You have inherited some funds and decided to invest in one of two international companies – Coca Cola and Walmart. You research revealed and found the following possible performance of the investments.
- You have estimated the following probability distributions of expected future returns
for Coca Cola and Walmart.
Coca Cola Walmart
Probability Return Probability Return
0.1 –10% 0.2 2%
0.2 10 0.2 7
0.4 15 0.3 12
0.2 20 0.2 15
- 40 1 16
- What is the expected
rate of return for Coca Cola and Walmart?
Calculation of Expected rate of return for Coca Cola and Walmart
|
Coca Cola |
|
Walmart |
|||
|
Probability (A) |
Return (B) |
A*B |
Probability (C) |
Return (D) |
C*D |
|
0.1 |
-10 |
-1 |
0.2 |
2 |
0.4 |
|
0.2 |
10 |
2 |
0.2 |
7 |
1.4 |
|
0.4 |
15 |
6 |
0.3 |
12 |
3.6 |
|
0.2 |
20 |
4 |
0.2 |
15 |
3 |
|
0.1 |
40 |
4 |
0.1 |
16 |
1.6 |
|
|
Total |
15 |
|
Total |
10 |
So from above calculation we can see that expected rate of return for Coca Cola is 15% & for Walmart is 10%
- What is the standard deviation of expected returns for Stock X and for stock Y?
Calculation of standard deviation of Stock X
|
Stock X |
|||||
|
Given Return (A) |
Expected Return (B) |
A-B |
(A-B)2 |
Probability |
Probability * (A-B)2 |
|
-10 |
15 |
-25 |
625 |
0.1 |
62.5 |
|
10 |
15 |
-5 |
25 |
0.2 |
5 |
|
15 |
15 |
0 |
0 |
0.4 |
0 |
|
20 |
15 |
5 |
25 |
0.2 |
5 |
|
40 |
15 |
25 |
625 |
0.1 |
62.5 |
|
|
Total |
0 |
|
1 |
135 |
Standard devaiation = √Σ probability *(A-B)2
= √ 135
= 11.6189
Calcualtion of Standard Deviation of Stock Y
|
Stock Y |
|||||
|
Given Return (C) |
Expected Return (D) |
C-D |
(C-D)2 |
Probability |
Probability * (C-D)2 |
|
2 |
10 |
-8 |
64 |
0.2 |
12.8 |
|
7 |
10 |
-5 |
25 |
0.2 |
5 |
|
12 |
10 |
2 |
4 |
0.3 |
1.2 |
|
15 |
10 |
5 |
25 |
0.2 |
5 |
|
16 |
10 |
6 |
36 |
0.1 |
3.6 |
|
|
Total |
0 |
|
1 |
27.6 |
Standard Deviation = √Σ probability *(C-D)2
=√27.6
=5.2535
- Which stock is riskier and why?
Calculation of Stock Risk
Stock X = Standard Deviation /Expected Return
=11.6189/15
=0.7745
Stock Y = 5.2535/10
=0.5253
From the above calculation we can say that Stock Y is less risker than to Stock X as it's Coefficient of Variation(CV) is lower than Stock X. CV is the measure of calculation of risk.
(b) You received $2,000,000 and decided to invest $1,200,000 in Coca Cola stocks and $800,000 in stock Walmart. If the correlation of returns between Coca Cola and Walmart is 0.5, compute the following:
- The expected return from the portfolio (Please answer this)
- The standard deviation of returns from the portfolio (Please answer this)
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