I need question one answered. Attached are documents from the chapter to help add in the question.

A 1 D E F Final Examination FINC 5880 3 5 6 7 8 9 10 11 C Question 6. (15 points) Your portfolio is diversified. It has an expected return of 10.0% and a Session Corporation at $30 a share to your portfolio. beta of 1.10. You want to add 500 shares of Tundra9 Tundra has an expected return of 14.0% and a beta of 1.30. The total value of your current portfolio is $50,000. a. Calculate the expected return on the portfolio after the purchase of the Tundra stock? 12 13 14 15 16 17 18 19 20 b. Calculate the expected beta on the portfolio after you have added the new stock? c. Is your portfolio less risky or more risky than the market? Explain. 21 22 23 24 25 26 27 d. Will your portfolio likely outperform or underperform the market in a period when stocks are rapidly falling in value? Explain. 10.00% 1.1 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 G Name______________________________________ 2 4 B e. Is beta always an accurate predictor of a portfolio's performance? Explain? Old Expected return Old Beta Tundra shares 500 @ $30 a/ shar Tundra's expected return Tundra's beta Total value of current portfolio 10.00% 1.10 15000 14.0% 1.30 $50,000 Portfolio: expected return Park's beta #DIV/0! A 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 B C D E F G A B C D E 1 Tool Kit Chapter 25 2 Portfolio Theory and Asset Pricing Model 3 4 5 6 25-1 Efficient Portfolios 7 8 PORTFOLIO RISK AND RETURN: THE TWO-ASSET CASE 9 10 Suppose there are two assets, A and B. wA is the percent of the portfolio invested in 11 asset A. Since the total percentages invested in the assets must add up to 1, (1-w A) is 12 the percent of the portfolio invested in asset B. 13 14 The expected return on the portfolio is the weighted average of the expected returns 15 on asset A and asset B. 16 17 18 ^ ^ ^ 19 20 r p w A r A (1 w A ) r B 21 22 23 24 The standard deviation of the portfolio, p, is not a weighted average. It is: 25 26 27 2 2 2 p WA A (1 WA ) 2 B 2WA (1 WA ) AB A B 28 29 30 31 32 33 ATTAINABLE PORTFOLIOS: THE TWO ASSET-CASE 34 Asset A Asset B 35 5% 8% 36 Expected return, r hat 4% 10% 37 Standard deviation, 38 39 40 Using the equations above, we can find the expected return and standard deviation of 41 a portfolio with different percentages invested in each asset. 42 43 F 12/9/2012 G H I J K L M N O P Q R S T A B 44 Correlation = 45 Proportion of Portfolio in Security A (Value of wA) 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 1.00 0.90 0.80 0.70 0.60 0.50 0.40 0.30 0.20 0.10 0.00 C D rp p 1 Proportion of Portfolio in Security B (Value of 1-wB) 0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00 5.00% 5.30% 5.60% 5.90% 6.20% 6.50% 6.80% 7.10% 7.40% 7.70% 8.00% 4.0% 4.6% 5.2% 5.8% 6.4% 7.0% 7.6% 8.2% 8.8% 9.4% 10.0% AB = +1: Attainable S et of Risk/Return Combinations 10% B Expected return 5% A 0% 3% Correlation = 4% 6% 8% 10% Risk, 7% 5% p 9% 11% 0 79 Proportion of Portfolio in Security A (Value of wA) 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 Proportion of Portfolio in Security B (Value of 1-wA) 1.00 0.90 0.80 0.70 0.60 0.50 0.40 0.30 0.20 0.10 0.00 rp 0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00 p 5.00% 5.30% 5.60% 5.90% 6.20% 6.50% 6.80% 7.10% 7.40% 7.70% 8.00% 4.0% 3.7% 3.8% 4.1% 4.7% 5.4% 6.2% 7.1% 8.0% 9.0% 10.0% AB = 0: Attainable Set o f Ris k/Return Co mbinatio ns 10% B Expected return 5% A 0% 3% 4% 5% 6% 