Chapter 3 - Spreadsheet Exercises 3-1: CHAPTER 3 - MEASURING PORTFOLIO RISK 67

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1 CHAPTER 3 - MEASURING PORTFOLIO RISK 67 Chapter 3 - Spreadsheet Exercises 3-1: Using the data in Table 3-2 above, graph the expected distribution of monthly stock returns on each of Proctor & Gamble (PG), Boeing (BA), and Google (GOOG). Model Data: A. Enter the model data into the spreadsheet. Normal Distribution: A. The normal distribution is 99.74% within three standard deviations of the mean so the base of the calculations will be a column Z that goes from -3 standard deviations to +3 standard deviations. Enter -3 into cell A8 and =A8 +.1 into A9. Copy down the column until you get the full range from -3.0 to +3.0 B. We need a mean and a standard deviation as a base for the X axis of the graph itself. Start with 2% and 4%. Enter this into column A. C. Calculate the X values into column B. Start with cell B8 and use cell formulae so that we can change the parameters of the graph as we go. So B8 is = $A$3+($A8*$A$4). The $ in the formula prevents the cell address from changing as the formula is copied down the column. $A8 locks column A into the formula but allows 8 to change as the formula is copied down. D. Copy the formula down the column. Note that this gives us an X axis from -10% to 14%; three deviations in each direction from the mean. E. We calculate the probability mass using the Excel function NORMDIST. Start with cell C8 and use =NORMDIST($B8,C$3,C$4,FALSE). NORMDIST calculates the probability that we observe a return of $B8 given a normal distribution of mean C$3 and standard deviation C$4. The FALSE means that we are calculating a probability at $B8 rather than a cumulative normal to $B8. F. Copy across and down. Graph: G. Generate the graph from B7 through E68. H. Note that although the graph for Proctor & Gamble (PG) goes from -9.22% to and the graph for Boeing (BA) goes from -8.02% to 12.86% Google (GOOG) needs to range from % to 40.17%. So Google generates only a partial normal curve in this graph. I. To extend the x-axis adjust the mean and standard deviation in A3 and A4. The graph will redraw itself at each adjustment.

2 68 SECTION II - PORTFOLIO THEORY A B C D E 1 DATA 2 Graph PG BA GOOG 3 2% Mean 1.07% 2.42% 6.24% 4 4% Std Dev 3.43% 3.48% 11.31% 5 6 NORMAL DISTRIBUTION 7 Z X Axis PG BA GOOG % % % % % % % FIGURE 3-3: NORMAL DISTRIBUTION FROM MEAN AND STANDARD DEVIATION DATA Boeing P&G Google -40% -30% -20% -10% 0% 10% 20% 30% 40% 50%

3 CHAPTER 3 - MEASURING PORTFOLIO RISK : Analyze the statistical patterns in the fifteen year track record on the S&P 500 index of stock market prices. Using the statistical rate of return calculate and interpret the total, average, and standard deviation of the returns. Using the time weighted rate of return calculate and interpret the total and average rates of return. Model Data A. Enter the data from Table 3-1. TABLE 3-1: S&P500 ANNUAL RETURNS Calendar Year End Annual Return (%) % % % % % % % % % % % Totals and Averages % B. Use =COUNT() to verify that there are 15 observations % return to column C. But leave the format in decimal terms. C. Use =SUM() to add the column values D. Verify this by using cell addresses =() to copy the rates of % 4.92% A. Note that if you entered the rates of return as a number (30.47) then you will need to divide by 100. So C2 is =B2/100 rather than =B2. B. If you entered the rates of return as percentages (30.47%) then excel has already interpreted them as E. To calculate the time weighted rates of return we need to add the dollar we started with so D2 is given by =1+B2 F. Note that adding the dollar we started with still allows us to calculate the arithmetic total and average. A. The total reflects the fact that we had to start with a fresh dollar in each month and that over the 15 months we earned an extra B. The average is the dollar we started with plus.1296 G. Use =PRODUCT() to calculate the time weighted total and =D21^(1/$B$18) to calculate the 15 th root. Standard Deviation and Variance H. In column E calculate the deviation from the mean. Set E2 to =B2-$B$20 and copy the formula down the column. A. Hover the mouse over the bottom right corner of the cell until the cursor turns into a plus sign, then right click and drag the formula down the column. B. The $ in $B$20 keeps this exact number in the formula as you drag; B2 changes to B3, B4 etc. C. If you entered the data as numbers (30.47) instead of percentages (30.47) or mathematical equivalents (0.3047) use the numbers in column C instead. I. The sum of the deviations should be zero. This confirms that the mean is in the middle (as it should be by definition). J. Calculate the squared deviation into column F K. Calculate the sum, the average, and the square root of the average squared deviation. A. If you started with rather than 30.47% then the squared deviation should sum to rather than The end result will be the same.

