Account for the way economy-wide drivers, namely growth, inflation and volatility, shape what assets return and the premiums investors demand for bearing risk.

FRM® Part II · Risk Management and Investment Management · Factors · FRM2.IM.2.b

The idea

Three economy-wide drivers explain much of what assets return: economic growth, inflation and volatility. Each defines bad times: weak growth, high or unexpected inflation, and high volatility. Assets are priced by how they behave in bad times, because an extra unit of wealth is most valuable then. An asset that loses in bad times must offer a higher expected return, a risk premium. An asset that pays off in bad times is a hedge and earns a low or even negative premium. Examples are nominal government bonds in a disinflationary recession and put options in a volatility spike. Equities load on growth and nominal bonds suffer when inflation rises. Inflation-linked bonds and commodities hedge inflation. Short volatility positions earn a premium but crash when volatility jumps. Let βk be the exposure to driver k and λk its premium. Expected return, written ER, is then roughly the risk-free rate plus each exposure times its premium: ER = rf + Σ βk × λk. The usual mistake is to equate premium with total volatility rather than bad-times exposure.

Formulas

Inflation risk premium from bond yields

inflation risk premium = nominal yield − real yield − expected inflation

nominal yield: the yield on a conventional government bond
real yield: the yield on an inflation-linked bond of the same maturity
expected inflation: expected average inflation over the bond's life

Nominal minus real yield is breakeven inflation, which includes the premium; treating breakeven as pure expected inflation overstates it. Ignores liquidity differences.

Multifactor expected return

E(R) = Rf + β1 × λ1 + β2 × λ2 + … + βk × λk

Rf: the risk-free rate
β1, β2, βk: the asset's beta to each factor
λ1, λ2, λk: each factor's risk premium, the expected return of its pure factor portfolio minus Rf

With growth, inflation and volatility as the factors and exposures signed so a positive one loses in bad times. A hedge, such as an asset that gains when volatility rises, has a negative exposure and lowers the expected return.

A practice question

From the question bank, with the reason each wrong option is wrong.

Which set of three economy-wide drivers is used to explain asset returns and the premiums investors demand?

Size, value and momentum.Why not: These are style factors built from stock characteristics, not economy-wide drivers.
Interest rates, liquidity and credit spreads.Why not: Lists market variables; they are not the standard three macro drivers of growth, inflation and volatility.
Economic growth, inflation and volatility. - correct
Employment, exchange rates and commodity prices.Why not: Lists individual macro variables rather than the three systematic bad-times drivers.

The macro framework uses growth, inflation and volatility as the economy-wide risks. Bad times are weak growth, high inflation and high volatility, and premia compensate for losing in them.

A harder one

A 10-year nominal government bond yields 4.5 percent and a 10-year inflation-linked bond from the same government yields a real 2.0 percent. Surveys put expected average inflation over the decade at 2.0 percent. Ignoring liquidity differences and using simple subtraction, the inflation risk premium embedded in the nominal yield is closest to:

2.5%Why not: This is the breakeven inflation rate (4.5 - 2.0), which includes expected inflation and the premium; it is not the premium alone.
0.5% - correct
2.0%Why not: Reports expected inflation (equal here to the real yield) instead of the excess of breakeven over expected inflation.
-0.5%Why not: Sign error: subtracts breakeven from expected inflation (2.0 - 2.5) instead of the reverse.

Breakeven inflation = nominal yield - real yield = 4.5% - 2.0% = 2.5%. Inflation risk premium = breakeven - expected inflation = 2.5% - 2.0% = 0.5%, the compensation for bearing inflation uncertainty.

The hardest tier

A pension plan holds 60 percent equities and 40 percent long-term nominal government bonds and relies on the bonds to cushion equity losses. Which economic environment is most likely to hurt both holdings at once?

Weak growth combined with rising inflation, which cuts earnings while pushing yields up. - correct
A recession with falling inflation, in which yields fall and bond prices rise.Why not: In a disinflationary recession bonds rally and hedge the equity loss, so diversification works.
A volatility spike from a financial panic, as investors flee to government bonds.Why not: Flight to quality lifts bond prices; it is the case where nominal bonds act as a hedge.
Strong growth with stable inflation, which supports earnings and leaves yields little changed.Why not: This is a good environment for equities and not harmful to bonds; it is not a bad-times scenario.

Stagflation raises discount rates and cuts earnings, so equities and nominal bonds fall together. When growth or volatility drives markets, bonds usually hedge; when inflation is the driver, the stock-bond correlation turns positive.

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