The following is part of the computer output from a regression of monthly returns on Waterworks...
The following is part of the computer output from a regression of monthly returns on Waterworks stock against the S&P 500 index. A hedge fund manager believes that Waterworks is underpriced, with an alpha of 2.3% over the coming month.
| Beta | R-square | Standard Deviation of Residuals |
| 0.9 | 0.65 | 0.09 (i.e., 9% monthly) |
a. Suppose you hold an equally weighted portfolio of 100 stocks with the same alpha, beta, and residual standard deviation as Waterworks. Assume the residual returns on each of these stocks are independent of each other. What is the residual standard deviation of the portfolio? (Round your answer to 1 decimal place.)
b. Calculate the probability of a loss on a market-neutral strategy involving equally weighted, market-hedged positions in the 100 stocks over the next month. Assume the risk-free rate is 0.5% per month. (Do not round intermediate calculations. Enter your answer as percent rounded to 5 decimal places.)
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The following is part of the computer output from a regression
of monthly returns on Waterworks...
Assume that stock market returns have the market index as a common factor, and that all...
Assume that stock market returns have the market index as a common factor, and that all stocks in the economy have a beta of 1.0 on the market index. Firm-specific returns all have a standard deviation of 22%. Suppose that an analyst studies 20 stocks and finds that one-half of them have an alpha of +1.5%, and the other half have an alpha of -1.5%. Suppose the analyst invests $1.0 million in an equally weighted portfolio of the positive alpha...
Assume that stock market returns have the market index as a common factor, and that all...
Assume that stock market returns have the market index as a common factor, and that all stocks in the economy have a beta of 1.7 on the market index. Firm-specific returns all have a standard deviation of 25%. Suppose that an analyst studies 20 stocks and finds that one-half of them have an alpha of +2.5%, and the other half have an alpha of −2.5%. Suppose the analyst invests $1.0 million in an equally weighted portfolio of the positive alpha...
Assume 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 31%. Suppose an analyst studies 20 stocks and...
Assume 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 31%. Suppose an analyst studies 20 stocks and finds that one-half have an alpha of 2.0%, and one-half have an alpha of –2.0%. The analyst then buys $1.1 million of an equally weighted portfolio of the positive-alpha stocks and sells short $1.1 million of an equally weighted portfolio of the negative-alpha stocks. a....
Assume a market index represents the common factor and all stocks in the economy have a...
Assume 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 43%. Suppose an analyst studies 20 stocks and finds that one-half have an alpha of 2.4%, and one-half have an alpha of –2.4%. 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 portfolio of the negative-alpha stocks. a....
Pinulo retums? 1 0 capital asset pricing model given historical data 2. Consider Table 1. (%)...
Pinulo retums? 1 0 capital asset pricing model given historical data 2. Consider Table 1. (%) 3.77 Table 1 Summary Statistics Alpha, Beta, Expected Return and Variance a/c to the Stocks Sample Single Index Model Covariance Residual and Return Alpha Beta with Market Expected Variance Variance Market (%) (%) Return (%) (%) 3.60 3.59 4.80 Market 4.20 0.00 8.70 (a) Consider Table 1. Using the single index model, calculate beta and alpha for stocks 1 and 2. Interpret your findings....
Assume the return on a market index represents the common factor and all stocks in the...
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 4.5%, 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 portfolio of the...
Assume the return on a market index represents the common factor and all stocks in the economy have a beta of 1. Firm-sp...
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Q2 (e) Assume for simplicity sake that one factor has been deemed appropriate to "explain" returns...
Q2
(e) Assume for simplicity sake that one factor has been deemed appropriate to "explain" returns on stocds (0) How and there is no idiosyncratic risk. Derive the arbitrage pricing theory would you perform a test of the predictions of the capital asset pricing model given historical data (APT) model 2. Consider Tablo 1 Return and Variance a/c to the Stocks Sample Covariance Residual AlphaBeta Expected Variance and Return | with Market | Variance | (96) Return Market 3.60 4.80...
Assume the return on a market index represents the common factor and all stocks in the...
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
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weighted portfolio of the...
Assume you wish to evaluate the risk and return behaviors associated with various combinations of two stocks, Alpha Sof...
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Assume that stock market returns have the market index as a common factor, and that all stocks in the economy have a beta of 1.0 on the market index. Firm-specific returns all have a standard deviation of 22%. Suppose that an analyst studies 20 stocks and finds that one-half of them have an alpha of +1.5%, and the other half have an alpha of -1.5%. Suppose the analyst invests $1.0 million in an equally weighted portfolio of the positive alpha...
Pinulo retums? 1 0 capital asset pricing model given historical data 2. Consider Table 1. (%) 3.77 Table 1 Summary Statistics Alpha, Beta, Expected Return and Variance a/c to the Stocks Sample Single Index Model Covariance Residual and Return Alpha Beta with Market Expected Variance Variance Market (%) (%) Return (%) (%) 3.60 3.59 4.80 Market 4.20 0.00 8.70 (a) Consider Table 1. Using the single index model, calculate beta and alpha for stocks 1 and 2. Interpret your findings....
Q2
(e) Assume for simplicity sake that one factor has been deemed appropriate to "explain" returns on stocds (0) How and there is no idiosyncratic risk. Derive the arbitrage pricing theory would you perform a test of the predictions of the capital asset pricing model given historical data (APT) model 2. Consider Tablo 1 Return and Variance a/c to the Stocks Sample Covariance Residual AlphaBeta Expected Variance and Return | with Market | Variance | (96) Return Market 3.60 4.80...
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...
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