Practical Portfolio Performance Measurement and Attribution, 3rd Edition

3The Mathematics of Portfolio Return

Time is your friend; impulse is your enemy. Take advantage of compound interest and don't be captivated by the siren song of the market.

Warren Buffett (1930–)

Mathematics is the gate and key of the sciences. … Neglect of mathematics works injury to all knowledge, since he who is ignorant of it cannot know the other sciences or the things of this world.

Roger Bacon, “Doctor Mirabilis” (1214–1294), Opus Majus

The foundations of portfolio return calculation were laid in the 1960s and early 1970s by Dietz,¹ the Bank Administration Institute (BAI)² and the UK's Society of Investment Analysts (SIA).³ All three of these important papers relate to the performance of pension funds. The calculation of portfolio return is the first step in the performance measurement process. We calculate portfolio returns because, fundamentally, the calculation of gain and loss in cash terms, in isolation, is insufficient, it doesn't allow for a fair comparison, and it doesn't allow for the assessment of the quality of performance. A $10,000 profit on a capital base of $100,000 is quite different from a $10,000 profit on a capital base of $1,000,000. Return calculations adjust for the capital base, and thus allow for a fair comparison against:

1. Expectations
2. History
3. Benchmarks
4. Other asset managers

Over the decades a variety of different return methodologies have evolved; the methodology employed will depend on data availability, data quality, accuracy required, ...