4 70 SECTION II - PORTFOLIO THEORY Population and Sample Statistics L. Calculate the variance and standard deviation as though the observations represented the entire population: n=15 M. Calculate the variance and standard deviation as though this were a sample taken from the population. So now, with the loss of a degree of freedom, n=14. N. Use Excel formulae =VARP() and =STDEVP() to calculate the population statistics and =VAR() =STDEV() to calculate the sample statistics. A B C D E F G H 1 Year Return % r 1+r Deviatio Squared $Begin $End n % % % 1, , % % % 1, , % % % 1, , % % % 1, , % % % 1, , % % % 2, , % % % 2, , % % % 3, , % % % 4, , % % % 5, , % % % 4, , % % % 4, , % % % 3, , % % % 4, , % % % 4, , n= sum= % % average= 12.96% % % 21 product= root= % 23 average= Statistics 26 Calculated Excel Functions 27 Populatio n 28 Variance % 3.038% 29 Std Dev 17.43% 17.43% Sample 32 Variance % 3.255% 33 Std Dev 18.04% 18.04% Excel skills: Functions

5 Population and Sample Variances CHAPTER 3 - MEASURING PORTFOLIO RISK 71 The variances, both population and sample, as well as both measures of standard deviation were calculated using the raw data in column B. The notion of an "average squared surprise" in variance is obvious if you click on cell B28. Notice that it divides the sum of the "differences squared" from cell F19, by the number of observations in cell B18. Notice also that we did not have to count the observations and type 15 in that cell, a function in Excel =COUNT(B2:B16) did the counting for us. The sample variance and standard deviation are calculated in cells C32 and C33 respectively. Note that in the direct calculation of the sample variance the population variance in is used and multiplied by (n/n-1) or (B17/(B17-1)) in Excel parlance, to account for the lost degree of freedom. The same Statistics are calculated in column C using functions built into Excel. C28 uses the Variance function =VARP(B2:B16) to calculate the population variance on the data in cells B2 thorough B26. While this cell is active, click the equal sign next to the formula bar at the top of the spreadsheet. A dialog box opens and tells you what the formula is, and over what range of cells it is operating. Any preprogrammed function in Excel is nicely explained in this dialog box. Excel Functions To see all of functions in Excel, just open the function wizard, or click on any blank cell, then click on the equal sign next to the formula bar again, and the cell reference window next to it will become a drop-down menu of the ten most recently used functions, as well as the "more functions" option. Click the more functions option, and now you can sort through Excel's categories of functions, the function names, and see a brief explanation of them all. This is how we choose "VARP" for the population variance, and "VAR" for the sample variance, which is calculated in cell C32. Cells C29 and C33 calculate the population standard deviation and sample standard deviation, respectively, using the Excel functions "=STDEVP(B2:B16)" and "=STDEV(B2:B16)". Some Interpretations Your client asks: "If I invested in this market, what would I expect any single year's return to be?" Assuming the returns were random and normally distributed, we could answer with the arithmetic average: 12.96%. This answer is only part of the story though because we have not talked about the variability around that expectation. Using the past 15 years as a sample of what might be, we need to use the sample standard deviation of the returns to talk about the likelihood of expected returns. The sample variance is calculated by dividing the sum of the squared differences by n-1 rather than n, where n = the number of observations. This gives us a sample variance of Taking the square root of the sample variance gives us a sample standard deviation of 18.04%. Now, using the properties of the normal distribution, we may be able to answer, "You could expect a random annual return in any year of 12.96% ± 18.04%, 68% of the time". In other words, 68% of the time, the return

6 72 SECTION II - PORTFOLIO THEORY for any year should be between -5.08% and 31.00%. If a higher certainty (confidence interval) were desired, then we could use two standard deviations above or below the mean for a 95% confidence, or three for 99%. Obviously, the more confident we are of the return, the wider the range of possible returns in that confidence interval. Does this guarantee that we cannot see a year when the returns fall outside these ranges? No, there is no guarantee with either statistics or investments. We are trying to measure risk, and to that extent, we have a measure. To say that an observation COULD NOT fall outside the range, we would have to conclude that we have eliminated ALL uncertainty of the return. In conclusion, our focus should be to understand what the statistics are telling us, and how we can use them to make informed decisions. The task of memorizing formulas and computing statistics is an entirely mechanical process. The former are things for which people in finance should strive, the later represent things machines are designed to do quickly and accurately.

