The 11 asset classes, deepened: risk drivers and one example per driver

Chapter 20 of 22 · Unit 7 · Portfolios and behaviour · 25 min read

Beginner path: read to Level 2 · Series 65 path: read to Level 3 · CFA path: read to Level 4

After this chapter you can

Name the risk drivers behind each of the 11 asset classes and say which ones matter most for each.
Work out how far a price should move when one driver changes, using duration, the Gordon model, cap rates, roll yield and the Fisher relation.
Split a foreign asset's dollar return into its local return and its currency return.
Rerun four historical episodes (TIPS in 2022, the baht in 1997, gold from 1980 to 2008 and cash in 1946) through that math and compare the estimate with what happened.

In this chapter

Level 1 · Plain words
Level 2 · How it works
Level 3 · The math
1. One equation per class
2. Which driver is largest, by the numbers
Level 4 · History, analysed
Sources
Gaps
Terms

In this chapter

Level 1 · Plain words
Level 2 · How it works
Level 3 · The math
1. One equation per class
2. Which driver is largest, by the numbers
Level 4 · History, analysed
Sources
Gaps
Terms

The overview article gave each asset class a job, a few risks and a table of numbers. Here we go one layer down. For each class we ask what moves its price, through which channel, and how large a move one change in that driver should cause. Each driver gets a historical example and a pointer to the chapter that holds its math. We keep the article's order and its anchors, so the "Deeper" link under each class in the article lands on the matching section here.

One warning before we start: our worked numbers are first approximations. They show the direction and the rough size of a move, and Level 4 tests a few of them against what happened. Where the estimate and the outcome differ, we say by how much and why.

Level 1 Plain words

For every reader: the idea in plain words, no formulas.

What a risk driver is

Every price is somebody's estimate of future cash, discounted for time and for risk. Anything that changes one of those three pieces is a risk driver. Profits that shrink change the cash. When interest rates rise, the discount for time grows. Panic raises the discount for risk. When we say a class is "exposed" to a driver, we mean that a change in the driver changes the class's price in a predictable direction.

Two classes can share a driver and still react in opposite directions. Higher inflation hurts an ordinary bond, whose payments stay fixed in dollars, and helps a TIPS bond, whose principal grows with prices. When the dollar strengthens, a US investor holding European shares loses on the conversion, and the same investor gains when buying a European holiday. Knowing the direction for each class is most of what diversification means in practice.

The eight drivers we use

We sort the forces that move asset prices into eight groups. The list is ours, chosen to cover the classes in the article with as few groups as possible.

Growth and earnings. How fast the economy and company profits grow. Stocks and real estate depend on it most.
Interest rates. The yield on safe government bonds. Every asset that pays cash later is worth less today when rates rise.
Inflation. The pace at which prices rise. It erodes fixed payments and raises the cost of holding cash.
Credit. The chance that a borrower stops paying, and how much a lender gets back if it does.
The dollar. For a US investor, any asset priced in another currency gains or loses with the exchange rate.
Liquidity and risk sentiment. How easily an asset can be sold without moving its price, and how much reward investors demand for holding risk at all. Both swing hardest in a panic.
Policy and politics. Central bank decisions, tax law, capital controls, regulation and elections.
Physical supply and demand. Barrels, bushels and ounces. This driver matters most for commodities and gold, which have no cash flow of their own.

One grid for all eleven classes

Our grid rates how hard each driver hits each class for a US investor: H for a first-order driver, M for a real but second-order one, L for a weak link. We based the ratings on the episodes in Level 2 and Level 4, and they remain judgments. Readers with a different time horizon may rate a few cells differently.

The eleven asset classes against the eight risk drivers, shaded by how strongly each driver moves each class for a US investor.

Show the numbers

Class	Growth	Rates	Inflation	Credit	Dollar	Liquidity and sentiment	Policy	Physical supply
US stocks	High	High	Medium	Low	Low	High	Medium	Low
International developed stocks	High	Medium	Medium	Low	High	High	Medium	Low
Emerging-market stocks	High	Medium	Medium	Medium	High	High	High	Medium
US bonds	Low	High	High	Medium	Low	Medium	Medium	Low
Municipal bonds	Low	High	Medium	Medium	Low	Medium	High	Low
TIPS	Low	High	Low	Low	Low	Medium	Medium	Low
Real estate (REITs)	High	High	Medium	Medium	Low	High	Medium	Low
Commodities	Medium	Low	High	Low	Medium	Medium	Medium	High
Gold	Low	High	Medium	Low	High	High	Medium	Medium
Currencies	Medium	High	High	Low	High	High	High	Low
Cash and Treasury bills	Low	Medium	High	Low	Low	Low	High	Low

Source: computed: the Chapter 20 grid (ratings are the chapter's judgments, read from its table), as of 2026-10-28.

