Negative real return

A deposit can pay you interest every year and still leave you poorer.

That happens when prices rise faster than the deposit earns. The rupees in the account go up. The things those rupees buy go up faster. What you can actually afford has fallen.

The workbook makes the point sharply. The nominal rate is always positive, because nobody hands over money for a negative headline rate. The real rate of return is different. It can be positive or negative. When inflation runs above the nominal rate, the real rate turns negative.

And the workbook spells out what that means: the return earned has been wiped out by rising prices.

The test is a comparison, not a calculation: is the nominal rate above or below the inflation rate?

Above. The real return is positive. The workbook's own illustration: a return of 7 percent against inflation of 6 percent leaves a real return of about 1 percent — small, but still growth.

Below. The real return is negative. Nothing has been lost in rupee terms, but purchasing power has shrunk.

The workbook computes the real rate two ways, and the second is the accurate one:

• Subtraction: real rate = nominal rate minus inflation rate. Quick, and approximate.
• Discounting: real rate = ((1 + nominal rate) divided by (1 + inflation rate)) minus 1. Its worked case is a bond paying 10 percent with 5 percent inflation, which gives 4.76 percent rather than the 5 percent subtraction suggests.

Where negative real returns bite hardest is in fixed and guaranteed products. Section 1.2.4 says so directly: the guarantee comes with the risk of lower returns, and the real return from such an investment may be very low and even negative in periods when inflation is high. The rate is locked for the whole tenor, so it cannot respond when inflation climbs.

The workbook does not supply a worked example in which the real rate actually turns negative. It states the condition and leaves the arithmetic to the reader.

Accurate form, as given in section 1.2.4:

(1 + NR) = (1 + RR) x (1 + IR), so RR = ((1 + NR) / (1 + IR)) − 1

A negative real return is simply the case where NR is less than IR.

The workbook states the condition but gives no negative worked case, so the figures below apply its own formula.

Mr Deshpande, aged 58, puts Rs 10,00,000 into a 10-year bank deposit paying 6.5 percent a year. Over the same ten years inflation runs at 7 percent.

Real rate, the accurate way

(1.065 / 1.07) − 1 = minus 0.47 percent a year. Subtraction would have said minus 0.5 percent — close, and still negative.

What the rupees do

He has more rupees than he started with — Rs 8.77 lakh more. He still cannot buy what Rs 10,00,000 bought him on day one. In today's money his corpus is worth about Rs 9,54,140, so roughly Rs 45,860 of purchasing power has quietly gone.

Now put that in a retirement plan. If the corpus meant to fund 20 years of expenses sits in a product earning a negative real return, the corpus shrinks in real terms every single year of retirement, even though the passbook says it is growing.

Chapter 1, section 1.2.2 (Real Rate of Return vs. Nominal Rate of Return), is where the sentence lives: the nominal return is always positive, the real rate can be negative, and a negative real return means the return has been wiped out by rising prices. Section 1.2.4 repeats the warning for fixed and guaranteed products.

The question is almost always conceptual rather than numerical: which of these can be negative (the real rate, not the nominal rate), or what does a negative real return imply. A harder version hands you a nominal rate below the inflation rate and asks what has happened to purchasing power.

• The nominal rate cannot be negative; the real rate can. This is the exact contrast the workbook draws, and it is the answer to the most common form of the question.
• A negative real return is not a capital loss. The rupee balance still grows. It is purchasing power that falls, which is why the loss is easy to miss.
• Fixed and guaranteed does not mean safe. Section 1.2.4 names low and negative real returns as the price of the guarantee, because the rate is locked for the tenor while inflation is not.
• Subtraction understates the real rate slightly. Use the discounting formula when the paper asks for the accurate figure, exactly as in the 10 percent and 5 percent case that gives 4.76 percent.
• Tax makes it worse, not better. A tax-adjusted return is computed on the nominal interest first; netting inflation off a post-tax return can push a marginally positive real return below zero.
• Do not treat this as the same thing as inflation risk. Inflation risk is the risk that prices rise faster than planned. A negative real return is the outcome when they already have.