Answer:
You should invest $8,970 in stock X and $4,030 in stock Y.
Explanation:
These can be estimated as follows:
PER = (ERX * wX) + (ERY * wY) ....................... (1)
Where,
PER = Portfolio expected return = 11.45%, or 0.1145
ERX = Expected return of X = 13%, or 0.13
ERY = Expected retun of Y = 8%, or 0.08
wX = Weight of X = ?
wY = Weight of Y = 1 - wX = ?
Substituting the values into equation (1), we have:
0.1145 = [0.13 * wX] + [0.08 * (1 - wX)]
0.1145 = 0.13wX + [0.08 - 0.08wX]
0.1145 = 0.13wX + 0.08 - 0.08wX
0.1145 - 0.08 = 0.13wX - 0.08wX
0.0345 = 0.05wX
wX = 0.0345 / 0.05
wX = 0.69
Since wY = 1 - wX
Therefore,
wY = 1 - 0.69
wY = 0.31
Total amount to invest = $13,000
Investment in stock X = Amount to invest * 0.69 = $13,000 * 0.69 = $8,970
Investment in stock Y = Amount to invest * 0.31 = $13,000 * 0.31 = $4.030
Therefore, you should invest $8,970 in stock X and $4,030 in stock Y.