8% 10% 7% 9% 11% Ris k, p E F G H I J K L M N O P Q R S T A 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 10% B C D E F G H I B Expected return 5% A 0% 3% Correlation = 4% 5% 6% 8% 10% 7% 9% 11% Ris k, p -1 Proportion of Portfolio in Security A (Value of wA) Proportion of Portfolio in Security B (Value of 1-wA) rp p 4.0% 112 2.6% 113 1.2% 114 0.2% 115 1.6% 116 3.0% 117 4.4% 118 5.8% 119 7.2% 120 8.6% 121 10.0% 122 123 124 AB = -1: Attainable S e t of Risk/Return Combinations 125 126 10% 127 128 B Expecte d re turn 129 130 131 5% 132 A 133 134 135 136 0% 137 2% 6% 10% 138 0% 4% p 8% 12% Risk, 139 140 141 142 Figure 25-1 143 Expected Return and Standard Deviation under Various Assumptions 144 Proportion of p 145 Proportion of Portfolio in Portfolio in Security A Security A Case I Case II Case III 146 _ (Value of wA) (Value of 1 wA) AB = +1.0 AB = 0.0 AB = 1.0 147 1.00 0.00 5.00% 4.0% 4.0% 4.0% 148 0.75 0.25 5.75% 5.5% 3.9% 0.5% 149 0.50 0.50 6.50% 7.0% 5.4% 3.0% 150 0.25 0.75 7.25% 8.5% 7.6% 6.5% 151 0.00 1.00 8.00% 10.0% 10.0% 10.0% 152 153 154 25-5 Calculating Beta Coefficients 155 156 157 downloaded stock prices from http://finance.yahoo.com for General 158 Weticker symbol, GE. We alsoand dividendsdata for the S&P 500 (^SPX) which contains Electric using its downloaded most actively 159 traded stocks, and the Fidelity Magellan mutual fund (FMAGX). We computed returns, as shown in 160 Chapter 6. We also obtained the monthly rates on 3-month Treasury bills from the FRED II data base 161 at the St. Louis Federal Reserve, http://research.stlouisfed.org. 162 1.00 0.90 0.80 0.70 0.60 0.50 0.40 0.30 0.20 0.10 0.00 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 Date January 2012 December 2011 November 2011 October 2011 September 2011 August 2011 July 2011 June 2011 May 2011 April 2011 March 2011 February 2011 January 2011 December 2010 November 2010 October 2010 September 2010 August 2010 July 2010 June 2010 May 2010 April 2010 March 2010 February 2010 January 2010 December 2009 November 2009 October 2009 September 2009 August 2009 July 2009 June 2009 May 2009 April 2009 0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00 5.00% 5.30% 5.60% 5.90% 6.20% 6.50% 6.80% 7.10% 7.40% 7.70% 8.00% rM, Market Return (S&P 500 Index) ri, GE Return 4.4% 4.5% 0.9% 13.6% -0.5% -4.8% 10.8% 9.8% -7.2% -5.8% -5.7% -8.9% -2.1% -5.0% -1.8% -3.2% -1.4% -4.0% 2.8% 2.0% -0.1% -4.2% 3.2% 4.6% 2.3% 10.1% 6.5% 16.4% -0.2% -1.2% 3.7% -1.4% 8.8% 13.1% -4.7% -10.2% 6.9% 11.8% -5.4% -11.3% -8.2% -13.3% 1.5% 3.6% 5.9% 13.3% 2.9% 0.5% -3.7% 6.2% 1.8% -4.9% 5.7% 12.3% -2.0% -13.1% 3.6% 18.8% 3.4% 3.7% 7.4% 14.4% 0.0% -12.4% 5.3% 6.6% 9.4% 25.1% rRF, Risk-Free rp, Fidelity Rate (Monthly Magellan Return on 3Fund Return Month T-Bill) 6.0% 0.00% -0.3% 0.00% -2.3% 0.00% 10.8% 0.00% -11.6% 0.00% -7.7% 0.00% -1.5% 0.00% -3.6% 0.00% -2.2% 0.00% 2.5% 0.01% -0.4% 0.01% 4.2% 0.01% 1.6% 0.01% 6.6% 0.01% 1.4% 0.01% 3.6% 0.01% 10.8% 0.01% -5.9% 0.01% 5.1% 0.01% -6.5% 0.01% -8.1% 0.01% 1.5% 0.01% 6.6% 0.01% 3.0% 0.01% -4.4% 0.01% 4.3% 0.00% 5.5% 0.00% -5.4% 0.01% 5.3% 0.01% 2.2% 0.01% 8.8% 0.02% -1.4% 0.02% 6.2% 0.02% 13.7% 0.01% Excess market return (rMrRF) 4.4% 0.9% -0.5% 10.8% -7.2% -5.7% -2.2% -1.8% -1.4% 2.8% -0.1% 3.2% 2.3% 6.5% -0.2% 3.7% 8.7% -4.8% 6.9% -5.4% -8.2% 1.5% 5.9% 2.8% -3.7% 1.8% 5.7% -2.0% 3.6% 3.3% 7.4% 0.0% 5.3% 9.4% Excess stock Excess portfolio return return (ri-rRF) (rp-rRF) 4.5% 13.6% -4.8% 9.8% -5.8% -8.9% -5.0% -3.2% -4.0% 2.0% -4.2% 4.6% 