Question

Dr. INVESTCO a young CEO who holds an MBA from the “MINI MOUSE” University understands completely the concept of International Diversification and especially the concept of risk minimization. However, he/she forgot all the formulae and cannot compute the following risk-return results.           

Please help him/her to compute the following relationships:

            TIME              R [Nestle]                  R [Myers]      Probability

            2016               14%                            35%                0.2

            2017               17                                24                    0.3

            2018               16                                28                    0.3

            2019               19                                32                    0.2

a.         Calculate the Expected Returns of the two Multinational stocks.

b.         Calculate the Variances of the two Multinational stocks.

c.         Calculate the risks of the two Multinational stocks and draw the Normal  Distribution Curves.

d.         Calculate the Covariance for the two Multinational stocks.

e.         Calculate the Correlation Coefficients of the two Multinational stocks.

f.          Calculate the beta of the two Multinational Stocks. Are the Stocks Aggressive or Defensive? Carefully explain your answers.

Answer 1

Due to multiple sub-parts, as per the guideline only the first 4 sub-parts are answered below:

These values were added to excel and the calculations for Expected returns, variance and covariance were performed.

Expected returns = E (R)= sum (probability of event * observed return)

Variance = [ R - E(R) ]² * probability of event

Covariance = [ R1 - E(R1) ] [ R2 - E(R2) ] * probability of event

These formula were applied in excel to derive the values in each sub parts.

Screenshot of excel with values

A B C D E F G H R[Nestle] R[Myers] Probability a= b = Cov(R1,R2) = 1 Time (R1) (R2) (P) R1* P R 2*P R1 - E(R1)|R2 - E(R2) a^2*P 16^2*P la*b*p 2 2016 14% 35% 0.2 0.028 0.07 -0.0250 0.0000 0.0001 0.0007 -0.0003 3 2017 17% 24% 0.3 0.051 0.072 0.0050 -0.0500 0.0000 0.0008 -0.0001 4 2018 28% 0.3 0.048 0.084 -0.0050 -0.0100 0.0000 0.0000 0.0000 5 2019 19% 32% 0.2 0.038 0.064 0.0250 0.0300 0.0001 0.0002 0.0002 Totals 0.165 0.000265 0.00168 -0.00021 E(R1) E(R2) Var(R1) Var(R2) Cov (R1,R2) 0.29

screenshot with formula for your reference

I Probability А R[Nestle] 1 Time (R1) 2 2016 0.14 3 2017 0.17 4 2018 0.16 5 2019 0.19 0.2 R [Myers] (R2) 0.35 0.24 0.28 0.32 G a= R1* P R2* P R1 - E(R1) =D2*B2 =D2*C2 =B2-$E$6 =D3*B3 =D3*C3 =B3-$E$6 =D4*B4 =D4*C4 =B4-$E$6 =D5*B5 =D5*C5 =B5-$E$6 =SUM(E2:E5) =SUM(F2:F5) E(R1) E(R2) H b= R2 - E(R2) =C2-$F$6 =C3-$F$6 =C4-$F$6 =C5-$F$6 0.3 0.2 Totals 2^2*p b^2* P Cov(R1,R2) = a*b*p =G2^2*D2 =H2^2*D2 =D2*62*H2 =G3^2*D3 =H3^2*D3 =D3*G3*H3 =G4^2*D4 =H4^2*D4 =D4*G4*H4 | =G5^2*D5 =H5^2*D5 =D5*65*H5 =SUM(12:15) SUM(12:5)=SUM(K2:K5) Var(R1) Var(R2) Cov (R1,R2)

Part a:

Substitute the given values in the formula

Expected returns = E (R)= sum (probability of event * observed return)

Expected return of Nestle = 0.2*0.14 + 0.3*0.17 + 0.3*0.16 + 0.2*0.19 = 0.165

Expected return of Myers = 0.2*0.35 + 0.3*0.24 + 0.3*0.28 + 0.2*0.32 = 0.29

Part b:

Substitute the given values in the formula

Variance = [ R - E(R) ]² * probability of event

Variance of Nestle = 0.2 * (0.14 - 0.165)² + 0.3 * (0.17 - 0.165)² + 0.3 * (0.16 - 0.165)² + 0.2 * (0.19 - 0.165)² = 0.000265

Variance of Myers = 0.2 * (0.35 - 0.29)² + 0.3 * (0.24 - 0.29)² + 0.3 * (0.28 - 0.29)² + 0.2 * (0.32 - 0.29)² = 0.00168

Part c:

Risk is the standard deviation. = sqrt ( Variance)

Risk of Nestle = sqrt (0.000265) = 0.01628

Risk of Myers = sqrt(0.00168) = 0.04099

Nestle Normal distribution graph

Nestle THHHH 0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2 0.22 0.24 0.26 0.28 0.3

Myers Normal distribution graph

Myers

Part d:

Substitute the given values in the formula

Covariance = [ R1 - E(R1) ] [ R2 - E(R2) ] * probability of event

Covariance = 0.2 * (0.14 - 0.165) * (0.35 - 0.29) + 0.3 * (0.17 - 0.165) * (0.24 - 0.29) + 0.3 * (0.16 - 0.165) * (0.28 - 0.29) + 0.2 * (0.19 - 0.165) * (0.32 - 0.29) = -0.00021

Part e:

Correlation co-efficient = covariance / (Std Dev of Nestle * Std Dev of Myers) = -0.00021 / (0.01628 *0.04099) = -0.3147