Chapter Five
Risk and Return: Past and Prologue
This chapter introduces the concept of risk and return. To induce rational investors to accept more risk they must be promised a sufficiently large enough return to overcome their risk aversion. The concept of excess returns or risk premiums is developed and Value at Risk (VaR) and the Sharpe performance measure are introduced. The primary focus of the chapter however is to calculate the expected return and risk of an individual security and to determine the return and risk of combinations of risky assets and riskfree investments. The chapter also presents historical return and risk data for some asset classes. The difference between real returns and nominal returns is presented along with the Fisher Effect. This chapter is a foundation chapter for understanding modern portfolio theory and the efficient frontier, topics covered in Chapter 6.
After covering this chapter, the student should be able to calculate ex post and ex ante risk and return statistical measures, such as holdingperiod returns, average returns, expected returns, and standard deviations. Readers should understand the differences between timeweighted and dollarweighted returns, geometric and arithmetic averages and have some idea when to use each. Students will also gain a basic understanding of returns and risk of various asset classes and understand that securities that offer higher returns have higher risk. In addition, the student should be able to construct portfolios of different risk levels, given information about risk free rates and returns on risky assets. The student should be able to calculate the expected return and standard deviation of these combinations.
Students will learn that theoretically one can easily construct portfolios of varying degrees of risk by simply altering the composition of the portfolio between riskfree securities and mutual funds. In addition, the student is introduced to the concept of further increasing returns (and risk) by buying additional risky securities with borrowed funds.
PPT 52 through PPT 57
The PPT begins by calculating holding period returns or HPRs and discusses why we calculate returns and sometimes annualize them. Annualizing with and without compounding is illustrated. This should be a review of the students’ basic finance course.
There are several methods for averaging returns over multiple periods. The first choice with respect to averaging is the choice of using the arithmetic or geometric average. The arithmetic average, by the nature of its calculation, assumes that at the start of each period any earnings are withdrawn and the original principal is maintained. Geometric mean calculations assume reinvestment of all gains and losses. The geometric mean will normally be lower because it is a compound return and a smaller growth rate is required for a given set of values if there is compounding. This is a common student question. The geometric mean is lower if the returns vary and the differences between the two will grow with a greater standard deviation of returns, particularly if negative returns are included in the series.
Timeseries returns may be averaged through calculating timeweighted returns or via dollarweighted returns. In timeweighted returns the investor is assumed to hold only one share of the security in each time period. The calculated returns are solely a function of the security performance over the time under evaluation. Once the return series is calculated, either a geometric or an arithmetic average may be calculated. Dollarweighted returns include the effects of the investor’s choices of when they bought and sold securities. Thus dollarweighted returns give the investor a truer estimate of the rate of return they earned based on security return performance and their own choices of when they bought and sold the security.
PPT 58 through PPT 511
The concept of real versus nominal rates and the Fisher Effect are presented. The reason for needing the exact version of the Fisher Effect is given in a hidden slide with a hyperlink so that the instructor may use it or not. Note that the approximation version and the exact version of the Fisher Effect will diverge at higher rates of inflation. The effects of inflation and taxes on an investor’s return are illustrated. Note that since taxes are paid out of nominal earnings you must take taxes out of the nominal return before finding the real return.
Historical Real Returns & Sharpe Ratios 19262008
Series  Real Returns%  Sharpe Ratio 
World Stk  6.00  0.37 
US Lg. Stk  6.13  0.37 
Sm. Stk  8.17  0.36 
World Bnd  2.46  0.24 
LT Bond  2.22  0.24 
Stocks have much higher real returns over long time periods. To illustrate what this implies we can calculate the following future values:
LT Bond portfolio: $1 x 1.022^{82} = $5.96; if you had invested $1 in the LT Bond portfolio for 82 years your $1 would have grown to the equivalent purchasing power of just under $6.
US Large Stock portfolio: $1 x 1.06^{82} = $118.87; if you invested $1 in the US Large Stock portfolio for 82 years your $1 would have grown to the equivalent purchasing power of just under $119.