Class	Growth	Rates	Inflation	Credit	Dollar	Liquidity and sentiment	Policy	Physical supply
US stocks	H	H	M	L	L	H	M	L
International developed stocks	H	M	M	L	H	H	M	L
Emerging-market stocks	H	M	M	M	H	H	H	M
US bonds	L	H	H	M	L	M	M	L
Municipal bonds	L	H	M	M	L	M	H	L
TIPS	L	H	L	L	L	M	M	L
Real estate (REITs)	H	H	M	M	L	H	M	L
Commodities	M	L	H	L	M	M	M	H
Gold	L	H	M	L	H	H	M	M
Currencies	M	H	H	L	H	H	H	L
Cash and Treasury bills	L	M	H	L	L	L	H	L

Read across a row to see what can hurt one class. Read down a column to see which classes fall together when one driver turns. The interest-rate column has the most H ratings, which is why 2022 hurt so many classes at once.

Level 2 How it works

For readers who want the mechanism, with the diagrams.

Beginner path stops here

Each section below takes one class from the article. A short chain diagram shows how its main drivers reach the price. The table lists each driver with its channel, a historical case and the chapter that analyses it. Then comes one worked impact per driver, with a number from the chapter's calculations.

US stocks

A share is a claim on a company's future profits. Its price equals earnings times a multiple, and the multiple reflects what investors expect from growth, interest rates and the reward they want for bearing risk. Each of those can move on its own, which is why a stock market can fall when profits are still rising.

Profits, interest rates and the risk premium feed the multiple and the earnings that set a stock price.

Driver	How it reaches the price	Historical case	Where the math is
Growth and earnings	profits fall in a recession and the multiple often falls with them	2008, S&P 500 about −37.0 % with dividends	Equity valuation
Interest rates	a higher discount rate lowers the value of distant profits	2022, S&P 500 −18.1 % as the Fed raised rates	Policy and the yield curve
Risk sentiment	investors demand a larger reward to hold stocks	19 Oct 1987, S&P 500 down 20.5 % in one day	Probability
Inflation	high inflation pushes up rates and squeezes margins	1973 to 1974, deep real losses	Risk and return

Earnings and the multiple together. Suppose profits fall 30 % in a recession and the price-to-earnings multiple slips from 20 to 16. The price falls −44.0 %, much more than the profit decline alone, because the two effects multiply.

The discount rate. Take the Gordon model with dividends growing 4 % a year. If the return investors require rises from 8 % to 9 %, through higher bond yields or a higher equity risk premium, the price changes by −20.0 %. One point on the discount rate moves the price by a fifth.

Growth expectations. Hold the required return at 8 % and cut long-run growth from 4 % to 3.5 %. The price changes by −11.1 %. Half a point of growth is worth more than a tenth of the market's value in this model, which is why news about the long-run economy can move stocks so much.

Deeper: the Gordon model, CAPE and DCF, and beta, factors and the risk premium.

International developed-market stocks

Foreign developed markets carry every driver of US stocks, measured in their own economies, plus one more for a US holder: the exchange rate. A European share that rises 10 % in euros can give a dollar investor more or less than 10 %, depending on what the euro did that year. Country weights matter too. Japan was about 45 % of the world index at its 1989 peak, so a broad international fund then was largely a bet on one market.

Local earnings and rates set the local return; the exchange rate converts it into dollars.

Driver	How it reaches the price	Historical case	Where the math is
Local growth and earnings	same channel as US stocks, in another economy	Japan after the Nikkei's 38,915.87 close on 29 Dec 1989	Factors and international markets
The dollar	a stronger dollar shrinks foreign gains once converted	the dollar's rise into 1985 and its fall after the Plaza Accord of 22 Sep 1985	Currencies
Risk sentiment	world markets fall together in a crisis	2008, MSCI EAFE about −43.0 % in dollars	Probability
Policy	each country's central bank, tax and regulation	the euro-area debt crisis of 2010 to 2012	Policy and the yield curve

The currency layer. A European index gains 10 % in euros while the euro falls 8 % against the dollar. The dollar return comes to +1.2 %. Flip the currency move to a euro that rises 8 %, and the same local gain becomes +18.8 %. The currency can be as large as the stock move itself.

Country concentration. An index weighted by market value gives the largest weight to whichever market has risen most, so a fund holder can end up most exposed to the market with the highest valuation. Japan in 1989 is the standard case, analysed in the factors chapter.

Deeper: the international return decomposition and what moves exchange rates.

