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Risk and Return 1. Calculate monthly returns for Darden Restaurants and the S&P 500. Be sure...

Risk and Return
1. Calculate monthly returns for Darden Restaurants and the S&P 500. Be sure to include the dividends for Darden in the return. Show All excel formulas.
Darden (DRI) S&P 500
Month Price Dividend Price
6/1/16 59.11 2098.86 DRI Return SP Return DRI- Ave S&P - Ave (DRI-Ave)x(S&P-Ave)
7/1/16 57.446472 0.56 2173.600098
8/1/16 58.043533 2170.949951
9/1/16 57.742203 2168.27002
10/1/16 61.009743 0.56 2126.149902
11/1/16 69.65522 2198.810059
12/1/16 69.10405 2238.830078
1/1/17 69.636215 0.56 2278.870117
2/1/17 71.520325 2363.639893
3/1/17 80.129959 2362.719971
4/1/17 81.585648 0.56 2384.199951
5/1/17 85.746788 2411.800049
6/1/17 87.202744 2423.409912
7/1/17 80.877548 0.63 2470.300049
8/1/17 79.708763 2471.649902
9/1/17 76.494789 2519.360107
10/1/17 79.883553 1.26 2575.26001
11/1/17 83.174545 2584.840088
12/1/17 94.715607 2673.610107
1/1/18 94.547913 0.63 2823.810059
2/1/18 91.521347 2713.830078
3/1/18 84.631676 2640.870117
4/1/18 92.186485 0.63 2648.050049
5/1/18 87.410004 2705.27002
6/1/18 93.269997 2767.320068
2. Calculate the average, standard deviation, and variance of returns for Darden and the S&P 500. Use the function wizard (fx). 3. Use the covariance equation to find the covariance between Darden and the S&P 500.
Average Sum
Std. Dev n-1
Variance COV
6. Use Regression Analysis to find the beta for Darden. You should get the same answer as in question 5. Print your results below. 4. Use the Correlation Coefficient equation to find the correlation between Darden and the S&P 500.
Corr
5. Use the Beta equation to find the beta of Darden.
Beta
7.

Answer the following concept questions:

a. What is the probability that the true beta for Darden is equal to zero?

b. If the market risk premium is 7% and the risk-free rate is 2%, what return would you expect to earn on Darden given YOUR beta calculation?

Solutions

Expert Solution

(1) Computation of the monthly return for Darden Restaurants and the S&P 500.We have,
Risk and Return
Darden (DRI) S&P 500
Month Price Dividend Price
06-01-2016 59.11 2098.86 DRI Return SP Return DRI- Ave S&P - Ave (DRI- Ave)2 (S&P - Ave)2 (DRI-Ave)x(S&P-Ave)
07-01-2016 57.44647 0.56 2173.6001 -1.866905769 3.56098539 -3.938421494 2.42762549 15.51116386 5.893365522 -9.56101241
08-01-2016 58.04353 2170.95 1.039334496 -0.12192431 1.039334496 -0.121924314 1.080216194 0.014865538 -0.126720145
09-01-2016 57.7422 2168.27 -0.519144829 -0.12344508 -0.519144829 -0.123445084 0.269511353 0.015238689 0.064085877
10-01-2016 61.00974 0.56 2126.1499 6.628669848 -1.94256793 6.628669848 -1.942567928 43.93926396 3.773570155 -12.87664145
11-01-2016 69.65522 2198.8101 14.17064976 3.41745222 14.17064976 3.417452219 200.8073146 11.67897967 48.42751846
12-01-2016 69.10405 2238.8301 -0.791283123 1.82007622 -0.791283123 1.82007622 0.62612898 3.312677445 -1.440195595
01-01-2017 69.63622 0.56 2278.8701 1.580464531 1.78843582 1.580464531 1.788435817 2.497868135 3.198502672 2.826559376
02-01-2017 71.52033 2363.6399 2.705646767 3.71981603 2.705646767 3.719816034 7.320524429 13.83703132 10.06450823
03-01-2017 80.12996 2362.72 12.03802416 -0.03891972 12.03802416 -0.038919719 144.9140256 0.001514745 -0.468516515
04-01-2017 81.58565 0.56 2384.2 2.515524811 0.90912085 2.515524811 0.909120855 6.327865077 0.826500729 2.286916067
05-01-2017 85.74679 2411.8 5.100333333 1.15762514 5.100333333 1.157625139 26.01340011 1.340095963 5.904274084
06-01-2017 87.20274 2423.4099 1.697971474 0.48137751 1.697971474 0.481377509 2.883107126 0.231724306 0.817365279
07-01-2017 80.87755 0.63 2470.3 -6.530982557 1.93488261 -6.530982557 1.934882612 42.65373316 3.743770721 -12.63668459
08-01-2017 79.70876 2471.6499 -1.445129123 0.05464328 -1.445129123 0.054643281 2.088398182 0.002985888 -0.078966597
09-01-2017 76.49479 2519.3601 -4.032146378 1.93029785 -4.032146378 1.930297853 16.25820441 3.726049803 -7.783243497
10-01-2017 79.88355 1.26 2575.26 6.077229653 2.21881353 6.077229653 2.218813533 36.93272025 4.923133494 13.4842394
11-01-2017 83.17455 2584.8401 4.119736637 0.3720043 4.119736637 0.372004301 16.97222996 0.1383872 1.532559748
12-01-2017 94.71561 2673.6101 13.87571402 3.43425574 13.87571402 3.434255736 192.5354395 11.79411246 47.65275046
01-01-2018 94.54791 0.63 2823.8101 0.488099073 5.61787044 0.488099073 5.617870444 0.238240705 31.56046833 2.742077358
02-01-2018 91.52135 2713.8301 -3.201092339 -3.89473721 -3.201092339 -3.894737206 10.24699216 15.16897791 12.46741343
03-01-2018 84.63168 2640.8701 -7.52793881 -2.68844986 -7.52793881 -2.688449862 56.66986272 7.227762663 20.23848606
04-01-2018 92.18649 0.63 2648.05 9.671094071 0.27187751 9.671094071 0.271877513 93.53006053 0.073917382 2.629353006
05-01-2018 87.41 2705.27 -5.181324573 2.1608342 -5.181324573 2.160834197 26.84612433 4.669204425 -11.19598332
06-01-2018 93.27 2767.3201 1.175347992 2.293673 1.175347992 2.293672999 1.381442901 5.260935827 2.695863953
Total 51.78789312 28.3339975 27.20063764 948.5438383 132.4137729 132.4137729
Average return 2.071515725 1.133359902