The Sharpe ratio is a measure of the excess return per unit of standard deviation risk. It literally measures the return per unit of risk taken. Higher Sharpe ratios indicate better the performance for that asset class. Notice that the Sharpe ratios are higher for the threestock portfolios than the bonds. Thus the stocks offered a higher rate of return per unit of risk. Does that mean investors should not hold bonds? No, adding bonds to a stock portfolio will eliminate proportionally more risk than the return sacrificed and can lead to higher Sharpe ratios.
PPT 512 through PPT 521
This section begins by illustrating calculations of expected returns and standard deviation exante for individual securities via scenario analysis. Expost average return and standarddeviation calculations are also provided. Basic characteristics of probability distributions are then covered including definitions of mean, variance, skew and kurtosis. For distributions that are skewed, the median and mean returns are different. For normal distributions the mean and variance or standard deviation are sufficient statistics to characterize the distribution.
Value at Risk
Value at Risk attempts to answer the following question:
How many dollars can I expect to lose on my portfolio in a given time period at a given level of probability?
The typical probability used is 5%.
In a given probability distribution we need to know what HPR corresponds to a 5% probability.
If returns are normally distributed then we can use a standard normal table or Excel to determine how many standard deviations below the mean represents a 5% probability:
From Excel: = Norminv (0.05,0,1) = 1.64485 standard deviations. In the Norminv function in Excel the 0.05 is the 5% probability, 0 is the mean and 1 is the standard deviation of a standard normal variate.
From the standard deviation we can find the corresponding level of the portfolio return:
VaR = E[r] + 1.64485s
For Example:
A $500,000 stock portfolio has an annual expected return of 12% and a standard deviation of 35%. What is the portfolio VaR at a 5% probability level?
VaR = 0.12 + (1.64485 * 0.35)
VaR = 45.57% (rounded slightly)
VaR$ = $500,000 x .4557 = $227,850
What does this number mean? The greatest annual expected loss 95% of the time is $227,85.
VaR is an easily understood qualitycontrol measure. Investment oversight boards can determine whether this loss is acceptable given the portfolio’s goals. The VaR calculation does not require normal distributions. The text illustrates calculating VaR if you have a normal distribution. If options or other complex instruments are included in the portfolio you will not have a normal distribution. You then have to approximate the distribution or perhaps use a Monte Carlo simulation to build a distribution of future returns.
VaR versus Standard Deviation:
For normally distributed returns VaR is equivalent to standard deviation (although VaR is typically reported in dollars rather than in % returns). VaR adds value as a risk measure when return distributions are not normally distributed. Note the actual 5% probability level will differ from 1.68445 standard deviations from the mean due to kurtosis and skewness if these are present. In these cases the standard deviation is a not a sufficient statistic to measure risk.
Risk Premium and Risk Aversion
The riskfree rate is the rate of return that can be earned with certainty. The risk premium is the difference between the expected return of a risky asset and the riskfree rate. The risk premium may be called an ‘excess return.’ The excess return can be depicted as:
Excess Return or Risk Premium_{asset} = E[r_{asset}] – rf
Risk aversion is an investor’s reluctance to accept risk. An investor’s aversion to risk is overcome by offering investors a higher risk premium.
PPT 522 through PPT 524
The geometric mean is the best measure of the compound historical rate of return. Nevertheless the arithmetic average is the best measure of the expected return. Notice the greater divergence of the GAR and AAR for small stocks. This is because of the high variance and the higher proportion of negative returns in the small stock portfolio. Although we don’t have statistical significance it appears that some of the portfolios exhibit kurtosis. Kurtosis of the normal distribution is zero. The World Stock, US Small Stock and World Bond portfolios appear to exhibit kurtosis. This indicates a higher percentage of observations in the tails that is predicted by the normal distribution. Nonzero value of skewness are also apparent, although we cannot tell if they are significant. The World stock and US Large Stock portfolios may exhibit negative skewness. This indicates a higher probability of extreme negative returns than is predicted in a normal distribution.
