Assume that an investor has a two-asset portfolio worth $1 million. Asset X has an expected return of 5%, and Asset Y has an expected return of 10%. The portfolio has $800,000 in Asset X and $200,000 in Asset Y. Based on these figures, compute the expected return of the portfolio.
Question
Answer:
The expected return of a portfolio is the weighted average of the expected returns of its individual assets, where the weights correspond to the proportion of each asset in the portfolio.
Given:
- Asset X has an expected return of 5%.
- Asset Y has an expected return of 10%.
- The portfolio has $800,000 in Asset X and $200,000 in Asset Y.
The formula for the expected return of the portfolio is:
Expected Return of Portfolio = (Weight of Asset X * Expected Return of Asset X) + (Weight of Asset Y * Expected Return of Asset Y)
Weight of Asset X = Value of Asset X / Total Portfolio Value
Weight of Asset Y = Value of Asset Y / Total Portfolio Value
Total Portfolio Value = $800,000 + $200,000 = $1,000,000
Calculations:
Weight of Asset X = $800,000 / $1,000,000 = 0.8
Weight of Asset Y = $200,000 / $1,000,000 = 0.2
Expected Return of Portfolio = (0.8 * 0.05) + (0.2 * 0.10)
Expected Return of Portfolio = 0.04 + 0.02
Expected Return of Portfolio = 0.06
Expected Return of Portfolio = 6%
Therefore, the expected return of the portfolio is 6%.
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