad investment classes</p> Signup and view all the answers

    Which component is part of the complete portfolio?

    <p>Both risky and risk-free assets</p> Signup and view all the answers

    What does 'capital allocation' specifically refer to?

    <p>Deciding how to distribute investments between risky and risk-free assets</p> Signup and view all the answers

    Which of the following is considered a risk-free asset?

    <p>Treasury bonds</p> Signup and view all the answers

    In the equation for the expected return of the complete portfolio, what does 'y' represent?

    <p>Percentage of assets in the risky portfolio</p> Signup and view all the answers

    What is the formula for calculating the standard deviation of the complete portfolio?

    <p>σC = y × σp</p> Signup and view all the answers

    Which of the following statements is true regarding money market instruments?

    <p>They are considered effectively risk-free compared to other assets.</p> Signup and view all the answers

    What primarily influences the risk associated with Treasury bonds?

    <p>Inflation rates</p> Signup and view all the answers

    What is the primary feature of the Capital Allocation Line (CAL)?

    <p>It illustrates the risk-return combinations from risky and risk-free assets.</p> Signup and view all the answers

    What characterizes a Passive Strategy in investing?

    <p>It avoids security analysis entirely.</p> Signup and view all the answers

    Which of the following best describes the Capital Market Line (CML)?

    <p>It uses market-index portfolios as the risky asset.</p> Signup and view all the answers

    What is one major advantage of passive investing?

    <p>It is inexpensive and straightforward.</p> Signup and view all the answers

    What is the average expense ratio of active management mutual funds?

    <p>1%</p> Signup and view all the answers

    How does active management differ from passive management?

    <p>Active management aims for higher returns through strategy.</p> Signup and view all the answers

    What does the risk premium to variance ratio express?

    <p>The excess return per increase in risk.</p> Signup and view all the answers

    What is an associated cost of hedge fund investments?

    <p>They have performance fees based on returns.</p> Signup and view all the answers

    Study Notes

    Historical Record - Time Series of Returns

    • Variance of returns over time is calculated by summing the squared differences between each individual return and the average return, then dividing by the number of returns minus one.
    • Standard deviation of returns is the square root of the variance.

    Historical Record - World Portfolios

    • World Large stocks portfolio includes companies from 24 developed countries with ~6000 stocks.
    • U.S. Large stocks portfolio includes the 500 largest companies listed according to market capitalization.
    • U.S. Small stocks portfolio includes the smallest 20% of companies listed on the NYSE, Nasdaq, and Amex.
    • World bonds portfolio includes bonds from the same 24 developed countries as the World Large stocks portfolio.
    • U.S. Treasury bonds portfolio tracks the Barclays Long-Term Treasury Bond Index.

    Measuring Rates of Return

    • Holding-Period Return (HPR) is the rate of return over a specific investment period.
    • HPR is calculated by dividing the difference between the ending price and the beginning price plus any cash dividends by the beginning price.
    • Arithmetic average return is calculated by summing all returns over multiple periods and dividing by the number of periods.
    • Geometric average return represents a single average rate of return that produces the same cumulative performance as the sequence of actual returns over multiple periods.
    • Dollar-weighted average return is the internal rate of return on an investment.

    Annualizing Rates of Return

    • Annual Percentage Rate (APR) is a per-period rate multiplied by the number of periods per year, neglecting compounding.
    • Effective Annual Rate (EAR) is the actual rate at which an investment grows, accounting for compounding.

    Asset Allocation across Portfolios

    • Asset allocation involves choosing broad investment classes for a portfolio (e.g., stocks, bonds, Treasury bills).
    • A complete portfolio encompasses all assets, including risky and risk-free investments.
    • Capital allocation determines the proportion of investment allocated between risky and risk-free assets.

    Risk-Free Asset

    • Treasury bonds are considered effectively risk-free in the context of capital allocation.
    • Money market instruments are also considered essentially risk-free.
    • CDs and commercial paper are considered to have minimal risk compared to most investments.

    Portfolio Asset Allocation

    • Expected return of the complete portfolio is calculated by weighting the expected return of the risky portfolio by the percentage of assets allocated to the risky portfolio and adding the product of the risk-free rate and the percentage of assets allocated to the risk-free asset.
    • Standard deviation of the complete portfolio is calculated by multiplying the standard deviation of the risky portfolio by the percentage of assets allocated to the risky portfolio.

    Capital Allocation Line (CAL)

    • The CAL represents the range of risk-return combinations achievable by varying the allocation between risky and risk-free assets.
    • The slope of the CAL is determined by the risk premium per unit of risk (variance) offered by the risky portfolio.

    Risk Aversion and Capital Allocation

    • Risk aversion plays a role in determining the optimal allocation of assets.
    • Investors with higher risk aversion prefer a lower risk premium per unit of variance, leading to a lower allocation to the risky portfolio.

    Passive Strategies and the Capital Market Line (CML)

    • A passive strategy avoids actively analyzing securities and relies on predetermined investment rules.
    • The CML is a special case of the CAL, using the market index portfolio as the risky asset.

    Costs and Benefits of Passive Investing

    • Passive investing is typically less expensive than active investment strategies.
    • Active management aims to outperform the market by identifying undervalued securities, potentially leading to higher returns but also incurring higher fees.
    • The expense ratio of active mutual funds often averages around 1%.
    • Hedge funds typically charge higher fees, ranging from 1%-2% plus a 10% cut of returns exceeding the risk-free rate.

    Frequency Distribution of Annual Returns

    • Past returns can be used to inform future return expectations, but past outcomes don't perfectly predict future results.
    • The frequency distribution of annual returns for various asset classes (e.g., U.S. Treasury bills and bonds, common stocks) demonstrates the variability of returns over time.

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    Description

    Test your knowledge on the fundamentals of investment returns, including variance and standard deviation of returns. Explore the different world portfolios and understand measuring rates of return, with a focus on various stock and bond categories.

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