PPT 525 through PPT 529
Investors can choose to hold risky and riskless assets. We may consider investments in a money market mutual fund as a proxy for the riskless investments that an investor might actually engage in. These combinations fall on a straight line (see below) because the standard deviation of the riskless asset is zero and because the correlation between the risky and the riskless asset is zero. Hence all combinations of the risky and the riskless portfolio are linear. The line that depicts the possible allocations between the risky and the riskless portfolio is termed the Capital Allocation Line or CAL.
The CAL is useful to describe risk/return tradeoffs and to illustrate how different degrees of risk aversion will affect asset allocation. Risk aversion will impact the combinations chosen by an investor. An investor with a low tolerance for risk will likely prefer to invest some funds in the riskless asset. An investor with a high tolerance for risk may choose to use leverage. Understanding the CAL now will help students understand the modeling in the next chapter when we consider multiple risky asset combinations.

The expected return is on the vertical axis and the standard deviation of the total portfolio is on the horizontal axis. With all of your money in the risk free asset (F) you will have a 7% return and a zero standard deviation. With 100% of your money in the risky asset you will have a 15% expected return and a 22% standard deviation. Combinations (y) less than one represent varying percentages invested in the risky asset P and (1y) the percentage invested in the risk free F. Combinations above P are possible by borrowing money at F. This is conceptually equivalent to buying stock on margin. More riskaverse investors would choose a lower y and less riskaverse investors would choose a larger y.
Quantifying Risk Aversion
Some efforts have been made to quantify risk aversion (A). The text assumes that the risk premium or excess return is proportional to the product of the risk aversion level A and the variance of the portfolio.
E(rp) = Expected return on portfolio p
rf = the risk free rate
0.5 = Scale factor
A x s_{p}^{2} = Proportional risk premium
A larger A indicates that the investor requires more return to bear risk. In the asset allocation decision the optimal weight in the risky portfolio P (W_{P}) is:
The coefficient of risk aversion A is generally thought to be between 2 and 4.
With an assumed utility function of the form:
U = E[r] – 1/2As_{p}^{2}
The A term can used to create indifference curves. Indifference curves describe different combinations of return and risk that provide equal utility (U) or satisfaction. Indifference curves are curvilinear because they exhibit diminishing marginal utility of wealth. The greater the A the steeper the indifference curve and all else equal, such investors will invest less in risky assets. The smaller the A the flatter the indifference curve and all else equal, such investors will invest more in risky assets.
PPT 530 through PPT 531
In a passive strategy the investor makes no attempt to either find undervalued strategies or actively switch their asset allocations. Investing in a broad stock index and a riskfree investment is an example of a passive strategy. The CAL that employs the market (or an index that mimics overall market performance) is called the Capital Market Line or CML. In competitive markets active strategies that entail more information production and trading costs might not consistently perform better than passive strategies after considering those costs. As active investors trade upon information, prices will incorporate that information. This implies that passive investors are able to “free ride” upon the activities of active investors.
Excess Returns and Sharpe Ratios Implied by the CML
The average risk premium implied by the CML for large common stocks over the entire time period is 7.86%. But the subperiod variation and the large standard deviation indicate that investors cannot be very confident about using the historical data to estimate what the risk premium is likely to be in any given time period. Sharpe ratios have varied considerably as well. Notice the higher risk premium and Sharpe ratio during the time period including the Great Depression. In periods of economic uncertainty we can expect to see higher risk premiums.
Chapter Fourteen
Financial Statement Analysis
Chapter Overview
This chapter discusses the income statement, balance sheet and the statement of cash flows. The text stresses the differences between accounting and economic income and provides good detail on return on equity (ROE), the decomposition of the ROE into component ratios for the purpose of financial analysis, and other ratios relevant for financial analysis. Financial statement comparability problems are also presented.