Emerging-market stocks

Emerging markets add three drivers that developed markets carry only weakly: capital that can leave quickly, currencies that can fall by half, and governments that can change the rules for foreign owners. Many companies and governments in these markets borrow in dollars while earning in their own currency, so a falling local currency raises their debt burden at the moment their revenue shrinks in dollar terms.

Capital flows and the dollar push the local currency; the currency feeds both the dollar return and the burden of dollar debt.

Driver	How it reaches the price	Historical case	Where the math is
The dollar and capital flows	money leaves when the dollar or US rates rise	the Thai baht, floated on 2 Jul 1997	Currencies
Credit	dollar debt grows in local terms when the currency falls	the 1997 Asian crisis	Credit
Policy and politics	capital controls, limits on foreign ownership, sudden rule changes	Malaysia's capital controls of 1998	Factors and international markets
Risk sentiment	the class is among the first to be sold in a panic	2008, MSCI Emerging Markets about −53.0 % in dollars	Probability

Currency and local return together. A local market gains 5 % in its own currency while that currency loses 15 % against the dollar. A US holder ends with −10.8 %.

Dollar debt. A company owes dollars and earns baht. If the baht goes from 25 to 50 per dollar, the debt measured in baht rises +100 % while the revenue stays in baht. A firm that was comfortably solvent can become insolvent without selling one fewer unit.

Deeper: the 1997 crisis analysed and carry, parity and the drivers of exchange rates.

US bonds

A high-quality bond's cash flows are fixed in dollars, so its price depends on the yield the market demands for those dollars. Duration measures how sensitive that price is. A bond fund with a duration of 6 years loses about 6 % for each one-point rise in yields. Corporate bonds add credit risk, and every bond loses buying power to inflation.

Inflation and policy push yields; yields move the price through duration; credit spreads add a second channel for corporate bonds.

Driver	How it reaches the price	Historical case	Where the math is
Interest rates	price falls by about duration times the yield rise	2022, Bloomberg US Aggregate about −13.0 %	Bonds and basis points
Inflation	erodes fixed coupons and pushes the Fed to raise rates	1979 to 1981, 10-year yield above 15 %	Policy and the yield curve
Credit	spreads widen when default risk rises	2008 and March 2020	Credit
Liquidity	even Treasuries can trade badly in a rush for cash	March 2020	Bonds and basis points

Rates. A fund with a duration of 6 years faces a one-point rise in yields. Its price changes by about −6.0 %. A one-point fall gives about +6.0 %.

Credit. A high-yield fund with a duration of 4 years sees its spread widen by 500 basis points, a smaller shock than the one of 2008. The price change from the spread alone is about −20.0 %, before any defaults.

Reinvestment. A retiree with $500,000 in short-term bonds earned $25,000 a year at 5 %. When short rates fell to 0.1 %, the same sum earned $500. No price fell, yet the income dropped by nearly all of it.

Deeper: duration, convexity and DV01 and spreads, default and recovery.

Municipal bonds

Munis carry the rate risk of any bond of the same maturity, a credit risk that varies a great deal from one issuer to the next, and a driver that taxable bonds lack: tax policy. Their after-tax value to a buyer depends on that buyer's tax rate, so a change in tax law changes what munis are worth to the people who own most of them.

Rates and issuer credit set the muni yield; the buyer's tax rate sets what that yield is worth.

Driver	How it reaches the price	Historical case	Where the math is
Interest rates	same duration channel as Treasuries	2022, Bloomberg Municipal Bond index about −8.5 %	Bonds and basis points
Tax policy	the value of the exemption moves with tax rates	changes in the top federal rate	Accounts and taxes
Credit	issuers range from strong states to weak single projects	Detroit's bankruptcy filing of July 2013; Puerto Rico, and the PROMESA law of 2016	Credit
Liquidity	many issues trade only a few times a year	the March 2020 sell-off in muni funds	Credit

Tax rates. A muni yields 3 % free of federal tax. To a buyer in a 35 % bracket its taxable-equivalent yield is 4.62 %; to a buyer in a 24 % bracket it is 3.95 %. A cut in tax rates lowers the value of the exemption, and muni prices tend to adjust down to match.

Credit. A lower-rated issuer with a 1 % yearly chance of default and a 50 % loss if it defaults carries an expected loss of 50 bp a year. The spread has to cover that loss, plus a premium for the uncertainty around it, before the buyer earns anything extra.

Deeper: the taxable-equivalent yield in a plan and ratings, spreads and default.

Treasury inflation-protected securities (TIPS)

A TIPS bond pays a fixed real yield on a principal that grows with the Consumer Price Index. That design removes inflation surprise as a risk, and it leaves a different one in place: the real yield can rise, and a TIPS bond's price falls with it through its own duration. Many buyers learned that in 2022.