7 CHAPTER 4 - DIVERSIFICATION 85 Chapter 4 - Spreadsheet Exercises 4-1: Model the Efficient Portfolio Frontier and find the minimum variance portfolio. Model Data: A. Begin with the data upon which the model is based. B. Use Tardis Intertemporal (TI) (E[R]=15%, F=20%) and Hypothetical Resources (HR) (E[R]=21%, F=40%) and a correlation coefficient D = 0.3. Parameters: C. Set up one column for the percentage of the portfolio in TI. Do not type numbers; use Enter 0%, 5%, 10%; highlight the three cells; float the cursor over the south east corner until it changes to a +; drag down the column to fill. You should now have a column that goes from 0% to 100% in 5% increments. Dependent values: D. Set up a second column for the percentage of the portfolio in HR. Use formulae. So for G4 use =1-F4 E. Set up two more columns. One for the expected return of the portfolio and one for the standard deviation. Calculate E[R] and F using cell references. F. Don t try entering the entire formula at once; build it one step at a time. Then check that the result in your spreadsheet for the 50%/50% portfolio matches your answers in Question 4-2 above. G. Graph the EPF with X=sigma and Y = E[R]. Excel will default X=E[R] so make sure that you override the default settings by specifying the series correctly under [Source Data]. If the EPF looks jerky float the cursor over the EPF and right click to get the menu. Use [Format Data Series] [Patterns] and check the option []smoothed line. H. Test the model by changing the model data. The expected return, standard deviation, and EPF should change as you change the model data. Minimum Variance Portfolio: I. With 5% increments the minimum variance portfolio looks to be where TI is 90%. Start in cell I22 where sigma is 19.58% J. From the menu bar choose [Tools] [Solver] K. Set target cell to I22 and choose equal to min L. By Changing Cells F22 M. Click on [Solve]. Excel will use trial and error to find the minimum variance. It then shows you the results and gives you the option of keeping the solver results or going back to the original values.

8 86 SECTION II - PORTFOLIO THEORY A B C D E F G H I 2 DATA PORTFOLIO 3 TI HR rho TI HR E[R] sigma 4 E[R] 15.0% 21.0% 0.3 0% 100% 21.00% 40.00% 5 sigma 20.0% 40.0% 5% 95% 20.70% 38.31% % 90% 20.40% 36.65% 7 15% 85% 20.10% 35.02% 22 90% 10% 15.60% 19.58% 23 95% 5% 15.30% 19.69% % 0% 15.00% 20.00% Excel skills: Solver

9 CHAPTER 5 - MODERN PORTFOLIO THEORY 99 Chapter 5 - Spreadsheet Exercises 5-1: MMM Estimate Beta for Minnesota Mining & Manufacturing (MMM) and, assuming a risk-free rate of 3%, chart the SML, indicating any abnormal returns for MMM. Model Data: A. Enter the data from the table at the right. B. The data should be entered in percentage format. Thus the rate of return for December 2005 is entered as -1.25% Excel then saves the number as but displays it as -1.25%. Alternatively the column can be formatted as percentage to two decimal places (from the menu bar [%] [500.0]) and then entered as C. If you are calculating rates of return from raw data remember to include quarterly dividends and the two for one stock split on September 30, 2003 Regression: D. From the menu bar choose [Tools] [Data Analysis] [Regression]. E. We are estimating the Market Model. The return on the Index is the independent variable X and the return on MMM is the dependent variable Y. Remember to include the labels and click on labels and line fit plots. F. [OK] Excel creates a new worksheet for the regression. G. You should see "= and $= Chart: H. The Line Fit Plot created by Excel comes in Microsoft default. I. Format the data series (float the mouse over the graph and right click to get the menu; click on format data series) removing from the regression line the marker and adding a custom line. J. Adjust the axes to make the labels more relevant. Excel skills: Regression 15% 10% A B C 1 Month MMM S&P Dec % -0.10% 3 30-Nov % 3.52% 4 31-Oct % -1.77% 5 30-Sep % 0.69% 6 31-Aug % -1.12% 7 31-Jul % 3.60% 8 30-Jun % -0.01% 9 31-May % 3.00% Apr % -2.01% Mar % -1.91% Feb % 1.89% Jan % -2.53% Dec % 3.25% Nov % 3.86% Oct % 1.40% Sep % 0.94% Aug % 0.23% Jul % -3.43% Jun % 1.80% May % 1.21% Apr % -1.68% Mar % -1.64% Feb % 1.22% Jan % 1.73% Dec % 5.08% Nov % 0.71% Oct % 5.50% Sep % -1.19% Aug % 1.79% Jul % 1.62% Jun % 1.13% May % 5.09% Apr % 8.10% Mar % 0.84% Feb % -1.70% Jan % -2.74% 5% 0% S&P500-4% -2% 0% -5% 2% 4% 6% 8% -10% -15%