Learning Objectives
After studying this chapter, the student should be able to analyze a firm using the basic financial statements to perform ratio analysis. The student should be able to identify the source of problems over time by decomposing the return on equity using the Du Pont procedure. Several examples are provided in the text. The effects of leverage on returns is also discussed and the concept that firms must earn a higher return than on reinvested funds than the required return to add value is amply illustrated. The student should also be able to identify comparability problems across firms due to the varying generally accepted accounting principles available to the firm and understand that accounting standards will be changing over the next several years due to the upcoming adoption of international financial accounting standards.
CHAPTER OUTLINE
PPT 142 through PPT 145
Financial statement analysis uses the firm’s accounting data. The financial statements are the starting point of a financial analysis. The income statement contains flows that occur during the current period that relate to profitability primarily. The balance sheet gives an analyst a snapshot for the firm’s financial position and a broad overview of the level of investments in major asset categories. Analysts typically work with common size statements to remove size distortions. Indexed or trend statements are used to analyze changes over time.
Accounting earnings are earnings reported on the income statement that follow a set of generally accepted, but widely divergent, accounting practices. Economic earnings are the sustainable cash flow to the stockholders that does not impair the productive capacity of the firm.
The statement of cash flows removes much of the effects of accrual accounting to give the analyst a better look at the cash flows of the firm. The statement of cash flows recognizes only transactions in which cash changes hands. Analyzing cash flows and estimating their future levels is the crux of financial forecasting. It may be worthwhile to go beyond the text and discuss cash flow modeling of the firm according to the statement of cash flows:
Cash Flow = Operating Cash Flow + Cash Flows from Investing + Cash Flow from Financing
Operating Cash Flow = Net income + Depreciation + Net Operating Sources of Funds
Net Operating Sources of Funds
= Working capital operating sources of funds – working capital operating uses of funds ^{[1]}
Cash Flow from Investing would include net investments in fixed assets and Cash Flow from Financing will contain changes in debt and equity accounts and dividends. Note that interest expense is not included in Cash Flow from Financing and is also not added back to Operating Cash Flow.
Not all sources of funds are equal in terms of their sustainability. A firm can increase its cash by becoming more profitable (generally a good thing), by divesting fixed assets (which could be good or bad depending on the earnings potential of the assets) or by increasing financing sources (which is probably not sustainable).
Financial statement analysis can often lead the analyst to general conclusions about a firm, but it rarely gives the analyst a sufficiently complete picture to make a forecast.
PPT 146 through PPT 147
Two broad activities are the responsibility of a firm’s financial managers: investment decisions and financing decisions. Investment, or capital budgeting, decisions pertain to the firm’s use of capital, while financial decisions pertain to the firm’s sources of capital. Aspects of both efficiency and profitability can be measured with a several ratios: efficiency is typically assessed using several turnover ratios, while the profitability of sales is commonly measured with various profit margins. When evaluating financing decisions, look at both leverage and liquidity. Aspects of each of these two concepts can be measured with an array of statistics.
PPT 148 through PPT 1412
Return on equity and return on assets are total earnings expressed on a perdollar invested basis. The firm’s financial policies affect how ROA and ROE are linked because ROE is after tax and ROA is before interest and taxes. Note that the text uses ROA = EBIT / Assets, whereas many other texts calculate ROA = NI / Assets. It is crucial that the instructor make this point with the students. In concept the text uses a measure of operating return on assets rather than an overall return on assets.
The relationship between ROA and ROE is presented:
This relationship can be used to illustrate a key point about leverage and the return on equity. Using debt in the capital structure can increase the ROE if the ROA is greater than the interest rate on the debt. Hence, the choice of the optimal capital structure will be dependent on expected earnings on investments in relation to the cost of debt. Few students will understand this, but they should for their investment choices and in their personal finances. Because the interest expense is a fixed cost it adds to the risk of the firm. There is no free lunch, seeking higher returns requires taking on more risk.
The concept of economic value added is another tool that can be used to analyze a company’s performance. Economic value added compares return on assets with a cost to the capital that is required to make the investment in assets. The main point of the analysis is that management adds value to stockholders by retaining earnings and reinvesting only if the ROE > k. The related point should also be made, namely that EPS growth can be generated simply by retaining earnings, but this does not mean the firm is adding value or maximizing shareholder wealth unless the return on the investment is greater than k.
