In order to expect that it will fund her retirement, Glenda needs her portfolio

Question

In order to expect that it will fund her retirement, Glenda needs her portfolio to have an expected return of 13.6 percent per year over the next 30 years. She has decided to invest in Stocks 1, 2, and 3, with 25 percent in Stock 1, 50 percent in Stock 2, and 25 percent in Stock 3. If Stocks 1 and 2 have expected returns of 9 percent and 10 percent per year, respectively, then what is the minimum expected annual return for Stock 3 that is likely to enable Glenda to achieve her investment requirement?

Explanation / Answer

Intorduction:

Expected Return of a portfolio is a measure used for checking returns on a portfolio, thus, averaging higher and lower returns from different stocks in a portfolio.

Solution:

E(R) = w1r1 + w2r2 + w3r3

Where,

E(R) = Expected Return/ Mean of the Portfolio

w1 = Weight of Stock 1,

w2 = Weight of Stock 2,

w3 = Weight of Stock 3,

r1 = Expected Return on Stock 1,

r2 = Expected Return on Stock 2,

r3 = Expected Return on Stock 3.

Hence,

0.136 = (0.25)(0.09) + (0.50)(0.10) + (0.25)(r3)

0.136 = 0.0225 +0.05 +(0.25)(r3)

0.136 - 0.0725 = (0.25)(r3)

0.0635/0.25 = r3

r3 = 0.254

r3 = 25.4%

Expected Return for Stock 3 = 25.4%

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