Question

Anne is a financial investor who actively buys and sells

Anne is a financial investor who actively buys and sells in the securities market. Now she has a portfolio of all blue chips, including: $13,500 of Share A, $7,600 of Share B, $14,700 of Share C, and $5,500 of Share D.

Required:

Compute the weights of the assets in Rachel’s portfolio?

If Rachel’s portfolio has provided her with returns of 9.7%, 12.4%, -5.5% and 17.2% over the past four years, respectively, calculate the geometric average return of the portfolio for this period.


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Answer 1

9514 1404 393

Answer:

a) weights: 0.32688, 0.18402, 0.35593, 0.13317

b) geometric average return: 5.42%

Explanation:

The total of amounts invested is ...

13500 +7600 +14700 +5500 = 41300

The respective weights for the weighted average are these values divided by the total. For example, 13500/41300 ≈ 0.32688. The remaining weight values are shown in the attached spreadsheet.

The weighted geometric average return is 1 less than the product of 1 more than the individual returns raised to the power of the weight*. That is, ...

weighted average return

= (1.097^0.327)(1.124^0.184)(0.945^0.356)(1.172^0.133) -1

= 1.0542 -1 = 5.42%

_____

* Technically, the weighted geometric average is root of the products of the values to the power of the weight. The root index is the sum of the weights. Here, the sum of weights is 1, so the root is simply the product itself.