CPI grows the principal; the real yield moves the price through real duration; the two together set the return.

Driver	How it reaches the price	Historical case	Where the math is
Real interest rates	price falls by real duration times the rise in the real yield	2022, 10-year real yield from about −1.0 % to about 1.5 %	Bonds and basis points
Inflation	the principal accrues with CPI, a gain in high-inflation years	2022, CPI up 6.5 % December to December	Macroeconomics
Liquidity	TIPS trade less than nominal Treasuries and can lag in a rush for cash	March 2020	Bonds and basis points
Tax	the yearly accrual is taxable income in a taxable account	every year, for a taxable holder	Accounts and taxes

Real rates. A TIPS fund with a real duration of 7 years faces a rise of 250 basis points in real yields. The price effect is about −17.5 %, more than even the inflation accrual of 2022 offset.

Breakeven inflation. A 10-year Treasury yields 4.0 % and a 10-year TIPS yields 1.8 %. The gap, 2.20 %, is the breakeven inflation rate: if CPI averages more than that over ten years, the TIPS holder comes out ahead.

Deeper: TIPS in 2022, run through the math and breakeven inflation.

Real estate (REITs)

A property is worth its net operating income divided by a cap rate, the yield buyers demand from that income. The cap rate moves with interest rates and with the market's view of the property type. Most REITs also borrow, so a change in property values moves the shares by more than the buildings moved.

Interest rates and the property cycle set the cap rate; rents set the income; debt magnifies the move in property value into the share price.

Driver	How it reaches the price	Historical case	Where the math is
Interest rates	higher rates push cap rates up and values down	2022, FTSE Nareit All Equity REITs about −25.0 %	Real estate
Growth and rents	rents and occupancy follow the economy and the property type	offices after 2020	Real estate
Credit and refinancing	maturing debt must be rolled at current rates	2008, FTSE Nareit All Equity REITs about −38.0 %	Credit
Risk sentiment	listed REITs trade like stocks in a crash	2008 and March 2020	Risk and return

The cap rate. A building earns $1 million of net operating income a year. At a 4 % cap rate it is worth $25,000,000; at 5 % it is worth $20,000,000, a change of −20.0 % with no change in rent.

Borrowing. If that property carries debt equal to half its value, the 20 % fall in the building becomes −40.0 % for the equity holder. At a loan-to-value of 35 %, closer to a typical listed REIT, it is −30.8 %.

Deeper: cap rates and REIT structure and REITs in 2022, analysed.

Commodities

Commodity investors hold futures, and a futures position earns three things: the change in the spot price, the roll yield from replacing an expiring contract with a later one, and the interest on the cash posted as collateral. Physical supply and demand set the spot price. The slope of the futures curve sets the roll.

Supply shocks and demand move the spot price; storage and the slope of the futures curve set the roll yield; collateral earns the bill rate.

Driver	How it reaches the price	Historical case	Where the math is
Physical supply	a small supply cut moves the price a lot when demand cannot adjust quickly	the oil embargo of October 1973	Microeconomics
Demand and growth	recessions cut demand for energy and metals	2008, Bloomberg Commodity index about −36.0 %	Macroeconomics
Curve slope and storage	contango makes each roll cost money; backwardation pays	April 2020, WTI May contract settled at −$37.63	Commodities and gold
Inflation	supply-driven inflation lifts commodity prices with it	the 1970s	Commodities and gold

The roll. The front contract trades at $60 and the next month at $61. With the curve unchanged, each roll returns −1.64 %, and twelve rolls a year give −18.0 %. An investor can lose money that way while the spot price goes nowhere.

Supply with inelastic demand. Suppose buyers cut their use by only 0.1 % for each 1 % rise in price in the short run. To clear a 5 % supply cut the price must rise by about +50 % at first. That elasticity is an illustration; published short-run estimates for oil are small, and Level 3 explains why the size matters.

Deeper: futures curves, carry and roll and supply, demand and elasticity.

Gold

Gold pays no income, so its price comes from what holders will pay to own it. Three drivers dominate: real interest rates, which set what a holder gives up by owning gold in place of an inflation-protected bond; the dollar, in which gold is priced; and fear, which raises demand for an asset with no issuer that can default. Central bank buying and jewelry demand add physical flows.

Real yields set the cost of holding gold; the dollar and crisis demand move the price; central bank buying adds physical demand.

