Module 2: Balancing Risk and Return

Define Financial Risk (Retirement Plan Investing Essentials, pp. 50-51)

Financial risk is the uncertainty of returns caused by the use of debt. The larger the proportion of a company's assets that is financed by debt (as opposed to equity), the larger the variability in the returns, other things being equal.

Define Liquidity Risk (Retirement Plan Investing Essentials, pp. 50-51)

Liquidity risk is the uncertainty of being able to sell an investment quickly and without significant price concession.

Define liquidity Risk (Retirement Plan Investing Essentials, pp. 50-51)

Liquidity risk is the uncertainty of being able to sell an investment quickly and without significant price concession.

1.3 What is the relationship between total return and return relative? (Retirement Plan Investing Essentials, p. 42—Example 2-4)

Return relative adds 1.0 to the total return in order that all returns can be stated on the basis of 1.0 (which represents no gain or loss), thereby avoiding negative numbers so that the cumulative wealth index or the geometric mean can be calculated.

4.1 Why is an average return for a financial asset useful but insufficient in and of itself when evaluating prospective investment opportunities? (Retirement Plan Investing Essentials, p. 51)

This is the case because the average return, however measured, though an extremely important piece of information for the investor, only tells the center of the return distribution. In essence, the average return does not tell an investor anything about the spread of the distribution.

1.5 Distinguish between the concepts of total return, return relative and the cumulative wealth index. (Retirement Plan Investing Essentials, pp. 41-42)

While total return and return relative measure changes in the level of wealth, the cumulative wealth index measures the aggregate effect of returns over time given some stated beginning amount. Measures how ones wealth changes over time or, in other words, we measure teh cumulative effect of returns compounding over time given some stated initial investment, which is frequently shown as $1. CWI of n= begg value or $1(1+R1) (1+R2a)....

4.6 What information is conveyed by the standard deviation with a normal distribution? (Retirement Plan Investing Essentials, p. 53)

With a normal distribution, once we know the standard deviation, the probability that a particular outcome will be above (or below) a specified value can be determined. Specifically, with a normal distribution, 68.3% of values fall within one standard deviation (1 or 2) of the mean, and 95% (99%) fall within two (three) standard deviations of the mean.

1.4 A stock was purchased for $30 per share. A dividend of $2 per share was received by the investor. What is the return relative if the stock is sold for (a) $34 or (b) $25? (Retirement Plan Investing Essentials, p. 42—Example 2-4)

(a) $2 + $4 = $6, and $6 divided by $30 is 20%. Therefore, the return relative is 1.20. (b) $2 + (-$5) = -3, and -3 divided by $30 is -10%. Therefore, the return relative is 0.90.

2.3 An investment was worth $100 at the end of 2010. At the end of 2011, it was worth $180. At the end of 2012, it was worth $100. During the entire period, no dividends or other income were received from the investment. What is this investment's (a) arithmetic mean rate of return and (b) geometric mean rate of return? (Retirement Plan Investing Essentials, pp. 45-46)

(a) The arithmetic mean rate of return would be calculated as follows: First year: $100 increasing to $180 is an 80% increase. Second year: $180 decreasing to $100 is a decrease of 44.44% (i.e., 180 - 100 = 80, and 80 divided by 180 is 44.44%). The arithmetic average of 180% and -44% is 18%. (.8-.44 = .36 / 2 = .18) The arithmetic mean is the sum of all the returns for each period divided by the number of periods. (b) The geometric mean rate of return is the return that will make the beginning value equal the ending value. It measures the compound rate of growth over time. In this case, the geometric mean return is 0% because it takes no return for $100 to become $100.

5.1 How did various major financial asset classes compare in terms of their respective returns and standard deviations over significant periods of time? (Retirement Plan Investing Essentials, pp. 55-56—Table 2-6)

1) Large common stocks, as measured by the well-known Standard & Poor's (S&P) 500, had a geometric mean annual return over an 85-year period of 9.6% (rounded). Hence, $1 invested in this market index at the beginning of 1926 would have grown at an average annual compound rate of 9.6% over this very long period of time. In contrast, the arithmetic mean annual return for large stocks was 11.5%. The best estimate of the "average" return for stocks in any one year, using this information, is 11.5%. The standard deviation for large stocks during this time period was 19.9%. 2) Smaller common stocks have greater returns and greater risk relative to large common stocks. Smaller here means the smallest stocks on the New York Stock Exchange (NYSE) and not the really small stocks traded in the over-the-counter market. The arithmetic mean for this series is much higher than for the S&P 500, typically 5 or 6 percentage points higher. However, smaller common stocks have much larger standard deviations and, therefore, the difference between their geometric and arithmetic means is greater. 3) Corporate and Treasury bonds have geometric means that are roughly 50% to 60% of the S&P 500, at 5.9% and 5.4%, respectively, but the risk is considerably smaller. Standard deviations for the bond series are less than half as large as that for the S&P 500. 4) Finally, as expected, T-bills have the smallest returns of any of the major assets, shown at 3.6%, as well as by far the smallest standard deviation

2.5 The total return for an investment over a period of time was 24.65%. During the same time, the inflation rate was 4.33%. What was the inflation-adjusted return? (Retirement Plan Investing Essentials, p. 49—Example 2-11)

1.2465/1.0433 = 1.1948, and 1.1948 minus 1 = .1948 or 19.48%.

