Question

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 50%.

Suppose an analyst studies 20 stocks and finds that one-half have an alpha of 4.6%, and one-half have an alpha of –4.6%. The analyst then buys $1.2 million of an equally weighted portfolio of the positive-alpha stocks and sells short $1.2 million of an equally weighted portfolio 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.)

Expected return:

Standard deviation:

b-1. How does your answer for standard deviation change if the analyst examines 50 stocks instead of 20? (Enter your answer in dollars not in millions. Do not round intermediate calculations. Round your answer to the nearest dollar amount.)

Standard deviation:

b-2. How does your answer for standard deviation change if the analyst examines 100 stocks instead of 20? (Enter your answer in dollars not in millions.)

Standard deviation:

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 50 % Suppose an analyst studles 20 stocks and finds that one-half have an alpha of 4.6 %, and one-half have an alpha of -46 % The analyst then buys $1.2 million of an equally welghted portfollo of the positive-alpha stocks and sells short $1.2 milion of an equally welghted 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.) Expected return Standard deviation b-1. How does your answer for standard deviation change if the analyst examines 50 stocks Instead of 20? (Enter your answer in dollars not in millions. Do not round intermediate calculations. Round your answer to the nearest dollar amount.) Standard deviation b-2 How does your answer for standard devlation change If the analyst examines 100 stocks Instead of 20? (Enter your answer in dollars not in millions.) Standard deviation

Answer 1

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Fill Z Paste Styles Cells ke - Microsoft Excel (Product Activation Failed) File Home Insert Page Layout Formulas Data Review View Add-Ins - 2x % Cut Σ AutoSum : A Calibri -11AA = = = Dr Wrap Text General Ea Copy BI U D- DA E E E s FMerce Merge & Center - Center $ % % , 4.0 .00 :.: Conditional Format Cell Format Painter Insert Delete Format Sort & Find & Formatting as Table Styles 2 Clear Filter Select Clipboard Font Alignment Number Editing UT416 USUT UU UVUW UX - UY UZ VA VB vc UD VE 416 417 If alpha = a(p) then for the long component we have R(p) = a(p) + B(p) *R(m) 418 Variance = no of stocks x (position in each stock x standard deviation)? 419 Shorting equally the 10 negative-alpha stocks and investing the proceeds equally in the 10 positive-alpha stocks eliminates the market 420 exposure and creates a zero-investment portfolio 421 422 ALL STOCKS HAVE BETA = 1 423 424 THE EXPECTED RETURN ON 20 STOCKS = 1200000 x [.046 +1.0 Rm)-1200000 x [-.046 + 1.0 Rm] 425 55200 + 1200000Rm + 55200 - 1200000Rm = 110400 426 427 428 The sensitivity of the payoff of this portfolio to the market factor is zero because the exposures of the positive alpha and negative alpha 429 stocks cancels out 430 431 Thus, the systematic component of total risk also is zero. The variance of the analyst's profit is not zero, however, since this portfolio 432 is not well diversified. For n = 20 stocks (i.e., long 10 stocks and short 10 stocks) the investor will have a $120,000 position 433 (either long or short) in each stock (1200000/10). Net market exposure is zero, but firm-specific risk has not been fully diversified 434 HO N KE CAPM UTILITY, SHARPE, beta convexity DGM beta port future INDEX INTL CAP BUD LEASING PV, FV, ANNUITY DIR right clean YIELD bond portfolio cap stru WACC RESI Rea ferences: AG470 |00130% - ED B * * O ENG 04-11-2019

ke - Microsoft Excel (Product Activation Failed) Add-Ins View - 2x Dr General File Home Insert Page Layout Formulas Data Review * Cut Calibri -11AA = = = E Copy Paste B Format Painter I U - D A Clipboard Font Wrap Text Merge Merge & Center Center Σ AutoSum : A Fill 2 Sort & SF $ - % % 4:0 .00 8. Insert Delete Format Conditional Format Formatting as Table Styles Cell Styles 2 Clear Filter Editing Find & Select Alignment Number Cells VB449 US UT UU UV UW UX UY UZ VA VB VC VD VE The variance from the positions in the 20 firms is : 20 x (120,000 x 0.50)^2 = and the standard deviation is = SQRT (VARIANCE) = 72000000000 268328 434 435 436 437 438 a 439 EXPECTED RETURN = STANDARD DEVIATION = 110400 268328 48000 440 441 b-1 442 If n = 50 stocks (25 long and 25 short), $48,000 is placed in each position (1200000/25) The variance from the positions in the 50 firms is: 50 X (48000 X 0.50)^2 = And the standard deviation is = 28800000000 169706 443 444 445 b-2 446 447 Similarly, if n = 100 stocks (50 long and 50 short), $24,000 (1200000/50) is placed in each position The variance is : 100 x ($24,000 x 0.50)^2 = The standard deviation is = 14400000000 120000 448 449 450 451 452 HO Rea N convexity DGM betaport future INDEX INTL CAP BUD LEASING PV, FV, ANNUITY DIR right clean KE CAPM UTILITY, SHARPE, beta ferences: AG470 YIELD bond portfolio cap stru WACC BO 130% RESI el - x 9 m * OENG 04-11-2019