Driver	How it reaches the price	Historical case	Where the math is
Real interest rates	a higher real yield raises the income a gold holder forgoes	2013, as real yields rose, gold about −28.0 %	Commodities and gold
The dollar	a weaker dollar tends to raise the dollar price of gold	the 1970s after convertibility ended in 1971	Currencies
Crisis demand	buyers turn to an asset with no default risk	2008 to 2011	Commodities and gold
Inflation	a hedge over very long spans, unreliable over a decade	the 1980 peak and the long fall after it	Commodities and gold

The forgone income. Holding $100,000 of gold when a 10-year TIPS pays a 2 % real yield gives up about $2,000 a year of real income. When the real yield is −1 %, the bond holder loses buying power each year and the gap reverses to −$1,000: a gold holder then gives up nothing and avoids a loss. That is the main reason gold has tended to do well when real yields were negative.

Nominal and real. A price that ends where it began has still lost to inflation. We work the 1980 to 2008 case in Level 4.

Deeper: gold from 1980 to 2008 in real terms and gold and real yields.

Currencies

An exchange rate is the price of one money in another. Interest rate gaps between countries move it in the short run, inflation gaps over long spans, and trade balances, risk sentiment and central bank action at any time. For most investors the currency is a layer on top of a foreign asset; a few hold it on purpose through a carry trade.

Rate gaps, inflation gaps, trade and risk sentiment move the exchange rate; central banks can override all of them for a while.

Driver	How it reaches the price	Historical case	Where the math is
Interest rate gaps	money flows toward the higher-yielding currency	the 2022 dollar, as the Fed raised rates faster than most	Currencies
Inflation gaps	higher inflation erodes a currency over years	the purchasing-power parity evidence	Currencies
Policy and intervention	a peg holds until it breaks	sterling on 16 Sep 1992; the Swiss franc on 15 Jan 2015	Currencies
Risk sentiment	carry trades unwind together in a panic	2008	Currencies

Covered interest parity. The dollar costs 150 yen, dollar rates are 5 % and yen rates 0.1 %. Covered interest parity sets the one-year forward at 143.00 yen. The forward discount equals the rate gap, so hedging the currency removes the interest advantage too.

Carry. An investor borrows yen at 0.1 % and holds dollars at 5 %. If the exchange rate stays put, the year returns +4.9 %. If the dollar falls 10 % against the yen, the result is −5.6 %. Small steady gains and an occasional large loss are the usual pattern of carry.

Deeper: parity conditions and carry and the peg breaks of 1992 and 2015.

Cash and Treasury bills

Cash almost never loses dollars. Its risks are inflation, which takes buying power, and the policy rate, which can fall and cut the income. A third risk applies to the container: a bank deposit above the insurance limit, or a money market fund, depends on who holds the money.

The policy rate sets what cash earns; inflation sets what it keeps; the holder of the deposit adds a small credit risk.

Driver	How it reaches the price	Historical case	Where the math is
Inflation	buying power falls whenever prices rise faster than the yield	1946, CPI up about 18.1 % with bills at 0.35 %	Time value of money
Policy rate	the yield on cash follows the Fed's target	near zero 2009 to 2015 and 2020 to 2021	Policy and the yield curve
Credit of the holder	a money fund can fall below one dollar a share	the Reserve Primary Fund, 16 Sep 2008	Credit derivatives and 2008

Inflation. Bills paying 5 % while prices rise 3 % give a real return of +1.9 %. Twenty years of 3 % inflation on a sum that earns nothing changes its buying power by −44.6 %.

The policy rate. The reinvestment example under US bonds applies with full force: $500,000 in bills earned $25,000 a year at 5 % and $500 at 0.1 %.

Deeper: cash in 1946 and the 1970s and the Fisher relation.

Level 3 The math

For Series 65 and CFA readers: formulas and worked examples.

Series 65 path stops here

Each box below gives the equation behind one class's main driver, a short derivation where it helps, and the size of the approximation error. The chapters linked under each class hold the full treatment.

One equation per class

The math Stocks: the Gordon model and the discount rate

With dividends growing at a constant rate $g$ and a required return $r$ above it, the price equals next year's dividend over the gap.

P = \frac{D_1}{r - g}

In words, the price equals next year's dividend divided by the required return minus the growth rate.

A move in $r$ or $g$ changes the price by a ratio of gaps, since $D_1$ cancels.

\frac{P_1}{P_0} - 1 = \frac{r_0 - g_0}{r_1 - g_1} - 1

In words, the percentage change in price equals the old gap between return and growth divided by the new gap, minus one.

With a gap of 4 points, one point more on $r$ gives −20.0 %. With a gap of 2 points the same shift gives −33.3 %, which is why stocks with high expected growth react hardest to rates.

The math Foreign assets: local return and currency return

A dollar investor's return on a foreign asset compounds the local return and the change in the currency's dollar value.

