Rate of return on a portfolio

The rate of return on a portfolio is the rate of return on a portfolio measured over a period of time.

Calculation

The rate of return on a portfolio can be calculated either directly or indirectly, depending upon the particular type of data available.

Direct historical measurement

Direct historical measurement of the rate of return on a portfolio applies one of several alternative methods, such as for example the time-weighted method, or the modified Dietz method.^[1]^[2] It requires knowledge of the value of the portfolio at the start and end of the period of time under measurement, together with the external flows of value into and out of the portfolio at various times within the time period. For the time-weighted method, it is also necessary to know the value of the portfolio when these flows occur (i.e. either immediately after, or immediately before).

Indirect calculation

The rate of return on a portfolio can be calculated indirectly as the weighted average rate of return on the various assets within the portfolio.^[3] The weights are proportional to the value of the assets within the portfolio, to take into account what portion of the portfolio each individual return represents in calculating the contribution of that asset to the return on the portfolio.

This method is particularly useful for projecting into the future the rate of return on a portfolio, given projections of the rates of return on the constituents of the portfolio.

The indirect calculation of the rate of return on a portfolio can be expressed by the formula:

r=A_{1}r_{1}+A_{2}r_{2}+\cdots +A_{n}r_{n}

which is the sum of the contributions $A_{1}r_{1}$ , $A_{2}r_{2}\cdots A_{n}r_{n}$ where:

r

equals the rate of return on the portfolio,

A_{i}

equals the weight of asset i in the portfolio, and

r_{i}

equals the rate of return on asset i in the portfolio.

Example

Rate of return r_m on a mining stock equals 10%
Rate of return r_c on a child care centre equals 8%
Rate of return r_f on a fishing company equals 12%

Now suppose that 40% of the portfolio is in the mining stock (weighting for this stock A_m = 40%), 40% is in the child care centre (weighting for this stock A_c = 40%) and the remaining 20% is in the fishing company (weighting for this stock A_f = 20%). To determine the rate of return on this portfolio, first calculate the contribution of each asset to the return on the portfolio, by multiplying the weighting of each asset by its rate of return, and then add these contributions together:

For the mining stock, its weighting is 40% and its rate of return is 10% so its contribution equals 40% x 10% = .04 = 4%
For the child care centre, its weighting is 40% and its rate of return is 8% so its contribution equals 40% x 8% = .032 = 3.2%
For the fishing company, its weighting is 20% and its rate of return is 12% so its contribution equals 20% x 12% = .024 = 2.4%

Adding together these percentage contributions gives 4% + 3.2% + 2.4% = 9.6%, resulting in a rate of return on this portfolio of 9.6%.

Discrepancies

If there are any external flows or other transactions on the assets in the portfolio during the period of measurement, and also depending on the methodology used for calculating the returns and weights, discrepancies may arise between the direct measurement of the rate of return on a portfolio, and indirect measurement (described above).

References

↑
- Carl Bacon. Practical Portfolio Performance Measurement and Attribution. West Sussex: Wiley, 2003. ISBN 0-470-85679-3
↑
- Bruce J. Feibel. Investment Performance Measurement. New York: Wiley, 2003. ISBN 0-471-26849-6
↑ Levy, A 2009, ECON331 'Uncertainty, risky assets (activities) and portfolio choice', lecture notes accessed 22 May 2009 elearning.uow.edu.au

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