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# PS1AK - 1 Calculate the geometric and arithmetic average...

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1. Calculate the geometric and arithmetic average total return, variances and covariances for the fol Daily covariance matrix 168% -125% -122% -208% 386% Apple Boeing Exxon GE WMT Apple Err:502 Err:502 Err:502 Err:502 Err:502 Boeing Err:502 Err:502 Err:502 Err:502 Err:502 Exxon Err:502 Err:502 Err:502 Err:502 Err:502 GE Err:502 Err:502 Err:502 Err:502 Err:502 WMT Err:502 Err:502 Err:502 Err:502 Err:502 Err:502 Err:502 Err:502 Err:502 Err:502 Return Daily arithmetic average Err:502 Err:502 Err:502 Err:502 Err:502 Daily geometric average Err:502 Err:502 Err:502 Err:502 Err:502 Expected annual return Err:502 Err:502 Err:502 Err:502 Err:502 2. What is your best estimate of the daily return on Apple stock? Of the annual return? Daily return Err:502 daily arithmetic average Annual return Err:502 EAR based on daily geometric average 3. Your investment horizon is one year. What is the risk-free rate (Bloomberg)? 1-year T-bill rate 0.43% as of 4/25/10 Source: http://www.bloomberg.com/markets/rates/index.html 4. If you only want to invest in these 5 securities, what is the optimal risky portfolio (ORP) according Annual Expected return Err:502 Extreme expected return is driven by the very large negative Standard deviation Err:502 Annual covariance = 252 * daily covariance, and thus annual Sharpe ratio Err:502 Weights for ORP are shown in Q1, and were found using Solver 5. If you want to invest \$50,000, have average risk aversion (A=3) and your preferences can be desc Amount to be invested 50,000 Coefficient of risk aversion (A): 3 Let w be the weight on the risky portfolio: Err:502 T-Bills Apple Boeing Exxon GE WMT Err:502 Err:502 Err:502 Err:502 Err:502 Err:502 w=[E(R p )-R f ]/(A σ 2 )

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llowing securities, using daily data from Yahoo!Finance for the years 2008 and 2009 Weights 168% -125% -122% -208% 386% 100% Need to use 365 days per year, not just 252 observations per year as done by the Geomean() function, to ge Alternatively, you need to annualize by assuming 252 days per year if you used 252 days for the geometric m g to the Markowitz portfolio selection model? What is its annual expected return, standard deviation a expected annual returns for Boeing, Exxon and GE variance = 252 * daily variance Err:502 cribed by the utility function U=E(R)-0.5As2, how much money (\$ amounts) should you invest in each o Sum Err:502
et the average return for all days, not just trading days mean and Sharpe ratio? of the 5+1 (T-bills) securities?

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1. Download the daily prices for the S&P 500 (series SPY) from Yahoo!Finance for the years 2008 and See worksheet SPY 2. Download the daily 10-year Treasury note yields (series ^TNX) from Yahoo!Finance for the years 2 See worksheet ^TNX 3. What are the alpha and beta coefficients, their standard errors and the residual variances for the 5 s Single Index Model Apple Boeing Exxon GE Beta, alpha Err:502 Err:502 Err:502 Err:502 Err:502 Err:502 Err:502 Standard error Err:502 Err:502 Err:502 Err:502 Err:502 Err:502 Err:502 R2, Standard error_y Err:502 Err:502 Err:502 Err:502 Err:502 Err:502 Err:502 F, df Err:502 Err:502 Err:502 Err:502 Err:502 Err:502 Err:502 SS_reg, SS_residual Err:502 Err:502 Err:502 Err:502 Err:502 Err:502 Err:502 Market Model Apple Boeing Exxon GE Beta, alpha Err:502 Err:502 Err:502 Err:502 Err:502 Err:502 Err:502 Standard error Err:502 Err:502 Err:502 Err:502 Err:502 Err:502
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PS1AK - 1 Calculate the geometric and arithmetic average...

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