1.6 Use the following figures to calculate the cumulative wealth index for the period 2014-2018 for $1 invested at the end of 2013. (Retirement Plan Investing Essentials, pp. 41-42) Year Total Return (%) 2014 10 2015 8 2016 5 2017 -12 2018 20 1.7 What is the rate of return over the entire period (2014-2018) in the previous question? (Retirement Plan Investing Essentials, pp. 41-42)

1.6==>The calculation would be as follows: 1.00 (1.10) (1.08) (1.05) (.88) (1.20) = 1.317. 1.7==> The rate of return is the cumulative wealth index minus 1, or 1.317 - 1.0 = .317 or 31.7%. (There might be some rounding differences between Table 2-1 on page 40 of the text and the Total Return figures used in the various examples of Chapter 2.)

2.1 A U.S. investor bought some Canadian stock for C$250 when the value of the Canadian dollar stated in U.S. dollars was $0.80. One year later, the stock is selling for C$300, and Canadian dollars are now at $0.70. No dividends were received. What was the return relative? 2.2 What was the total return to the U.S. investor after the appropriate currency adjustment? (Retirement Plan Investing Essentials, pp. 42-44— Example 2-6)

2.1==> The increase from 250 to 300 is 50, and 50 divided by 250 is an increase of 20%. In other words, the stock went up 20%, and the return relative is 1.20. 2.2==> [1.2 x (.7/.8)] - 1.0 = .05 or 5%

5.4 How can a cumulative wealth index be calculated using geometric mean data for asset classes across time periods? (Retirement Plan Investing Essentials, p. 57)

A cumulative wealth index can be calculated for financial asset return series. To calculate cumulative wealth for each of the series considered, merely raise (1 1 the geometric mean) to the power represented by the number of time periods. When a cumulative wealth index is calculated using asset classes, common stocks far outpace corporate bonds, U.S. Treasury bonds and U.S. T-bills. However, the variability of the common stock series is considerably larger than that for bonds or T-bills.

5.3 How does a logarithmic scale facilitate comparisons of different series of returns across time? (Retirement Plan Investing Essentials, p. 56, Footnote 14)

A logarithmic scale greatly facilitates comparisons of different return series across time because the same vertical distance represents the same percentage change in a particular series return. The logarithmic scale allows the user to concentrate on rates of return and ignore the dollar amounts involved.

3.2 On what sort of time horizon is it realistic to expect adequate expected return for having assumed the risk associated with various securities? (Retirement Plan Investing Essentials, p. 50)

Although investors may receive their expected returns on risky securities on a longrun average basis, they often fail to do so on a short-run basis. It is a fact of investing life that realized returns often differ from expected returns.

Define Business Risk (Retirement Plan Investing Essentials, pp. 50-51)

Business risk is the risk of doing business in a particular industry or environment. For example, AT&T, the traditional telephone powerhouse, faced major changes in the rapidly changing telecommunications industry when alternatives became available.

Describe Currency Risk and Country Risk (Retirement Plan Investing Essentials, pp. 50-51)

Exchange rate risk is the variability in returns caused by currency fluctuations Country risk is the political risk that the country may not be economically stable.

Define Inflation Risk (Retirement Plan Investing Essentials, pp. 50-51)

Inflation risk is the chance that the purchasing power of invested dollars will decline. It affects all securities even if the nominal return is safe (e.g., a Treasury bond). This risk is related to interest rate risk, since interest rates generally rise as inflation increases, because lenders demand additional inflation premiums to compensate for the loss of purchasing power.

Define Interest Rate Risk (Retirement Plan Investing Essentials, pp. 50-51)

Interest rate risk is the variability in a security's returns caused by changes in the level of interest rates. Other things being equal, security prices (especially bonds) move inversely to interest rates. Interest rate risk affects bonds more directly than common stocks, but it affects both types of securities and is a very important consideration for most investors.

Define Market Risk (Retirement Plan Investing Essentials, pp. 50-51)

Market risk is the variability in returns caused by fluctuations in the overall market. All securities are exposed to market risk, although it affects primarily common stocks. Market risk includes a wide range of factors including recessions, wars, structural changes in the economy and changes in consumer preferences

4.7 What is a risk premium? (Retirement Plan Investing Essentials, p. 54)

Risk premium is the additional return investors expect to receive, or did receive, by taking increased amounts of risk. For example, the difference between stocks and a risk-free rate (proxied by the return on T-bills) is referred to as the equity risk premium.

