Minimum Variance Portfolio Weights (Using Solver) Kellogg (K) xxon (XOM) Average Return, E(r) 50.00% 50.00% Variance of Return, Var(r)², 8.31% 13.11% Standard Deviation of Return, o 0.01394 0.02814 Covariance of Returns, Cov(fx.fxoM) 11.80% 16.77% Correlation of Returns, Px.com (Excel) 0.00641 0.32366 Expected Portfolio Return Portfolio Standard Deviation Using Covariance Portfolio Standard Deviation Using Correlation 10.71% 11.71% 11.71% Proportio Proportio n of XOM n of K -100% 200% -90% 190% -80% 180% -70% 170% -60% 160% -50% 150% -40% 140% -30% 130% -20% 120% -10% 110% 0% 100% 10% 90% 20% 80% 30% 70% 40% 60% 50% 50% 60% 40% 70% 30% 80% 20% 90% 10% 100% 0% 110% -10% 120% -20% 130% -30% 140% -40% 150% -50% 160% -60% 170% -70% 180% -80% 190% -90%

Assume we beleive a 1 factor APT model describes securities returns. Consider 2 assets with the following data Security A B Suppose the relevant variances are: Component Systematic Factor Expected Return 5.65% 9.06% € A EB Variance 10.0365 0.0387 0.039 Beta 0.5 1.6 1. The beta of an equally weighted portfolio is: Number 2. The the variance of an equally weighted portfolio is (answer exactly): Number 3. Compute the risk free rate : Number

Portfolios A and B are both well-diversified. The risk-free rate is 8%. The return for the market is 10%. Portfolio A has an expected return of 15% and beta of 1.1. Portfolio B has an expected return of 9% and beta of 0.20. Portfolio A's variance is 9%, whilst Portfolio B's variance is 5.5%. Calculate for Portfolio A and Portfolio B the following: 1. Sharpe's Measure, 2. Treynor's Measure, 3. Jensen's Measure. Which is the better portfolio according to each measure?

Consider the expected return and standard deviation of the following two assets:   Asset 1:  E[r1]=0.1  and  σ1=0.2    Asset 2: E[r2]=0.3  and  σ2=0.4     (a) Draw (e.g. with Excel) the set of achievable portfolios in mean-standard deviation space for the cases: (i) ρ12= -1, (ii) ρ12=0.   (b) Suppose ρ12=-1. Which portfolio has the minimal variance? What is the variance and expected return of that portfolio?     (c) Derive the formula for the variance of a portfolio with four assets.

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PLEASE DO THIS IN EXCEL

Dependent Variable: PORTFOLIO Method: Least Squares Sample: 1991M01 2009M12 Included observations: 228 Variable с MARKET SIZE VALUE MOMENTUM R-squared Adjusted R-squared S.E. of regression Sum squared resid Log likelihood F-statistic Prob(F-statistic) Coefficient Std. Error t-Statistic 0.003080 0.002256 1.364876 0.0037 0.580669 0.054438 10.66651 0.0000 0.752523 0.057275 13.13866 0.0000 0.054039 0.059387 0.909954 0.3638 0.056782 1.044482 0.2974 0.595842 0.032935 Mean dependent var S.D. dependent var Akaike info criterion Schwarz criterion Prob. 457.2243 Hannan-Quinn criter. 82.19105 Durbin-Watson stat 0.000000 0.007051 0.051348 -3.966880 -3.891675 -3.936537 1.693594 1) Is the model statically significant? Make sure to justify your answer. Write down the model equation (5 marks)

Suppose that there are four risky assets whose expected returns E(r) and variance- covariance matrix (S) are shown in the spreadsheet below. We also consider the portfolio weights of two portfolios x and y of risky assets (see Cells B8:E9): 1 8 Portfolio x 9 Portfolio y A FOUR-ASSET PORTFOLIO PROBLEM Variance-covariance, S 20 Portfolio variance, 21 Portfollo standard deviation o 0.10 0.01 0.03 0.05 11 Portfolio x and y statistics: Mean, variance, covariance, correlation 12 Mean, Ejr, 13 Variance, 14 Covariance() 15 Correlation P 16 17 Calculating returns of combinations of Portfolio x and Portfolio y 18 Proportion of x 19 Mean portfolio return, r 0.01 0.30 0.06 -0.04 0.20 0.20 10.50% 0.1216 0.0714 0.4540 ? ? ? 0.3 0.03 0.06 0.40 0.02 0.30 0.10 ? 0.05 0.02 0.50 0.40 0.10 0.10 0.60 Mean, Er Variance, 0.2014 Question il Question ili Mean returns E(r) ? 7% 9% 11% 20% Question i i. Write the Excel formula used to estimate the mean and variance of portfolio y in cells E12 and E13,…

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