10 160 SECTION IV - MONEY MARKETS MONEY RATES Prime Rate: 8.00%. The base rate on corporate loans posted by at least 75% of the nation s 30 largest banks. Discount Rate: 6.00% The charge on loans to depository institutions by the Federal reserve Banks. Federal Funds: 7.000% high, 4.500% low, 6.500% near closing bid, 7.000% offered. Reserves traded among commercial banks for overnight use in amounts of $1 million or more. Fed funds target rate 5.000%. Call Money: 6.75%. The charge on loans to brokers on stock exchange collateral. Commercial Paper: Placed directly by General Electric Capital Corp: 4.99% 30 to 59 days; 5.01% 60 to 89 days; 5.03% 90 to 119 days; 5.05% 120 to 149 days; 5.06% 150 to 179 days; 5.07% 180 to 239 days; 5.08% 240 to 270 days. Euro Commercial Paper: Placed directly by General Electric Capital Corp: 2.59% 30 days; 2.75% two months; 2.84% three months; 2.89% four months; 2.95% five months; 3.02% six months. Certificates of Deposit: 5.05% one month; 5.14% three months; 5.26% six months. Bankers Acceptances: 5.04% 30 days; 5.07% 60 days; 5.12% 90 days; 5.15% 120 days; 5.19% 150 days; 5.24% 180 days. Foreign Prime Rates: Canada 5.75%; European Central Bank 2.50%; Japan 1.375%; Switzerland 3.05%; Britain 4.50%. Treasury Bills : Results of the Monday May 8, 2006 auction of short term US Government bills: 4.740% 13 weeks; 4.830% 26 weeks. Tuesday May 9, 2006 auction: 4.620% 4 weeks. Eurodollars: 5.05% one month; 5.11% two months; 5.15% three months; 5.19% four months; 5.24% five months; 5.26% six months. LIBOR: London Inter-Bank Offer Rate: 5.08% one month; 5.16% three months; 5.27% six months; 5.40% one year. Overnight Repurchase Rate: 4.70% Dealer financing rate for overnight sale and repurchase of Treasury securities. Financial Pages - May 10, 2006

11 188 SECTION IV - MONEY MARKETS Chapter 11 - Spreadsheet Exercises 11-1: Using the table of Money Rates on page 160, graph the various money rates so that the relationship between them is highlighted. Model Data; A. Choose a date system. We can set up a row of days and a second row of months. When months are specified we use months directly; when days are specified we convert the days to months by dividing by 30. B. Enter the data by instrument type. Begin with Commercial Paper and Bankers Acceptances Graph; C. Begin with the Chart Wizard on these two Money Market Instruments. Make sure that you include the labels. So highlight A1 through J3 then choose chart wizard. D. Clean up the graph by setting the horizontal axis to minimum 0 maximum 270 days with an interval of 30 days. E. To get the labels to show choose the last point in each series, float your mouse and right click, left click, right rick, to get the menu that begins [format data point]. In format data point choose [data labels] series name. Adding series. F. To add a series you should know that Microsoft chart will only draw a line through consecutive points. To see this delete the observation in Cell E3. The line from 90 days to 150 days disappears. G. To add Treasury Bills set up a separate table area with the relevant data. H. Right click in the chart to get the chart menu. Choose [Source Data] [Series] [Add]. Use the field specification and mouse to highlight and choose the series name (A6), X values (B5:D5) and Y values (B6:D6). I. Add subsequent series in the same way, adding each one to the table structure in which the rate pattern best fits. A B C D E F G H I J 1 Days Commercial Paper 4.99% 5.01% 5.03% 5.05% 5.06% 5.07% 5.07% 5.08% 5.08% 3 Bankers Acceptances 5.04% 5.07% 5.12% 5.15% 5.19% 5.24% 4 5 Days Treasury Bills 4.62% 4.74% 4.83% Excel skills: Graphs

12 CHAPTER 11 - MONEY MARKET INSTRUMENTS 189 FIGURE 11-1: MONEY MARKET YIELD CURVES GENERATED FROM BANKERS ACCEPTANCE, COMMERCIAL PAPER, AND T-BILL RATES. 5.3% 5.2% BA 5.1% 5.0% Commercial Paper 4.9% 4.8% T-Bills 4.7% 4.6% 4.5% Days to Maturity

13 190 SECTION IV - MONEY MARKETS 11-2: Use the T-Bill quote below to verify the ask yields. TREASURY BILLS Maturity Days to Mat Bid Ask Chg Ask Yld May 18, May 25, June 1, June 8, June 15, June 22, Aug 10, Aug 17, Oct 26, Nov 2, Nov 9, Financial Pages, May 11, 2006 Model Data: A. Begin with the data upon which the model is based. Use the knowledge that Treasury Bills mature every Thursday. So all we need to enter is the date of the quote. Do this in A1 B. To begin enter 7 in B3. B4 is set to = B3 + 7 and drag the formula down the column until we reach 182 days to maturity. C. Calculate the Maturity by setting A4 to = $A$1 + B4 This gives us the date 7 days from the quote date. Drag the formula down the column. Use [format] to format the date with the day of the week. D. To automate the list replace B3 with =IF(WEEKDAY(A1,1)>4, 12-WEEKDAY(A1,1), 5-WEEKDAY(A1,1)) The WEEKDAY function returns the day of the week. If the day of the week is greater than 4 (Wednesday) then subtract this number from 12, otherwise subtract it from 5. E. Test the spreadsheet so far by entering several dates at random into A1. Regardless of the date, the maturity column should show the next 26 Thursdays. Parameters: F. Enter the ask rates. There s nothing you can do about this, you just have to type it in. Make sure that you either enter the quotes as percent (4.47%) or as mathematical equivalent (0.0447).