10.1% 16.4% -1.2% -1.4% 13.1% -10.2% 11.8% -11.3% -13.3% 3.6% 13.3% 0.5% 6.2% -4.9% 12.3% -13.1% 18.8% 3.7% 14.4% -12.4% 6.5% 25.1% 6.0% -0.3% -2.3% 10.8% -11.7% -7.7% -1.5% -3.6% -2.2% 2.5% -0.4% 4.2% 1.6% 6.6% 1.4% 3.6% 10.8% -5.9% 5.0% -6.5% -8.1% 1.5% 6.6% 3.0% -4.4% 4.3% 5.4% -5.4% 5.3% 2.1% 8.8% -1.4% 6.2% 13.7% J K L M N O P Q R S T A B C D E F G H I 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 March 2009 February 2009 January 2009 December 2008 November 2008 October 2008 September 2008 August 2008 July 2008 June 2008 May 2008 April 2008 March 2008 February 2008 Minimum Maximum Average 8.5% -11.0% -8.6% 0.8% -7.5% -16.9% -9.1% 1.2% -1.0% -8.6% 1.1% 4.8% -0.6% -3.5% -16.9% 10.8% 0.9% 18.8% -27.8% -25.1% -3.8% -12.0% -23.5% -8.0% -0.7% 6.0% -12.2% -6.0% -11.7% 11.7% -5.4% -27.8% 25.1% -3.2% 13.9% -7.6% -7.5% 4.9% -11.3% -21.6% -18.0% -0.1% -3.9% -8.4% 3.1% 6.5% -2.2% -1.6% -21.6% 13.9% -1.3% 0.02% 0.03% 0.01% 0.00% 0.02% 0.06% 0.10% 0.15% 0.14% 0.16% 0.15% 0.11% 0.11% 0.18% 0.00% 0.18% 0.4% 8.5% -11.0% -8.6% 0.8% -7.5% -17.0% -9.2% 1.1% -1.1% -8.8% 0.9% 4.6% -0.7% -3.7% -17.0% 10.8% 0.5% 18.8% -27.8% -25.2% -3.9% -12.0% -23.5% -8.1% -0.9% 5.9% -12.3% -6.2% -11.8% 11.6% -5.6% -27.8% 25.1% -3.6% 215 Standard deviation (annual) 20.5% Correlation with market return, r R-square Slope 41.2% 0.82 0.67 1.64 25.9% 0.96 0.92 1.21 0.2% -0.21 0.05 0.00 20.6% 1.00 1.00 1.00 41.3% 0.82 0.67 1.64 J K L M N O P Q R S T 13.9% -7.6% -7.6% 4.9% -11.3% -21.7% -18.1% -0.2% -4.1% -8.5% 2.9% 6.4% -2.3% -1.8% -21.7% 13.9% -1.7% 25.9% 0.96 0.92 1.21 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 Using the AVERAGE function and the STDEV function, we found the average historical returns and standard deviations. (We converted these from monthly figures to annual figures. Notice that you must multiply the monthly standard deviation by the square root of 12, and not 12, to convert it to an annual basis.) These are shown in the rows above. We also use the CORREL function to find the correlation of the market with the other assets. Using the function Wizard for SLOPE, we found the slope of the regression line, which is the beta coefficient. We also use the function Wizard and the RSQ function to find the R-Squared of the regression. Using the Chart Wizard, we plotted the GE returns on the y-axis and the market returns on the x-axis. We also used the menu Chart > Options to add a trend line, and to display the regression equation and R2 on the chart. The chart is shown below. We also used the regression feature to get more detailed data. These results are also shown below. GE Analysis Figure 25-8 Calculating a Beta Coefficient for General Electric GE Regression Results using Data Analysis Regression (see columns to right) Beta Coefficient 1.6396 t statistic 9.59 Probability of t stat. 0.000% Lower 95% confidence interval 1.30 Upper 95% confidence interval 1.98 His toric Re alize d Re turns on G E (%) 30% f(x) = 1.6396248705x - 0.0038689749 R = 0.6668184536 0% -30% 0% 30% SUMMARY OUTPUT Regression Statistics Multiple R R Square Adjusted R Square Standard Error Observations 0.8165895258 0.6668184536 0.6595753765 0.069444039 48 Intercept Coefficient t statistic Probability of t stat. Lower 95% confidence interval Upper 95% confidence interval -0.00387 -38.60% 70.1% -0.02 0.02 ANOVA df Regression Residual Total His toric Re alize d Re turns on the Marke t (%) Intercept X Variable 1 SS MS F Significance F 1 0.4439708 0.4439708 92.0628684215 1.49E-012 