Final answer:
To calculate the expected return of Michael's portfolio, we use the formula accounting for the weight and expected return of each stock. The portfolio's expected return is the sum of each stock's weighted return, resulting in an expected portfolio return of 10.534 percent.
Step-by-step explanation:
The question asks what is the expected return of Michael's portfolio, which consists of investments in three different stocks with distinct percentages and expected returns.
To calculate this, we need to apply the formula for the expected return of a portfolio which takes into account the weight of each asset in the portfolio and its expected return. The formula is as follows: Expected Portfolio Return = (Weight of Asset 1 × Expected Return of Asset 1) + (Weight of Asset 2 × Expected Return of Asset 2) + (Weight of Asset 3 × Expected Return of Asset 3).
Accordingly, Michael's portfolio is 33 percent invested in Stock R, 15 percent in Stock S, and the remainder in Stock T. The expected returns for Stock R, S, and T are 8.4 percent, 9.8 percent, and 12.1 percent respectively. First, we need to realize that if Michael's portfolio is 33 percent in R and 15 percent in S, then it should be 52 percent in T (because 100%-33%-15% = 52%). Now we can calculate the expected return of the portfolio using the given percentages (as decimals) and the expected returns for each stock:
- Expected return from Stock R = 33% or 0.33 of the portfolio × 8.4% or 0.084 expected return
- Expected return from Stock S = 15% or 0.15 of the portfolio × 9.8% or 0.098 expected return
- Expected return from Stock T = 52% or 0.52 of the portfolio × 12.1% or 0.121 expected return
Now we sum these expected returns for each part of the portfolio:
(0.33 × 0.084) + (0.15 × 0.098) + (0.52 × 0.121) = 0.02772 + 0.0147 + 0.06292 = 0.10534
The expected return of Michael's portfolio is 10.534 percent.