PPT 1413 through PPT 1426
Ratio analysis is used to highlight specific aspects of performance. All ratios require a benchmark (although ‘rules of thumb’ have been developed for some) for comparison. The benchmark may be the same ratio in a different time period or the value of a competitor or group of competitors. Ratios are very important to the investment community and are used extensively in security analysis. They are also used by credit rating agencies to establish security ratings.
ROE = Net Income/Equity is the key bottom line ratio in financial statement analysis because it is a measure of the accounting return to equity. Literally it measures the firm’s ability to convert a dollar of equity invested in the firm into bottom line profitability. ROE can be decomposed as follows:
Ratio (1) Tax Burden (TB) measures the percentage of pretax profit that the firm keeps after paying taxes. Ratio (2) Interest Burden (IB) measures the percent of EBIT kept after paying interest expense. This ratio is 1 if the firm has no debt. One can see this by restating the relationship as follows:
The IB ratio is closely related to the times interest earned or TIE = EBIT / Interest expense. A high TIE indicates a low probability of bankruptcy. 1 – (1/TIE) = maximum sustainable drop in EBIT that just allows the firm to cover its interest expense. With a TIE of 5 for instance, the firm could lose 1 – (1/5) = 80% of its EBIT and still just cover its interest expense.
Ratio (3) Operating Profit Margin measures the percentage of sales revenue that remains after subtracting cost of goods sold, selling and administrative expenses and depreciation. Ratio (4) Asset Turnover Ratio (ATO) measures the efficiency of the firm at generating sales per dollar invested in the assets. The Margin x ATO = ROA.
Ratio (5) Leverage ratio = 1 + Debt / Equity. The leverage ratio is a measure of the percentage of debt in total capitalization. Note that it appears that using more debt as a percent of capital will increase ROE, but using more debt also reduces the interest burden ratio.
The various debt ratios are all algebraically equivalent. Knowing the Debt / Asset ratio, one can find the Equity / Asset ratio because the two ratios must sum to 1. Taking the ratio of these two will give one the Debt / Equity ratio and adding 1 to that will give the leverage ratio.
The decomposition process allows an analyst to see what factors have the most significant influence on the summary measure. For example, analysis and comparison of the factors 3, 4 and 5 highlight profit margin on sales, total asset turnover and leverage (equity multiplier). When factors 3 and 4 are multiplied together, the analyst has a measure of EBIT/Assets. This measures the operational profit of the firm without the financial leverage. The decomposition is useful in highlighting relevant factors influencing overall profit.
The types of ratios and the individual ratios that are used for the different types of ratios vary in importance for different industries. For example, inventory turnover is not critical for a service firm while inventory turnover is critical for a manufacturer.
Profitability ratios measure profits to sales, assets or equity. All profitability measures that include net income are subject to potential problems in comparability. Since net income is influenced by financial leverage, if firms use different amounts of borrowing, it is difficult to compare the profitability directly. We would expect firms with more leverage to have higher levels of profitability but firms using higher degrees of leverage are also riskier than firms that do not use as much debt.
Management efficiency or activity ratios are used to assess the effectiveness of management in generating sales. The most common types of management efficiency ratios are turnover measures that tie sales to assets or groups of assets. Generally, higher levels of turnover mean that the company is using its assets more efficiently in generation of sales.
Liquidity ratios are designed to measure the firm’s ability to meet a short term obligation. The current ratio and the quick ratio are commonly used to measure liquidity.
Leverage ratios are used to investigate the firm’s use of debt. Timesinterestearned and fixedchargecoverage ratios are used to assess the firm’s ability to service debt. Debt to assets and debt to equity are used to assess how much debt financing the firm is using.
The pricetoearnings and markettobook ratios are presented. These ratios are regularly reported and discussed in the financial press. The relevance of the market to book ratio varies with industries. The relevance depends on how accurately the book value reflects economic value and how significant asset levels are in the production of profits and sales. Analysts also use the pricetosales ratio as an indicator of how a stock is valued, particularly if a firm has low or negative earnings.