46 0.2218338 0.0048225 47 0.6658047 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% -0.0038689749 0.0100242 -0.385964 0.7013025072 -0.024047 0.0163087 -0.024047 1.6396248705 0.1708843 9.5949397 1.4908882E-012 1.2956525 1.9835972 1.2956525 -30% Magellan Analysis Figure 25-9 Calculating a Beta Coefficient for Fidelity's Magellan Fund Magellan Regression Results(See columns J-N) Beta Coefficient 1.2074 t statistic 22.35 Probability of t stat. 0.000% Lower 95% confidence interval 1.10 Upper 95% confidence interval 1.32 His toric Realized Re turns on Mage llan (%) 20% Coefficient t statistic Probability of t stat. Lower 95% confidence interval Upper 95% confidence interval 0% -10% 0% 10% -20% -0.00199 -62.90% 53.2% -0.01 0.00 0.9569064382 0.9156699315 0.9138366691 0.0219542474 48 ANOVA df Regression Residual Total 20% Historic Re a lize d Re turns on the Ma rket (%) -10% Regression Statistics Multiple R R Square Adjusted R Square Standard Error Observations Intercept f(x) = 1.2073772635x - 0.0019931964 10% R = 0.9156699315 -20% SUMMARY OUTPUT Intercept X Variable 1 SS MS F Significance F 1 0.2407418 0.2407418 499.475662561 2.42E-026 46 0.0221715 0.000482 47 0.2629133 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% -0.0019931964 0.0031691 -0.628952 0.5324913664 -0.008372 0.0043858 -0.008372 1.2073772635 0.0540239 22.348952 2.4215781E-026 1.0986328 1.3161217 1.0986328 A 299 300 301 302 303 304 305 306 307 308 309 310 311 312 313 314 315 316 317 318 319 320 321 322 323 324 325 326 327 328 329 330 331 332 333 334 335 336 337 338 339 340 341 342 343 344 345 346 347 348 349 350 351 352 353 354 355 356 357 358 359 360 361 362 363 364 365 366 367 368 369 370 371 372 373 374 375 376 377 378 379 380 381 382 383 384 B C D E F G H I J K L M N O P Q R S T The Market Model vs. CAPM We have been regressing the stock (or portfolio) returns against the market returns. However, CAPM actually states that we should regress the excess stock returns (the stock return minus the short-term risk free rate) against the excess market returns (the market return minus the short-term risk free rate). We show the graph for such a regression below. Notice that it is virtually identical to the market model regression we used earlier for GE. Since it usually doesn't change the results whether we use the market model to estimate beta instead of the CAPM model, we usually use the market model. CAPM (excess return) Model Regression Results (See columns J-N) Beta Coefficient 1.6383 t statistic 9.60 Probability of t stat. 0.0% Lower 95% confidence interval 1.29 Upper 95% confidence interval 1.98 Excess Returns on GE, % 30% 20% Coefficient t statistic Probability of t stat. Lower 95% confidence interval Upper 95% confidence interval 0% -20% -10% 0% 10% 20% 1.638 Regression Statistics Multiple R R Square Adjusted R Square Standard Error Observations 30% -0.00367 -0.37 71.6% -0.02 0.02 ANOVA df Regression Residual Total -10% -20% 0.8168331316 0.6672163649 0.6599819381 0.0694503134 48 Intercept f(x) = 1.6382814253x - 0.00366863 R = 0.6672163649 10% -30% SUMMARY OUTPUT Intercept X Variable 1 Excess Ret urns on t he Ma rket , % Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% -0.00366863 0.0100246 -0.365964 0.7160693361 -0.023847 0.0165097 -0.023847 1.6382814253 0.1705914 9.6035385 1.4500626E-012 1.2948987 1.9816642 1.2948987 -30% Table 25-2 Regression Results for Calculating Beta Panel a: General Electric (Market model) Regression Coefficient t Statistic Probability