Question

Assume you wish to evaluate the risk and return behaviors associated with various combinations of two​ stocks, Alpha Software and Beta​ Electronics, under three possible degrees of​ correlation: perfect​ positive, uncorrelated, and perfect negative. The average return and standard deviation for each stock appears​ here:

Asset   Average Return,overbar r                   Risk (Standard Deviation), s
Alpha   5.1%   30.3%
Beta                    11.2%      50.5%

a. If the returns of assets Alpha and Beta are perfectly positively correlated​ (correlation coefficient equals plus 1​), over what range would the average return on portfolios of these stocks​ vary? In other​ words, what is the highest and lowest average return that different combinations of these stocks could​ achieve? What is the minimum and maximum standard deviation that portfolios Alpha and Beta could​ achieve?

b. If the returns of assets Alpha and Beta are uncorrelated​ (correlation coefficient equals 0​), over what range would the average return on portfolios of these stocks​ vary? What is the standard deviation of a portfolio that invests​ 75% in Alpha and​ 25% in​ Beta? How does this compare to the standard deviations of Alpha and Beta​ alone?

c. If the returns of assets Alpha and Beta are perfectly negatively correlated​ (correlation coefficient equals negative 1​), over what range would the average return on portfolios of these stocks​ vary? Calculate the standard deviation of a portfolio that invests​ 62.5% in Alpha and​ 37.5% in Beta.

________________________________

a. If the returns of assets Alpha and Beta are perfectly positively correlated​ (correlation coefficient equals plus 1​), the range is between ______​% and ______​% ​(Round to one decimal​ place.)

The range of the standard deviation is between _____​% and _____​% ​(Round to one decimal​ place.)

b. If the returns of assets Alpha and Beta are uncorrelated​ (correlation coefficient equals 0​), the range is between _______​% and ______% ​(Round to one decimal​ place.)

The standard deviation of a portfolio that invests​ 75% in Alpha and​ 25% in Beta is _____​%.​(Round to two decimal​ places.)

c. If the returns of assets Alpha and Beta are perfectly negatively correlated​ (correlation coefficient equals negative 1​), the range is between ______​% and _____​%

​(Round to one decimal​ place.)

The standard deviation of a portfolio that invests​ 62.5% in Alpha and​ 37.5% in Beta is ____​%. ​(Round to two decimal​ places.)

Answer 1

If the returns of assets Alpha and Beta are perfectly positively correlated​ (correlation coefficient equals plus 1​), the range is between 5.1% and 11.2​% ​(Round to one decimal​ place.)

The range of the standard deviation is between 5.1​% and 50.5% ​(Round to one decimal​ place.)

b. If the returns of assets Alpha and Beta are uncorrelated​ (correlation coefficient equals 0​), the range is between 5.1% and 11.2% ​(Round to one decimal​ place.)

The standard deviation of a portfolio that invests​ 75% in Alpha and​ 25% in Beta is 25.9964​%.​(Round to two decimal​ places.)

c. If the returns of assets Alpha and Beta are perfectly negatively correlated​ (correlation coefficient equals negative 1​), the range is between 5.1% and 11.2​%

​(Round to one decimal​ place.)

The standard deviation of a portfolio that invests​ 62.5% in Alpha and​ 37.5% in Beta is 0.08
Asset Alpha (&) Beta (8) Average Return Ra=5.1% RB = 11.2% Rink (S) Sa - 30.37 Sp - 50.5% As we know that Poortfolio Retury Rp = Rawa + RBWB where Ra & RB are the average betwory and was wp are the weights of security ad B. Portfolio Rink o 8o – so we + So wp? + 2 So wa Sp. wp Hop where ras is Cosselation coefficient. (a) When r=1 (Perfect Positive Cosselation exint) then RR = 5.180 + 11.2X1 If wao, Wp = 100%) -11.2 x and Są to +(50.5)*x 1 + @ Sp=150.5 Range of Portfolio Pettore 50-5-4-2 to sostine = 303 to 6. If watoo, wp=0 then Rp = 5.1x1 = 5.1%. and sp² = (5. 1 1 5.1 Sp- £5.1 Range of lootfolio Beton : Range of Portfolio Rink will be from 5.1 to 0.5 Y. . Return . 5.1 to 112 %

(b when r=0 (No corelation) then Res when Wao cobro - IX 11.2 - 11LY. then = wa Rd = 5.1%. When op=o range of Portfolio Return reeill be some i.e. 5.1 to 11.2%. . when Wa=0.75 Wp = 0.25 then she sawah + sa wf + 2Sa So We Wp rap = 30.3% (0.75 + 505) + (0.25 + 2×30.5*0.75 X50.500.25yo se = 516.4256+159.3906 sp= 675.8162 Sp = 25.9964) Portfolio Standard deviation lower than both a and ß. Therefore tur portfolio is less sinkien than both d and ß individual rink - (C) If r=-1 then Rp = WIRA = 11.2 Cenen Waco and Rp = Ward = 5.1 when wp=0 Range of Portfolio Return will be some ie (s. 1 to 11.2%) When Waa 8254, WB = 37.5% then Sp² = 60.3² (0.625 60.5x (0.375) + 2x 30. 300. 625x50.5 su = 358.6289 +358.6289 - 717:27 sp=0 h [Sp=0.08 xo.375X
​%. ​