1 + R_{\text{USD}} = (1 + R_{\text{local}})(1 + R_{\text{FX}})

In words, one plus the dollar return equals one plus the local return times one plus the currency's change against the dollar.

The sum $R_{\text{local}} + R_{\text{FX}}$ is a good guess for small moves and misses by the cross term $R_{\text{local}} R_{\text{FX}}$ . For a 30 % local fall and a 50 % currency fall the cross term is 15 points, and the true result is −65.0 %.

The math Bonds: duration, and credit as a second yield

For a small change in yield, the percentage change in a bond's price is close to minus its modified duration times that change.

\frac{\Delta P}{P} \approx -D_{\text{mod}} \, \Delta y

In words, the price falls by about the duration times the rise in yield, written as a decimal.

For a corporate bond the yield is the Treasury yield plus a spread, and the same duration applies to a change in either. The expected yearly loss from default is the probability of default times the loss given default.

\text{EL} = \text{PD} \times \text{LGD}

In words, expected loss equals the chance of default times the fraction lost when default happens.

For large moves duration overstates the loss on an ordinary bond, because convexity cushions it; the bond chapter adds the convexity term.

The math Munis: the taxable-equivalent yield

A tax-free yield $y_{\text{muni}}$ is worth more to a buyer with a higher tax rate $t$ .

\text{TEY} = \frac{y_{\text{muni}}}{1 - t}

In words, the taxable-equivalent yield is the muni yield divided by one minus the buyer's tax rate.

A state that also exempts its own bonds raises $t$ to the combined rate for its residents. The formula makes the tax driver visible: when $t$ falls, the muni must yield more, and its price falls, to stay as attractive as a taxable bond.

The math TIPS: real duration plus the inflation accrual

A TIPS return over a year is close to the inflation accrual on the principal, plus the real coupon, minus real duration times the change in the real yield.

R_{\text{TIPS}} \approx \pi_{\text{accrual}} + r - D_{\text{real}} \, \Delta r

In words, a TIPS bond earns the inflation added to its principal and its real coupon, and loses its real duration times any rise in the real yield.

The accrual uses CPI with a lag of about three months, so a year's accrual differs from the December-to-December CPI change when inflation is moving fast. The accrual and the price effect also compound, so the product form below is more accurate than the sum for large moves.

1 + R \approx (1 + \pi_{\text{accrual}})(1 - D_{\text{real}} \, \Delta r)

In words, one plus the return is close to one plus the accrual times one minus the price effect of the real-yield change.

The math REITs: cap rates and borrowing

A property's value is its net operating income divided by the cap rate, so at constant income the value moves by the ratio of old to new cap rates.

V = \frac{\text{NOI}}{c}

In words, value equals net operating income divided by the cap rate.

When debt stays fixed, the equity absorbs the whole change in value, so its percentage move is the asset's move divided by the equity share.

\frac{\Delta E}{E} = \frac{\Delta V / V}{1 - \text{LTV}}

In words, the percentage change in equity equals the percentage change in property value divided by one minus the loan-to-value ratio.

The second equation also runs in reverse. Given a REIT's share move and its loan-to-value, it gives the cap rate the market must have applied, which we use in Level 4.

The math Commodities: three sources of return, and elasticity

A fully collateralised futures position earns the spot change, the roll yield and the collateral yield.

R_{\text{futures}} \approx \Delta S + \text{roll} + r_{\text{collateral}}

In words, a futures investor earns the change in the spot price plus the roll yield plus the interest on the cash held as collateral.

With an unchanged curve, one roll from a front price $F_1$ to a next price $F_2$ returns $F_1 / F_2 - 1$ , negative in contango, positive in backwardation. Repeated $n$ times a year it compounds to $(F_1/F_2)^n - 1$ .

On the spot side, a supply cut of $\%\Delta Q$ against demand with short-run price elasticity $\varepsilon$ needs a price change of about the cut over the size of the elasticity.

\%\Delta P \approx \frac{\%\Delta Q}{|\varepsilon|}

In words, the price rise needed to clear a supply cut is about the size of the cut divided by how strongly demand responds to price.

The approximation holds for small moves. A demand elasticity near zero makes the price change very large, which is why oil swings so far on small changes in supply.

The math Gold: real prices and forgone real income

Gold has no cash flow, so we measure it against what an alternative would have paid. Its real price restates a nominal price in today's dollars with the CPI.

P_{\text{real}} = P_{\text{nominal}} \times \frac{\text{CPI}_{\text{now}}}{\text{CPI}_{\text{then}}}

In words, a past price in today's money equals the past price times today's CPI divided by the CPI at the time.

The yearly cost of holding gold in place of a TIPS bond is the amount held times the real yield. When the real yield is negative that cost turns into a gain, which links the gold price to real rates without any cash flow of its own.