of t Statistic Lower 95% Confidence Interval Upper 95% Confidence Interval Intercept Slope -0.0039 1.6396 -0.39 1.64 0.70 9.59 -0.02 1.30 0.02 1.98 Panel b: Magellan Fund (Market model) Intercept Slope -0.0020 1.2074 -0.63 22.35 0.53 0.00 -0.01 1.10 0.00 1.32 Panel c: General Electric (CAPM: Excess returns) Intercept Slope -0.0037 1.6383 -0.37 9.60 0.72 0.00 -0.02 1.29 0.02 1.98 Note: The market model uses unadjusted returns, the CAPM model uses returns in excess of the risk-free rate. Performance Measures for Magellan Using CAPM (not Market Model) Jensen's Alpha Intercept from CAPM regression -2.31% per year -0.61 t statistic 54.588% Probability that the intercept is not zero Sharpe's Reward-to-Variability Ratio Average annual return in excess of risk-free rate divided by standard deviation Magellan -1.7% -0.07 divided by 25.9% S&P 500 0.5% 0.02 divided by 20.5% Treynor's Reward-to-Volatility Ratio Average annual return in excess of risk-free rate divided by beta Magellan -1.7% -1.4% divided by 1.21 S&P 500 0.5% 0.5% divided by 1.00 LINEST Results: y=mx+b Read me. Slope (m) 1.2069657846 Std. Error of m 0.0539295325 R2 0.9158870005 F 500.88336269 SS Regression 0.2414481506 t-stat for slope Prob of t 22.3804236487 2.281942E-026 SS MS F Significance F 1 0.4448473 0.4448473 92.2279509873 1.45E-012 46 0.2218739 0.0048233 47 0.6667212 -0.0019282515 Intercept (b) 0.0031690892 Std. Error of b 0.0219555155 Std. Error of y 46 Degrees of freedom 0.0221740544 SS Residual -0.6084560453 t-stat for intercept 0.545877996 Prob of t U 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 Upper 95.0% 0.0163087 1.9835972 Upper 95.0% 0.0043858 1.3161217 V U 299 300 301 302 303 304 305 306 307 308 309 310 311 312 313 314 315 316 317 318 319 320 321 322 323 324 325 326 327 328 329 330 331 332 333 334 335 336 337 338 339 340 341 342 343 344 345 346 347 348 349 350 351 352 353 354 355 356 357 358 359 360 361 362 363 364 365 366 367 368 369 370 371 372 373 374 375 376 377 378 379 380 381 382 383 384 Upper 95.0% 0.0165097 1.9816642 V SECTION 25-1 SOLUTIONS TO SELF-TEST Stock A has an expected return of 10 percent and a standard deviation of 35 percent. Stock B has an expected return of 15 percent and a standard deviation of 45 percent. The correlation coefficient between Stock A and B is 0.3. What are the expected return and standard deviation of a portfolio invested 60 percent in Stock A and 40 percent in Stock B? Stock A: expected return Stock A: standard deviation Stock B: expected return Stock B: standard deviation Correlation between A and B % portfolio in A % portfolio in B Portfolio: expected return Portfolio: standard deviation 12% 35% 15% 45% 0.30 60% 40% 13.2% 31.5% SECTION 25-4 SOLUTIONS TO SELF-TEST The standard deviation of stock returns of Park Corporation is 60 percent. The standard deviation of the market return is 20 percent. If the correlation between Park and the market is 0.40, what is Park's beta? Standard deviation of Park Standard deviation of market Correlation between Park and market 12% 15% 0.80 Park's beta 0.64 SECTION 25-7 SOLUTIONS TO SELF-TEST An analyst has modeled the stock of Brown Kitchen Supplies using a two-factor APT model. The riskfree rate is 5 percent, the required return on the first factor (r 1) is 10 percent and the required return on the second factor (r2) is 15 percent. If bi1 = 0.5 and bi2 = 1.3, what is Brown's required return? Risk-free rate r1 r2 b1 b2 Brown's required return 10% 10% 15% 0.50 1.30 16.50%