14 CHAPTER 11 - MONEY MARKET INSTRUMENTS 191 Dependent values: G. Build the formula. There are two ways to do this. You can build the components of the formula in separate columns or you can build the formula one step at a time. We do both. H. To build one step at a time: A. = (B4*C4/360) this calculates the discount or interest B. = (1-(B4*C4/360)) this calculates the discounted price or investment C. = (B4*C4/360)/(1-(B4*C4/360)) this calculates the holding period return I. The Money Market and Ask Yield can then be calculated from the Holding Period Return J. Drag down these formulae to complete the table. A B C D F G 1 May 11, 2006 Holding Money Market Period Ask 2 Date Days to Mat Ask Yield Return Yield 3 Thursday, May 18, % 0.09% 4.47% 4.54% 4 Thursday, May 25, % 0.18% 4.55% 4.61% 5 Thursday, June 1, % 0.26% 4.54% 4.61% 6 Thursday, June 8, % 0.36% 4.61% 4.67% 22 Thursday, October 26, % 2.29% 4.91% 4.98% 23 Thursday, November 2, % 2.39% 4.93% 4.99% 29 Thursday, November 9, % 2.50% 4.95% 5.02% Excel skills: Formula Building

15 CHAPTER 12 - PRICES AND YIELDS 207 Chapter 12 - Spreadsheet Exercises 12-1: Build a Business Calculator bond spreadsheet. Model Data: A. Set up the titles and descriptions. Begin with a bond we know, so use the 4 year 6% coupon bond. B. Use [format][cell][date] to set the date formats. C. To set up the 360/ACT and the payments per year use the validator. A. In cell C6 click on [Data][Validation][Settings] B. Under Allow choose [List] and then indicate as source A16:A17 C. Now when you click in C6 a drop down box appears giving you a range of valid choices. D. Do the same thing in C7 with the source A19:A21 Notice that we have allowed for four payments per year as well as than the one and two payments per year our calculator allows. D. To translate these choices into codes use =VLOOKUP() A. In cell B6 use =VLOOKUP(C6,A16:B17,2,false). This function tells excel to look for the value in C6 in the first column of the table defined by A16:B17 and returns the value in column 2. The false means that vlookup should find an exact match. B. Test this to make sure that when you choose ACT the code is 1 and when you choose 360 the code is 0. This code translates our ACT/360 into excel speak. C. In cell C6 vlookup the number of payments per year. E. Set up Yield to calculate price and price to calculate yield. You can shade the calculation cells to highlight the cells you should not overwrite. Calculate Price and Yield A. In C9 use the =PRICE() formula. Click on [Insert] [Function] or click on the [fx] icon in the toolbar. B. Look under [Financial] If there are no financial formulae then you need to switch them on. To do this click on [Tools][Add-Ins] and make sure that both Analysis Toolpak and Solver Add-In are clicked. C. Under Financial functions choose =PRICE() and click on [OK]. This will bring up the form into which you can enter the cell addresses for each variable in the formula. For frequency enter B7 and for basis enter B6. D. When you complete the form and click on [OK] the formula in C9 should be =PRICE(C2,C4,C3,C8,C5,B7,B6). E. Follow the same procedure in C13 but use =YIELD() rather than =PRICE(). Test A. Change the data at random and check the results against your Business Calculator.

16 208 SECTION V - DEBT MARKETS 12-2: Add to your spreadsheet from 12-1 a price yield curve. Model Data: A. Start with the Bond Calculator from B. Enter Yields in column E. Enter 0%, 1%, 2% to establish the pattern and copy down until you get to 20% C. Calculate prices into column F. A. Since you know the function you can enter =PRICE() into F2. Excel will return #N/A. Click on [fx] and the price function applet opens up. B. Since we will be copying this formula down the column we need to lock the cell references where necessary. This is easiest if you click in the cell reference and then hit your computer s [F4] key. The [F4] key locks both the column and the row so C2 becomes $C$2 with a single keystroke. C. Lock everything in the formula except the yield. D. The formula should be =PRICE($C$2,$C$4,$C$3,E2,$C$5,$B$7,$B$6) E. Copy this formula down column F Graph: A. Highlight E1 to F22 and use the chart wizard. B. Choose the XY(scatter) graph C. Adjust the x axis so that it goes from 0% to 20% D. Test by changing the bond information and watching as the Price Yield Curve changes. A B C D E F G H I 1 BOND CALCULATOR YIELD PRICE 2 Settlement Date SDT Aug 15, % Coupon CPN 6.00% 1% Redemption Date RDT Aug 15, % Redemption Value RV % ACT 4% /Y 5% Yield YLD 8.00% 6% Price PRI % % % Price PRI % Yield YLD 8.50% 11% % Calculator Codes 13% ACT 1 14% % % /Y 1 17% /Y 2 18% /Y 4 19% % 56.99