The math Currencies: covered parity and carry

Covered interest parity ties the forward rate $F$ to the spot rate $S$ and the two interest rates, with the exchange rate quoted as units of the quote currency per unit of the base currency.

F = S \, \frac{1 + i_{q}}{1 + i_{b}}

In words, the forward rate equals the spot rate times one plus the quote currency's rate, divided by one plus the base currency's rate.

An unhedged carry trade borrows in the low-rate currency and holds the high-rate one, and its return over a year depends on the rate gap and the currency move $\Delta s$ .

R_{\text{carry}} = (1 + i_{\text{invest}})(1 + \Delta s) - (1 + i_{\text{fund}})

In words, the carry return equals the grown value of the investment, after the currency move, minus what the borrowed money costs to repay.

The math Cash: the Fisher relation

The real return on cash is its nominal yield deflated by inflation.

1 + r_{\text{real}} = \frac{1 + i}{1 + \pi}

In words, one plus the real return equals one plus the nominal yield divided by one plus inflation.

For low rates the real return is close to $i - \pi$ . For high ones the exact form matters: at 8 % yields and 12 % inflation the gap says −4 points and the exact form gives −3.6 %.

Which driver is largest, by the numbers

Putting the worked impacts side by side shows how different the sensitivities are. A one-point rise in the discount rate cuts a stock priced at a 4-point gap by −20.0 %; the same point cuts a 6-year bond fund by −6.0 % and a property at a 4 % cap rate, if its cap rate follows rates one for one, by −20.0 %. Cash gains from the same move. Those numbers do not say stocks are riskier than bonds in every year, because earnings and the risk premium often move against rates. They say that when rates do rise with nothing else changing, the long-dated cash flows of stocks and buildings react the most.

Worked example A rate shock across a simple mix

We take an investor with 60 % in stocks priced at a 4-point gap, 30 % in a bond fund with duration 6 and 10 % in REITs at a 4 % cap rate, and raise rates by one point with nothing else moving. The stock leg loses −20.0 %, the bond leg −6.0 % and the REIT leg, before borrowing, −20.0 %. Every leg falls together, the pattern that 2022 showed and that the portfolio chapter takes up.

Level 4 History, analysed

For readers who want past episodes run through the Level 3 math.

TIPS in 2022

2022 TIPS lost money in the year of highest inflation

In 2022 the 10-year TIPS real yield rose from about −1.0 % at the end of 2021 to about 1.5 % at the end of 2022 (FRED, series DFII10), while CPI rose 6.5 % from December to December (BLS). Bloomberg's US TIPS index lost about −12.0 % for the year.

See it on the timeline

We run the TIPS equation from Level 3 with a real duration of about 7.0 years for the index at the end of 2021. Real yields rose 250 bp, so the price effect comes to about −17.5 %. Adding the CPI accrual of 6.5 % gives −11.0 % by the sum and −12.1 % by the product form. Between those two estimates we find the index's actual loss of about −12.0 %.

Most of the remaining gap has known causes. Each month's accrual lags CPI by about three months, the index's duration fell during the year as yields rose, and the real coupon added a little income. None of them changes the conclusion: in 2022 the rise in real yields outweighed the inflation protection by a wide margin. TIPS protect against an inflation surprise relative to the breakeven rate. They do not protect against a rise in real rates, and in 2022 the Fed's response to inflation produced that kind of rise within one year.

Emerging markets and the dollar in 1997

1997 Thailand floated the baht

On 2 Jul 1997 Thailand gave up the baht's link to the dollar. The currency, held near 25 baht per dollar before the float, traded at more than 50 per dollar by January 1998, and the crisis spread across East Asia.

See it on the timeline

Our currency equation from Level 3 gives the dollar value of the baht: a move from 25 to 50 per dollar is −50.0 %. A Thai firm with dollar debt saw that debt rise +100 % in baht. A US investor in Thai shares took both hits at once. If local prices had fallen 30 %, which is an illustration and not the measured fall, the dollar result would be −65.0 %, worse than either piece alone because the two compound.

Other markets went through the same mechanism that year and the next: dollar borrowing looked cheap while the peg held, and the peg's break turned it into the largest cost on the balance sheet. That is why the emerging-market row in the Level 1 grid rates the dollar and policy both H.

REITs and cap rates in 2022

2022 REITs fell as rates rose

From the first hike on 16 Mar 2022 to the 4.25 to 4.50 % target set on 14 Dec 2022, the Fed raised its rate by 425 basis points, and the 10-year Treasury yield went from 1.51 % to 3.88 % over the calendar year (FRED, series DGS10). The FTSE Nareit All Equity REITs index lost about −25.0 % in 2022.

