Percentage return

Rs 900 of interest sounds better than Rs 500. It is not always the better investment.

X put in Rs 10,000 and earned Rs 900. Y put in Rs 5,000 and earned Rs 500. In rupees X is ahead. But X used twice the money to get there.

The percentage return fixes this. Divide the return by the original investment and multiply by 100. X earned 9 percent. Y earned 10 percent. Y did better.

The workbook explains why the conversion matters: it puts every investment on a base of Rs 100, so two investments of different sizes can be compared directly.

One thing the percentage still does not handle is time. Two returns over different holding periods are not comparable either, and that needs annualising.

The calculation. Section 5.2.1 gives it as Return on Investment divided by Original Investment, multiplied by 100.

The workbook's own pair:

The ranking reverses when you move from rupees to percentages. That reversal is the entire teaching point of the section.

What goes into the numerator. Everything the investment produced: periodic income such as interest or dividend, plus the capital gain or loss, whether realised by selling or unrealised and represented by a change in value. The workbook's mutual fund case: bought at a NAV of Rs 12, a dividend of Re 0.80 received, NAV a year later Rs 12.50. The total return is 0.80 + 0.50 = Rs 1.30. If the NAV had instead fallen to Rs 11, the total return is 0.80 minus 1.00 = minus Re 0.20.

Where it stops. A percentage return still says nothing about how long the money was invested. 40 percent over 6 years and 8.5 percent per annum cannot be compared as they stand. The workbook's fix is to annualise: multiply the absolute rate of return by 365 divided by days held, 12 divided by months held, or 1 divided by years held. Here, 40 percent x 1/6 = 6.67 percent a year, which is below the deposit's 8.5 percent. For horizons beyond a year the accepted measure is CAGR, because it also accounts for compounding.

So the workbook builds a ladder: rupee return, then percentage return, then annualised return, then CAGR, then XIRR where there are many cash flows on many dates.

Percentage return = (Return on investment / Original investment) x 100

where the return on investment is periodic income plus capital gain or loss, realised or unrealised.

To annualise it, multiply by 365 / days held, 12 / months held or 1 / years held, depending on how the holding period is expressed.

Two retirement investors compare a year's results.

Mrs Pillai invested Rs 8,00,000 in a debt fund. She received no payout, and the value rose to Rs 8,52,000.

Return in rupees   = 8,52,000 - 8,00,000 = Rs 52,000
Percentage return  = 52,000 / 8,00,000 x 100 = 6.5 percent

Mr Pillai invested Rs 2,50,000 in an equity fund at a NAV of Rs 125, so 2,000 units. He received a dividend of Rs 4 a unit, and the NAV rose to Rs 133.

Dividend received  = 2,000 x 4 = Rs 8,000
Change in value    = 2,000 x (133 - 125) = Rs 16,000
Return in rupees   = 8,000 + 16,000 = Rs 24,000
Percentage return  = 24,000 / 2,50,000 x 100 = 9.6 percent

She earned more than twice as many rupees and did the worse job of it per rupee committed. If they had Rs 2,50,000 more to invest between them, the percentage — not the rupee figure — tells them where it should go.

One caution from the same section: both of these are one-year figures, so they happen to be comparable. Had Mr Pillai's 9.6 percent been earned over three years, it would first have to be annualised before being set against her 6.5 percent.

Chapter 5, section 5.2.1, introduces the rupee or absolute return and then the percentage return as the fix for it; 5.2.2 adds annualising and 5.2.3 the CAGR. The X-and-Y pair with the reversed ranking is printed in the workbook and is the question most likely to appear.

Expect a computation — you are given the amount invested and the income and capital gain, and asked for the percentage — and a comparison question where the larger rupee return belongs to the worse investment. A second-order question asks what a percentage return still fails to capture (the holding period, and therefore compounding).

• The bigger rupee return is often the worse investment. That is the whole reason the section exists, and it is what the X-and-Y options are testing.
• Divide by the original investment, not by the closing value. Using the end value understates the return.
• Include the periodic income, not just the price change. The workbook's Rs 1.30 comes from a Re 0.80 dividend plus Re 0.50 of NAV gain.
• Unrealised gains count. The workbook says gains may be realised by selling or unrealised and represented by the change in value — either way they form part of the return calculation.
• A percentage return is not an annual return. 40 percent over six years is 6.67 percent a year. Quoting the 40 percent against a deposit's 8.5 percent per annum is the classic error.
• Percentage return is not CAGR. The simple percentage ignores compounding; CAGR is the accepted measure once the horizon passes one year.
• Do not confuse it with absolute return, which the workbook uses for the rupee figure that this measure is designed to replace.