PPT 1427 through PPT 1429
Some of the issues that shortterm borrowing brings to analysis are illustrated by the example using Growth Industries, Inc. Key ratios and the statement of cash flows for Growth Industries, Inc. show that careful analysis of financial ratios can indicate problems that may not be presented in the annual report. The analysis shows that ROE is declining while ROA is remaining steady. The firm is using large amounts of longterm debt to maintain its 20% growth in assets and this is not sustainable for very long.
PPT 1430 through PPT 1436
Since financial ratios are based on accounting data, an analyst must be aware of differences in accounting methods that could affect comparison of ratios. Some of the key problems of comparability include different inventory valuation methods. This is an important factor since it influences cost of goods sold, which is the major component of costs on most income statements. There are also various problems related to depreciation. First, accounting depreciation is different from economic depreciation. Firms can also choose different methods of depreciation. Depreciation affects reported income and reported asset values. Inflation can distort reported income and the balance sheet. Differences in international accounting standards make comparisons of international firms difficult. With the increased pressure on firms to meet expected earnings, more management of earnings is taking place in today’s environment. Fair value accounting uses market values rather than book values in the firm’s financial statements. Market value is a truer picture of the current value of the firm, as market value is forward looking and book value is backward looking. The trend is toward market value accounting Financial Accounting Standards Board (FASB) Rule 157 classifies assets in one of three categories: Level 1: Assets that are traded in active markets and should be valued at market prices, Level 2: Asset that are not actively traded, but their values may be estimated from market data on similar assets, Level 3: Assets that can only be valued with inputs that are difficult to observe. Level 2 and Level 3 assets may be valued using pricing models and the values may be ‘marked to model.’
Note that banks must mark to market some of their asset holdings. Bankers have fought mark to market rules for years, sometimes claiming it couldn’t be done, and other times claiming it shouldn’t be done. The financial crisis has exacerbated the debate. We learned from the S&L crisis of the 1980s and from Japan in the 1990s that you should have mark to market rules. Otherwise the financial statements are hiding losses in periods of distress. It may make sense to mark to a calculated fundamental value rather than market value if market value is at fire sale prices during periods when markets are not functioning properly.
A list of items used by analysts to assess the quality of earnings is displayed in the PPT. A firm in the modern corporate environment has a great deal of flexibility in reporting and quality is a real issue.
International accounting conventions are presented in the final part of this section. Quality of earnings refers to the realism and sustainability of reported earnings. This implies that
Remember that earnings are supposed to translate into cash flow and we are always trying to identify the trend in expected future cash flows.
International Accounting Conventions
Overseas firms have far more discretion in their ability to set aside reserves for future contingencies (or not) than U.S. firms have. This means foreign firms’ earnings are more subject to managerial manipulation. Foreign firms typically use accelerated depreciation on their financial statements and U.S. firms do not, so foreign firms have lower reported earnings, ceteris paribus. Treatment of intangibles varies widely between countries as well, increasing comparability problems. The International Financial Reporting Standards (IFRS) have been adopted by the European Union and by over 100 countries.
In 2007 the SEC began allowing foreign firms to list their securities in U.S. markets if they prepared their statements using IFRS. In 2008 the SEC ruled that large U.S. multinational firms may start using IFRS rather than GAAP in 2010 and that all firms should use IFRS by 2014. IFRS standards are principle based rather than rules based. The IFRS standards will generally allow more flexibility in reporting standards.
The last section of the chapter provides a discussion of Benjamin Graham’s techniques for investing. Graham was the founder of modern fundamental analysis. Graham believed careful analysis of a firm’s financial statements could turn up bargain stocks and his work was used by generations of analysts.
He developed many different rules for determining the most important financial ratios, but as his ideas became popular they stopped working.
[1] Operating sources and uses should include changes in working capital accounts related to operations such as inventories and receivables and should exclude nonoperating sources and uses such as bank loans and short term notes payables.
There are no reviews yet.