Question

Need a help with both parts pelase.

Assume the return on a market index represents the common factor and all stocks in the economy have a beta of 1. Firm-specific returns all have a standard deviation of 47 % Suppose an analyst studies 20 stocks and finds that one-half have an alpha of 45 %, and one-half have an alpha of-4.5 %. The analyst then buys $1.5 million of an equally weighted portfolio of the positive-alpha stocks and sells short $1.5 million of an equally weighted portfollo of the negative-alpha stocks a. What is the expected return (in dollars), and what is the standard deviation of the analyst's profit? (Enter your answers in dollars not in millions. Do not round intermediate calculations. Round your answers to the nearest dollar amount.)

I need help with b1 and b2. Thank you.

Answer 1

SEE THE IMAGE. ANY DOUBTS, FEEL FREE TO ASK. THUMBS UP PLEASE

ke - Microsoft Excel (Product Activation Failed) Review File Home Insert Page Layout Formulas Data View Add-Ins Σ AutoSum - Cut AS EWrap Text Calibri 11 General E Copy Fill Merge & Center Insert Delete Format Paste B I U +.0 .00 .00 0 Conditional Format Cell Sort & Find & % Format Painter Clear Filter Select Formatting as Table Styles Editing Clipboard Font Alignment Number Styles Cells UW449 VC US UT UV UW UX UY UZ VA VB VD VE VF 449 450 451 452 If alpha a(p) then for the long component we have R(p) a(p) + B(p)*R(m) Variance no of stocks x (position in each stock x standard deviation)2 453 Shorting equally the 10 negative-alpha stocks and investing the proceeds equally in the 10 positive-alpha stocks eliminates the market 454 455 exposure and creates a zero-investment portfolio 456 457 ALL STOCKS HAVE BETA = 1 458 THE EXPECTED RETURN ON 20 STOCKS 1500000 x [.0451.0 Rm]-1500000 x [-.045 1.0 Rm] 459 460 67500 1500000Rm 67500 - 1500000Rm = 135000 461 462 The sensitivity of the payoff of this portfolio to the market factor is zero because the exposures of the positive alpha and negative alpha 463 464 stocks cancels out 465 466 Thus, the systematic component of total risk also is zero. The variance of the analyst's profit is not zero, however, since this portfolio 20 stocks (i.e., Iong 10 stocks and short 10 stocks) the investor will have a $150,000 position (either long or short) in each stock (1500000/10). Net market exposure is zero, but firm-specific risk has not been fully diversified is not well diversified. For n = 467 468 469 CONvexity DGMbeta LEASING PV, FV, ANNUITY RESI e KE CAPM UTILITY, SHARPE, beta INTL CAP BUD YIELD bond portfolio port future INDEX DIR right clean cap stru WACC Rea erences: AG470 120% WA 07:54 TENG 08-11-2019

ke - Microsoft Excel (Product Activation Failed) Review File Home Insert Page Layout Formulas Data View Add-Ins Σ AutoSum - Cut AS Wrap Text Calibri 11 General Copy Fill Merge & Center Insert Delete Format Paste B I U $ % , +.0 .00 .00 0 Conditional Format Cell Sort & Find & Format Painter Clear Filter Select Formatting as Table Styles Clipboard Number Editing Font Alignment Styles Cells UW465 VB US UT UV UW UX UY UZ VA VC VD VE VF 465 Thus, the systematic component of total risk also is zero. The variance of the analyst's profit is not zero, however, since this portfolio 466 467 is not well diversified. For n 20 stocks (i.e., long 10 stocks and short 10 stocks) the investor will have a $150,000 position (either long or short) in each stock (1500000/10). Net market exposure is zero, but firm-specific risk has not been fully diversified 468 469 The variance from the positions in the 20 firms is : 20 x (150,000 x 0.47)^2 = 470 99405000000 471 SQRT (VARIANCE) = and the standard deviation is = 315286 472 473 a 135000 EXPECTED RETURN = STANDARD DEVIATION = 315286 474 475 If n 50 stocks (25 long and 25 short), $60,000 is placed in each position (1500000/25) 50 X (60000 X 0.47)^2 = 476 b-1 The variance from the positions in the 50 firms is 477 39762000000 And the standard deviation is 478 199404 479 Similarly, if n 100 stocks (50 long and 50 short), $30,000 (1500000/50) is placed in each position 480 b-2 The variance is: 100 x ($30,000 x 0.47)^ 2 = 481 19881000000 The standard deviation is = 482 141000 483 484 485 RESI e KE CAPM UTILTY, SHARPE, beta YIELD bond portfolio CONVEXITY DGM beta LEASING PV, FV, ANNUITY КE САРМ port future INDEX DIR right clean cap stru WACC INTL CAP BUD Rea erences: AG470 120% WA X 07:54 TENG 08-11-2019