Real Rate Of Return

With an 8% nominal return and 3.5% inflation, the approximate real return is:

1. A.About 2.3%This divides 8 by 3.5 instead of subtracting. The result of dividing two percentages is a ratio, not a return, so the units do not even match what the question asks for.
2. B.About 11.5%This adds inflation to the nominal return instead of removing it. Inflation destroys purchasing power, so the real return must be smaller than the nominal return, never larger.
3. C.About 5%This is in the right neighborhood and would come from rounding inflation down to 3%. The stem gives 3.5% precisely, and subtracting it leaves 4.5%, which is also closer to the exact Fisher result of about 4.35%.
4. D.About 4.5%Correct - nominal minus inflation.

Why: 8% - 3.5% = 4.5%.

An investment's real return is:

1. A.The nominal return plus inflationAdding inflation moves in the wrong direction. Inflation consumes purchasing power, so it must be removed from the nominal return, leaving a real return below the nominal one.
2. B.The nominal return minus inflationCorrect - real return strips out inflation.
3. C.The after-tax returnAfter-tax return is also an adjusted return, which is what makes this tempting. The two adjust for different things: taxes remove what the government takes, while the real return removes what inflation takes.
4. D.The coupon rateA coupon rate is a fixed nominal contractual payment, stated before any inflation adjustment. It is an input to a return calculation, not a real return.

Why: Real (inflation-adjusted) return is the nominal return minus the inflation rate.

An investor holds bonds from thirty unrelated issuers across many industries, and inflation then accelerates across the whole economy. How is the resulting erosion of her real return classified?

1. A.Nonsystematic, because each issuer's ability to pay is affected to a different degree.Wrong. What is eroding is the real value of the payments, which is independent of any issuer's finances.
2. B.Nonsystematic, because further diversification across issuers would reduce the exposure.Wrong. More issuers simply means more streams of fixed payments, every one of them eroded by the same inflation.
3. C.Systematic, because a general rise in prices erodes every fixed payment at once.Correct. Purchasing power risk arises from an economy-wide condition and reaches every fixed-income holding together.
4. D.Systematic, but only for issuers whose costs rise faster than their revenues do.Wrong. That describes business risk at particular firms, a separate exposure that diversification does address.

Why: Systematic risks are driven by conditions affecting the whole market or economy, which is why they cannot be diversified away. Inflation is exactly such a condition, reducing what every fixed payment buys whoever the issuer happens to be. Spreading across thirty issuers protects against one of them defaulting, a nonsystematic exposure, and does nothing about the general price level. An investor who wants to address this has to change the type of instrument, moving toward inflation-adjusted or floating-rate securities.

Celeste Diaz earns a nominal 8.40% on a $133,357 portfolio while inflation is 3.90%. Using the exact multiplicative relationship, what is the real return?

1. A.12.30%This adds inflation to nominal return, which moves in the wrong direction.
2. B.4.50%This uses the common subtraction approximation rather than the exact calculation requested.
3. C.4.33%This uses the exact relationship between nominal growth and inflation.
4. D.46.43%This forms a ratio of the two percentages rather than adjusting growth factors.

Why: The exact real return divides the growth factor of the nominal return by the inflation growth factor and subtracts one. Simple subtraction is an approximation and can differ from the exact answer.