4.2 How do investors typically measure risk when assessing investments? (Retirement Plan Investing Essentials, pp. 51-52)

Risk reflects the chance that the actual outcome of an investment will differ from the expected outcome. If an asset's return has no variability, in effect it has no risk. Thus, a one-year Treasury bill (T-bill) purchased to yield 10% and held to maturity will, in fact, yield (a nominal) 10%. No other outcome is possible, barring default by the U.S. government, which is typically not considered possible. Investors typically equate risk by the dispersion or with the variability of returns, specifically how rates of return vary over time. The risk of financial assets can be measured with an absolute measure of dispersion, or variability of returns, called the variance.

2.4 Explain when an investor should use an arithmetic mean rate of return and when a geometric mean rate of return should be used. (Retirement Plan Investing Essentials, p. 47)

The arithmetic mean rate of return should be used when the investor wants to refer to the typical performance for a single period. That is the return that is "representative" of the periodic returns. The geometric mean rate of return is a better measure of the change in value (or wealth) over time (involving multiple periods). The geometric mean is preferable when the true average compound rate of growth is desired. Over multiple periods, such as years, the geometric mean shows the true average compound rate of growth that actually occurred—that is, the annual average rate at which an invested dollar grew, taking into account the gains and losses over time.

5.2 When looking at the variability in financial asset return series, how are the geometric and arithmetic means related to the variability observed? (Retirement Plan Investing Essentials, p. 55)

The difference between the geometric and arithmetic means is related to the variability of the financial asset return series. The linkage between the geometric mean and the arithmetic mean can be approximated. If we know the arithmetic mean of a series of asset returns and the standard deviation of the series, we can approximate the geometric mean for this series. As the standard deviation of a series increases, the superiority of the arithmetic mean relative to the geometric mean also increases. Geometric mean is normally less than arithmetic.

3.1 How does an investment decision involve the dual concepts of risk and expected return? (Retirement Plan Investing Essentials, pp. 49-50)

The investment decision can be described as a trade-off between risk and expected return. It is not sensible to talk about investment returns without talking about risk, because investment decisions involve a trade-off between the two. Investors must constantly be aware of the risk they are assuming, understand how their investment decisions can be impacted, and be prepared for the consequences.

4.5 What is the standard deviation for the returns shown in Learning Objective 1.6? (Retirement Plan Investing Essentials, pp. 52-53) The mean return is 6.2%. Return (%) Mean Return Difference Difference Sq.: 10....................6.2...........................3.8.....................14.44 8.....................6.2............................1.8......................3.24 5 .................... 6.2...........................-1.2.....................1.44 -12....................6.2...........................-18.2..................331.24 20.................... 6.2...........................13.8.....................190.44 .........................................................................................540.80

The standard deviation is the square root of 135.20 (which is the quotient of 540.80/4), or 11.63%.

1.2 An investor purchased a security for $1,000 and sold it six months later for $1,800. During the six-month period, the investor received $200 in cash dividends. What is the investor's total return? (Retirement Plan Investing Essentials, pp. 38-39)

The total return is any cash received plus price changes, divided by the purchase price. In this case, $200 plus $800 is $1,000, and $1,000 divided by the purchase price of $1,000 is 100%.

1.1 Describe the two components of return on a typical investment. (Retirement Plan Investing Essentials, pp. 36-37)

The two components of return are yield and capital gain or loss. 1) Yield: The yield component is the periodic cash flows from the investment in the form of interest, dividends or other such cash income. 2) Capital Gain/Loss: The change in value of the asset, either appreciation or depreciation, is called capital gain or loss.

4.3 Discuss the two measures of risk typically utilized to quantify risk when assessing investment alternatives. (Retirement Plan Investing Essentials, p. 52)

The two measures of risk typically utilized to quantify risk when assessing investment alternatives are variance and standard deviation. Variance is the absolute measurement of dispersion/variability of returns from a financial asset used as a means of measuring risk. Standard deviation is an alternative measure of total risk related to variance and, accordingly, can be calculated from variance. Standard deviation is the square root of variance.

4.4 Which of the two measures of risk is used more often when performing investment analysis and calculations? (Retirement Plan Investing Essentials, p. 52)

Though the two measures, variance and standard deviation, tend to be referenced interchangeably when discussing the concept of variability or risk, the most commonly used measure of dispersion of risk over a period of time is standard deviation. Standard deviation, which measures the deviation of each observation from the arithmetic mean of the observations, is a reliable measure of variability because all the information in a sample is used. Since standard deviation is measured in the same units as the mean, standard deviation is used more commonly than variance when performing investment analysis and calculations.