17 CHAPTER 14 - DURATION 231 Chapter 14 - Spreadsheet Exercises 14-1: Calculate the bond price, duration, modified duration, and convexity of a semi-annual coupon bond. Begin with a principal value of $10,000., coupon rate of 5%, and maturity of 5 years. Price the bond to yield 7% Model Data: A. Enter the bond and market information. To ensure that you get a five year bond use for the maturity date a date exactly five years later. =EDATE(B7,12*5) The EDATE formula adds a specific number of months to any date. Duration Calculation A. Begin with the time column. Enter 1, 2, 3 and then coy down to continue the series. B. Calculate the cash flow from the bond data. To test this change the principal and coupon rate and make sure that the cash flow changes accordingly. C. Calculate the Net Present Value. The best way is to build the formula one step as a time. Begin with =$B$8. Then add the /2. Then add the (1+ ) et cetera. Eventually F2 is calculated as =E2/((1+($B$8/2))^D2) and you have checked that the formula is logically constructed. The $ anchors the cell address to the market yield as the formula is copied down the column. D. Bond Prices are rounded to the nearest penny, so calculate the total as =ROUND(SUM(E2:E10),2). This rounds the actual total to 2 decimal places rather than showing 2 decimal places but calculating to 16 decimal places. E. Calculate the percentage of investment the same way. Thus G2 is calculated as =F2/$F$12. Check that the total of the column is 1.00 F. Calculate the duration; thus H2 is calculated as =D2*G2. G. Calculate the convexity; thus I2 is calculated as =D2*(1+D2)*G2 Verification: A. We can double check our calculations by using Excel s built in functions. So in F13 we calculate the bond price with the =PRICE() formula. C11 is thus calculated as =PRICE(B7,B4,B3,B8,100,2,0)*B2/100. The PRICE function calculates the price of the bond just as does the business calculator; the *B2/100 calculates the price of the bond with the principal value in B2. B. Double check the duration by using the =DURATION() function. To make this easier enter =Duration(). Excel resolves this as #N/A. Then click on the function icon [fx] to generate the formula applet in which you can build the formula from cell references. Test: A. Test the model by changing the parameters. Change the coupon rate to 9%, the principal to $10,000., the market yield to 8%, the market date to =now(). In each case the price you calculate with the model, the price you calculate using the =PRICE() function, and the price you calculate with your financial calculator should be equal. Excel skills: Model Building

18 232 SECTION V - DEBT MARKETS A B C D E F G H I 1 BOND Time Cash Flow NPV % Duration Convexity 2 Principal: $1, Coupon: 5% Maturity: August 15, MARKET Date: August 15, Yield: 7% Analytics Price: , Duration: Totals: Convexity:

19 CHAPTER 14 - DURATION : Generate the tangent to the Price Yield Curve of a bond. Model Data: A. Set up a bond and generate the Price Yield Curve. Calculations: B. Set up a second Price column into which we can calculate a price estimate using modified duration. C. Build the formula for the price estimate using the equation )P = Modified Duration * )Y * P D. The formula for F2 should be =$B$11+($B$13*(B$9-D2)*$B$11) E. Add the estimate to the graph using from the chart menu [Source Data] [Series] [Add] F. Some of the values will be silly - like negative prices. This illustrates the limitations of using modified duration to estimate price changes over large variations in yields. G. Experiment with different yields to see how the tangency line moves along the curve. Embellishments: H. We can add a current price and yield indicator by setting up a third data series in columns H and I I. Enter 0% into H2. H3 and H4 equal the yield in =$B$9 J. Enter 0 into I4. I2 and I3 equal the price calculated into =$B$11 K. Use [Source Data] [Series] [Add] to add this series to the graph. L. Edit data series to de-click [smoothed line]. You can also change the pattern to a dotted line M. Now as you change the parameters of the bond or the yield the current price and yield is mapped out. A B C D E F G H I 1 BOND Yield Price Estimate Yield Price 2 Principal: 0% % Coupon: 6.00% 1% % Maturity: Aug 15, % % 0 5 3% % MARKET 5% Date: Aug 15, % Yield: 6% 7% % Price: % Duration: % Modified Duration: % % % % % % % (7.80) 20 18% (17.60) 21 19% (27.40) 22 20% (37.20)

20 234 SECTION V - DEBT MARKETS FIGURE 14-9: THE PRICE YIELD CURVE AND TANGENCY LINE REPRESENTING THE PRICE ESTIMATE FROM MODIFIED DURATION Price 250 Price Yield Curve Yield - 0% 2% 4% 6% 8% 10% 12% 14% 16% 18% 20% (50)

