Rolling returns

Ask how a scheme did over one year and the answer depends heavily on which day you start and which day you stop. Start at a market bottom and the number looks brilliant. End at one and it looks dreadful. The scheme did not change; only the dates did.

The workbook names this weakness of holding period returns: they may not present an accurate picture of the returns from a fund if the initial value or the end value used for calculation was too high or low.

Rolling returns fix it by refusing to pick one start date. Instead they calculate the return for every consecutive holding period of the chosen length within a longer evaluation window, rolling the start forward daily, weekly or monthly, and then average the results. One lucky or unlucky date becomes just one observation among many.

The standard return first (Chapter 10, section 10.4). A holding period return is calculated for a fixed period such as one month, three months, one year, three years or since inception. For periods over one year it is a CAGR; for periods under one year, a simple absolute return.

Then roll it. The workbook's example: all consecutive one year returns in a three-year period with a daily/weekly/monthly rollover is calculated and averaged.

The more observations, the less any single start or end date can move the average. The spread of the individual returns is useful too: it shows how differently investors who entered at different times actually fared, which is the consistency Chapter 10 says investors should look for alongside the headline return.

Rolling return = (R1 + R2 + … + Rk) ÷ k

where each R is the annualised return for one holding period,
and k is the number of consecutive periods in the evaluation window

Illustrative. The NAVs are hypothetical, and a quarterly rollover is used to keep the table short.

A scheme's NAV at each quarter-end over two years:

One-year returns, rolled every quarter:

Rolling one-year return = (10 + 10 + 20 + 10 + 15) ÷ 5 = 13.00%

A salesperson quoting only the Q2 → Q6 year would show 20 per cent — but Q2 was a dip, so that start date flatters the scheme. Four of the five investors earned 10 to 15 per cent. For comparison, the two-year point-to-point CAGR is √(25.30 ÷ 20.00) − 1 = 12.47 per cent.

On Rs 1,00,000, the difference between the flattering 20 per cent and the typical 10 per cent is Rs 10,000 in a year.

Chapter 10 (Risk, Return and Performance of Funds), section 10.4, defines rolling returns immediately after holding period returns, as the cure for their start-and-end-date distortion, and then discusses why consistency of return matters. Expect a definition question and a question on which weakness of holding period returns rolling returns address.

• Rolling returns average many holding periods; a holding period return is one period with one start and one end.
• The problem they solve is the start or end value being unusually high or low — not taxes, not loads.
• Holding period, evaluation period and rollover frequency are three different things. In the workbook's example they are one year, three years and daily/weekly/monthly.
• CAGR for periods over one year, simple absolute return under one year — the rule for each individual holding period return.
• A high rolling average does not remove the need to look at risk; Chapter 10 says return alone is not adequate to decide.