question archive Shamma Al Ghantoot has invested $63,400 in ABC shares and $31,800 in XYZ shares
Shamma Al Ghantoot has invested $63,400 in ABC shares and $31,800 in XYZ shares
Subject:FinancePrice:3.86 Bought25
Shamma Al Ghantoot has invested $63,400 in ABC shares and $31,800 in XYZ shares. Assume the market can have five states: very good, good, neutral, bad and very bad. The probabilities for each state and the returns of two shares are given in the table below: State of the Stock 1: Stock 2: Probability of of Occurrence ABC XYZ Economy Very good Good 15% 15% 8% 9% 20% 12% Neutral 30% 7% 9% Bad 6% 20% 15% 6% -3% Very bad 4% Note: If your answer is in percentage points, round to two decimal points. o If your answer is in decimals, round to four decimal points. O a. Calculate the expected return for each stock separately. (2 points) Stock 1: Stock 2: b. Calculate the standard deviation of each stock separately. (2 points) Stock 1: Stock 2: c. Based on the information given and/or your findings above, explain which stock is a better investment. Why? (1 point) d. Calculate the expected return of a portfolio consisting of these two stocks. (1 point)
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ANSWER: -
a. EXPECTED RETURN = PROBABILITY * RETURN
STOCK 1 = (0.1 * 4% ) + (0.15 * 5%) + ( 0.5 * 3%) + (0.15 * 2%) + (0.1 * 1%)
= 3.05 %
STOCK 2 = (0.1 * 11% ) + (0.15 * 8%) + ( 0.5 * 5%) + (0.15 * 2%) + (0.1 * -3%)
= 4.8 %
b. STANDARD DEVIATION ( RISK )
| STATE OF ECONOMY | PROB ( P ) | STOCK 1 ( X ) | STOCK 2 ( Y ) | X -  |
Y -  |
P * (X - )2 |
P * (Y -  ) 2 |
| Very Good | 0.10 | 4% | 11% | 0.95 | 6.2 | 0.09 | 3.84 |
| Good | 0.15 | 5% | 8% | 1.95 | 3.2 | 0.57 | 1.54 |
| Neutral | 0.50 | 3% | 5% | -0.05 | 0.2 | 0.00 | 0.02 |
| Bad | 0.15 | 2% | 2% | -1.05 | -2.8 | 0.17 | 1.18 |
| Very Bad | 0.10 | 1% | -3% | -2.05 | -7.8 | 0.42 | 6.08 |
| TOTAL | 1.25 | 12.66 |
STANDARD DEVIATION FOR STOCK 1 = √ 1.25 (i.e. Square root of 1.25 )
= 1.12
STANDARD DEVIATION FOR STOCK 2 = √ 12.66 (i.e. Square root of 12.66 )
= 3.56
c. ANALYSIS
| STOCK | EXPECTED RETURN | STANDARD DEVIATION ( RISK ) |
| STOCK 1 | 3.05 % | 1.12 |
| STOCK 2 | 4.80 % | 3.56 |
( i ) Stock 2 is better based on expected return,
( ii ) Stock 1 is better based on risk,
d. Expected return on a Portfolio = PROBABLITY * EXPECTED RETURN
| STOCK | EXPECTED RETURN | PROBABILITY |
| STOCK 1 | 3.05 % | 0.5 |
| STOCK 2 | 4.80 % | 0.5 |
EXPECTED RETURN = ( 0.5 * 3.05 % ) + ( 0.5 * 4.80 % )
= 3.93 %
CONCLUSION: -
a & b
| STOCK | EXPECTED RETURN | STANDARD DEVIATION ( RISK ) |
| STOCK 1 | 3.05 % | 1.12 |
| STOCK 2 | 4.80 % | 3.56 |
c.
( i ) Stock 2 is better based on expected return,
( ii ) Stock 1 is better based on risk,
d. Expected return of the portfolio = 3.93 %