21 254 SECTION V - DEBT MARKETS Chapter 16 - Spreadsheet Exercises 16-1: Build a bond yield calculator including accrued interest. Model Data: A. Enter the Bond (Principal, Coupon, and Maturity Date) and Market Information (Price and Settlement Date). Parameters: B. Enter the parameters for the type of bond in cells B18:C20. Treasury Securities price on actual days in the year. This is basis code 1 in the excel functions =PRICE(), =YIELD() et cetera. US Corporate Bonds trade 30/360 with the 31 st counted as the 1 st of the following month. This is basis code 0 in the excel functions. European Corporate Bonds trade 30/360 with the 31 st counted as the 30 th of the month. C. Cell B7 is constrained to these three choices with [Data][Validation] Settings [List] with the source defined as B18:B20 D. Set a hidden code in A7 with a =VLOOKUP(). Test this parameter by selecting the type of bond with the drop down box in B7. Verify that A7 shows the correct code in every instance. Hide the code by setting the color of the type to white. Calculator: E. This spreadsheet uses a number of built-in excel functions. A. =COUPDAYS() Number of days in the semi-annual period. B. =COUPDAYBS() Number of days from the previous coupon payment to the settlement date. C. =COUPDAYSNC() Number of days from the settlement date to the next coupon payment. D. =COUPPCD() Date of the previous coupon payment E. =COUPNCD() Date of the next coupon payment F. =COUPNUM() The number of coupon payments remaining to maturity F. The accrued interest is calculated from the coupon, the days to accrue, and the days in the semi-annual period. G. Verify that the answers given by your excel calculator are the same as those given by your business calculator. Excel skills: Bond Formula Building

22 CHAPTER 16 - BUYING AND SELLING BONDS 255 A B C D E 1 BOND INFORMATION BOND CALCULATOR 2 3 Principal $ 1,000,000 Base Price: $ 987, Coupon 6.000% Accrued Interest: $ 19, Maturity August 15, 2005 Invoice Price: $ 1,007, US Corporate Coupon: $ 30, Last Coupon Date: February 15, Next Coupon Date: August 15, Coupons Remaining: 3 11 MARKET INFORMATION 12 Days to Accrue: Price Days to Next Coupon: Settlement June 13, 2004 Days in Semi-Annual Period: Nominal Yield: 6.000% 17 EXCEL FUNCTION CODES Income Yield: 6.076% 18 Treasury 1 Yield to Maturity: 7.120% 19 US Corporate 0 20 European Corporate 4 21

23 CHAPTER 17 - GOVERNMENT BONDS 265 Chapter 17 - Spreadsheet Exercises 17-1: Build a spreadsheet designed to graph the composition of asset categories in the financial markets as specified in the Table 17-1: Securities Outstanding for any specified year. Model Data: A. Enter the data into the spreadsheet Parameters: B. The key to this assignment is to generate a graph on-the-fly from the data given whenever a specific year is chosen. C. To do this we need the =INDEX() function. =INDEX() locates the value at the intersection of a specified row (category) and column (year). D. Set up a subset with the numbers 1 through 7 in column A, categories in column B, and the year at the top of column C. Remember to use cell addresses (Cell B3 is =B20 for example). E. In C1 use [Data][Validate] to set up a drop down box that restricts choice to $C$19:$I$19 F. To translate the year chosen into the column number use =MATCH($C$1,$C$19:$I$19,0) in C2. The =MATCH() function returns the relative position of the year chosen in C1 in the array C19:I19. G. Set C3 =INDEX($C$14:$I$20,A3,C$2). This goes to the array C14:I20 and finds the value in row (category number in A3) and column (year number in C2). H. Test by changing the year a number of times and then copy down the column. Graph: I. Use the chart wizard to generate a graph from the data in B3:C9. J. When you select a different year in C1 the numbers and the chart both will change accordingly. K. For the pie chart use [Format data Series][Data Labels] Category Names and Percentages. Then move the labels slightly and excel will automatically add the connecting lines. Excel skills: Lookup and Match Functions

24 266 SECTION VI - DEBT MARKET INSTRUMENTS A B C D E F G H I 1 Year -> US Treasury Securities 3, Federal Agency Debt 2, Municipal Debt 2, Mortgage Backed Securities 5, Asset Backed Securities 1, Money Market Instruments 2, Corporate Debt 4, TOTAL 23, US Treasury Securities 2,196 3,307 2,967 2,968 3,205 3,575 3, Federal Agency Debt ,852 2,143 2,359 2,637 2, Municipal Debt 1,184 1,294 1,481 1,604 1,765 1,892 2, Mortgage Backed Securities 1,333 2,352 3,565 4,126 4,705 5,309 5, Asset Backed Securities ,072 1,281 1,543 1,694 1, Money Market Instruments 1,157 1,177 2,661 2,542 2,551 2,526 2, Corporate Debt 1,350 1,938 3,372 3,836 4,096 4,462 4, TOTAL 7,745 11,229 16,970 18,500 20,224 22,095 23,586 22

25 CHAPTER 17 - GOVERNMENT BONDS 267 FIGURE 17-1: GRAPHS GENERATED FROM THE SPREADSHEET FOR 2004 Money Market Instruments 12% Corporate Debt 20% 2004 US Treasury Securities 17% Federal Agency Debt 12% Asset Backed Securities 8% Mortgage Backed Securities 22% Municipal Debt 9% Corporate Debt Money Market Instruments Asset Backed Securities Mortgage Backed Securities Municipal Debt Federal Agency Debt US Treasury Securities - 1,000 2,000 3,000 4,000 5,000 6,000