Note: Monthly return = [ Dividend income + ( Ending price - Begenning price)] / Begenning price

(2-a) Computation of the average return.We have,

Average return = Sum of all return / Number of return

For Darden:

Average return =51.78789312 / 25 = 2.071515725 %

For S&P 500:

Average return = 28.3339975 / 25 = 1.133359902 %

(2-b) Comutation of variance.We have,

For Darden:

Variance = Sum of (DRI- Ave)2 / n - 1

Variance = 948.5438383 / 25 - 1 = 39.52265 %

For S&P 500:

Variance = Sum of (S&P- Ave)2 / n - 1

Variance = 132.4137729 / (25 - 1) = 5.5172405 %

(2-c) Computation of the standard deviation.We have,

For Darden:

Standard deviation = Square root of variance

Standard Deviation = = 6.28670 %

For S&P 500:

Standard deviation = Square root of variance

Standard Deviation = = 2.348880 %

(3) Computation of the covariance between Darden and the S&P 500.We have,

Covariance =

Covariance =  132.4137729 / (25 -1) = 5.517240 %

(4) Computation of the correlation between Darden and the S&P 500.We have,

Correlation between Darden and the S&P 500 = Covariance / (Standard deviation of Dardan stock x Standard deviation of S&P500)

Correlation between Darden and the S&P 500 =5.517240 / ( 6.28670 x 2.348880)

Correlation between Darden and the S&P 500 = 0.373627

(5) Computation of beta for Darden stock by beta equation.We have,

Beta of Darden = Correlation Coefficient between darden stock and S&P x Standard deviation of S&P/ Standard deviation of darden stock

Beta of Darden = 0.373627 x 2.348880/ 6.28670 = 0.139597

Hence, the beta of stock is 0.139597

(6) Computation of beta for Darden stock by regresion analysis.We have,

Beta of Darden Stock = Covariance of Darden stock and S&P500 / (Standard deviation of darden stock)2

Beta of Darden Stock = 5.517240 / (6.28670)2 = 0.139597

Hence,the beta of Darden stock is 0.139597

(7-a) Computation of the probability that the true beta for Darden is equal to zero.We have,

True beta of Darden stock is equal to zero when expected average return is equal to risk-free rate of return.

Risk-free rate of return = 2 %

Average return = 2.071515725 %

Probability that the true beta is equal to zero = ( 2.071515725 - 2.00) / 2.00 = 0.0357*100 = 3.57 %

(7-b) Computation of the expected return of Darden stock.We have,

Using capital asset pricing model.We get:

Expected return = Risk-free return + Beta of stock x Market risk premium

Expected return = 2 + 0.139597 x 7 = 2.97718 %

Hence, the expected return of Darden stock is 2.97718 %.



jeff jeffy answered 2 years ago
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