26 CHAPTER 24 - OPTIONS 391 Chapter 24 - Spreadsheet Exercises 24-1: Build a payout graph that can be used for all four basic option positions for any strike price between $10 and $90. Show both the value and the profit line. Model Data: A. Set up a spreadsheet with input areas for buy/write, put/call, exercise price, and option premium. Use [Data] [Validation] to restrict B1 to Buy and Write and to restrict B2 to Put and Call. These can be coded into D1:D2 and E1:E2 and then set the foreground color to white to hide them. B. Set up stock prices (S) from $0 to $100 C. Restrict the strike price to values between $10 and $90 by using [Data][Validation] Decimal, between, and then set the minimum to =A10 and the maximum to =A18. This way if you change the prices of the underlying stock then you the allowable range of strike prices will change as well. D. Add Value and Profit columns. Understanding the Relationships E. When setting up this type of spreadsheet it is best to start by summarizing the relationships involved. So we set up a table with the following information OPTION Buy Call Put Write Set Basic Values and Graph F. Begin with the easiest. Set the parameters to buy and call G. Set the Value to the maximum of 0 and S-X: =MAX(0,A9-$B$3). H. Set the Profit to the Value minus the premium =B9-$B$4 I. Set the Breakeven price to equal the exercise price plus the premium =B3+B4 J. Generate the graph K. Change the strike price and premium to test the responsiveness of the graph. Expand to Conditional Values L. The Value of the option depends both on the buy/write and on the put/call data so build and test one at a time. M. First use an =IF() to test for put or call: A. The formula =IF($B$2="Call",MAX(0,A9-$B$3),MAX(0,$B$3-A9)) checks to see if the option is coded to a call. If yes then the value is calculated as =MAX(0, S-X); if no then the option is a put and the value is calculated as =MAX(X-S) B. The formula =IF(B2="Call",B3+B4,B3-B4) does the same check for the breakeven price. Double check the result by putting the breakeven price into one of the prices in A9:A19. N. Next use a second =IF() to test for buy or write A. The formula =IF($B$2="Call",MAX(0,A9-$B$3),MAX(0,$B$3-A9)) * IF($B$1="Buy",1,-1)*combines two =IF()

27 392 SECTION VIII - OPTIONS MARKETS statements. The first is the one we developed to test for put or call. The second checks to see if the option is a buy. If yes then multiply by 1, if no then multiply by -1. The multiply by -1 turns all the positive values realized by the buyer on exercise into losses for the writer. B. The formula =(IF($B$1="buy",-1,1)*$B$4)+B9 does the same check for the profit line. The -1 subtracts the premium if the option is a buy; the 1 adds the premium if the option is a write. O. We can change the graph to show the payout per contract rather than per share by multiplying all results in Value and Profit by 100. Excel skills: Flying Changes A B C D E 1 Position: Buy Put Buy 2 Option: Call Call Write 3 Strike Price: $ X 4 Premium: $ Breakeven: $ S Value Profit FIGURE 24-11: PAYOUT GRAPH GENERATED FOR A PURCHASED CALL AT $40 Value $70 $60 $50 $40 $30 $20 $10 $- $0 $(10) $10 $20 $30 $40 $50 $60 $70 $80 $90 $100 $(20)

28 CHAPTER 26 - PRICING OPTIONS 425 Chapter 26 - Spreadsheet Exercises 26-1: Create an options pricing calculator for the Black Scholes option ricing formula. Model Data A. Begin with the data needed in the Black Scholes formula. Begin with the data used in the example so that we can verify results step by step. B. Time in C4 is forced to a fraction of the format?/365 to emphasize the unit of measurement. To force the format use [Format] [Cells] [Fraction] and pick as eighths. Then pick custom and change the 8 to 365. C. To get the sigma in B6 use [Insert] [symbol] and choose from [Basic Greek]. Use the same procedure to get the square root symbol from [Mathematical Operators]. Calculations D. Calculate the sub steps in the Black Scholes Formula. This allows us to verify steps along the way and to use intermediate results like the delta hedge ratio. A. Note that 91 days is actually years. To make sure that we get the same numbers as in the textbook example enter.25 rather than 91/365. After the spreadsheet is built and the formulae verified we can come back and change it. B. To get the superscript in the F 2 enter F2 in the label and edit it in the formula space in the menu bar at the top of the spreadsheet. Highlight the 2 and click on [Format][Cells] and click on [Superscript]. E. Use =NORMSDIST() to get the cumulative normal distribution to d 1 and d 2. To verify the example in the text use =ROUND(,2) to round d 1 and d 2. F. In calculating the Call and Put prices use =ROUND(,2) to round the result to the nearest penny Excel skills: Model Building A B C D E F 1 Model Data Call Option 2 Stock Price S $ Price $ Exercise Price X $ In the Money 28.8% 4 time t 91/365 Out of the Money 71.2% 5 interest rate r 5.0% Delta Hedge Ratio: 36 6 standard deviation σ 40% 7 8 Calculations Put Option 9 ln (S/X) Price $ (r + σ 2 /2) t In the Money 71.2% 11 σ%t 0.2 Out of the Money 28.8% 12 d N[d 1 ] d N[d 2 ] e -rt