See it on the timeline

We ask what cap rate the market applied. Suppose REITs started the year valued at a 4 % cap rate with debt at 35 % of value, and their income held steady. A fall of about a quarter in the shares needs a property value fall of about a sixth, which at constant income means a cap rate of about 4.78 %. That is a rise of under one point, against a 10-year yield up 237 bp.

The cap rate rose less than Treasury yields, and the estimate makes sense: rents were still rising in most property types in 2022, which offset part of the rate shock in the income line. Offices went the other way, with falling occupancy on top of higher rates. The starting cap rate and the debt ratio here are round illustrations; the Gaps section says what a full study would need.

Gold from 1980 to 2008 in real terms

1980 Gold peaked at about 850 dollars

On 21 Jan 1980 the London gold price reached about $850 an ounce (LBMA), after a decade of high inflation and negative real rates. Gold did not regain that nominal price until January 2008.

See it on the timeline

The real-price equation restates the 1980 peak in January 2008 dollars with CPI-U levels of 77.8 and 211.08: about $2,306. A buyer at the 1980 high who sold at the same nominal price 28 years later lost −63.1 % of buying power, before storage costs.

Real rates explain much of the path. Under Volcker, real yields turned strongly positive in the early 1980s, raising the income a gold holder gave up, and they stayed positive for most of the next two decades. Erb and Harvey (2013) look at gold as an inflation hedge and find that it hedges well over a century or more and poorly over the horizons most investors hold it. The 1980 to 2008 span fits that finding.

Commodities and the roll in April 2020

2020 Oil futures settled below zero

On 20 Apr 2020 the May contract for WTI crude oil settled at −$37.63 a barrel (CME, EIA), as demand collapsed in the pandemic and storage near the delivery point in Cushing, Oklahoma, ran short.

See it on the timeline

The futures equation from Level 3 explains why an investor in an oil fund lost far more than the spot price alone would suggest. With storage scarce, the front contract fell far below later months, putting the curve into steep contango. Each roll then sold a cheap contract and bought a dear one. Our worked roll of $60 to $61 costs −1.64 % a month; the spring 2020 curve was many times steeper than that at the front, so funds that rolled monthly gave up a large share of their value to the roll alone.

The episode also shows the elasticity point. Demand for oil fell by a large fraction in weeks, supply could not adjust that fast, and the only way to clear the market for May delivery was a price that paid buyers to take the oil.

Cash in 1946 and the 1970s

1946 Inflation took about 15 % of a saver's cash

In 1946, as wartime price controls ended, consumer prices rose about 18.1 % (BLS) while 30-day Treasury bills paid about 0.35 % (SBBI). A saver in bills lost about −15.0 % of buying power in one year.

See it on the timeline

The Fisher relation gives −15.0 % for 1946. In 1974 bills paid about 8.0 % and inflation ran about 12.2 % (SBBI), so the real return was −3.7 %. The nominal yield in 1974 was more than twenty times the 1946 yield, and cash still lost buying power. A high yield on cash protects a saver only when it is high relative to inflation.

These two years are the clearest examples of cash's one large risk. In nominal terms bills almost never lose money; in real terms they lost heavily in the late 1940s and again through much of the 1970s, which is why the cash row in the Level 1 grid rates inflation H.

Sources

Kroll, Stocks, Bonds, Bills, and Inflation (SBBI) Yearbook, 2024 edition, data 1926 to 2023: 30-day Treasury bill returns and inflation for 1946 and 1974.

Federal Reserve Bank of St. Louis, FRED: DFII10, 10-year TIPS real yield and DGS10, 10-year Treasury yield, read 2026-10-28.

US Bureau of Labor Statistics, Consumer Price Index for All Urban Consumers (CPI-U), not seasonally adjusted, January 1980, January 2008, December 1945 to December 1946 and December 2021 to December 2022.

S&P Dow Jones Indices, S&P 500 total returns, 2008 and 2022.

MSCI, EAFE and Emerging Markets index returns in US dollars, 2008.

Bloomberg US Aggregate, Municipal Bond, US TIPS and Commodity index returns.

Nareit, FTSE Nareit All Equity REITs index annual returns.

LBMA gold price, historical series.

CME Group and the US Energy Information Administration on the WTI May 2020 contract settlement of 20 Apr 2020.

Bank of Thailand, the baht exchange rate around the float of 2 Jul 1997.

Claude B. Erb and Campbell R. Harvey, "The Golden Dilemma," Financial Analysts Journal 69, no. 4 (2013).

Myron Gordon, The Investment, Financing, and Valuation of the Corporation (1962), for the constant-growth model.

The overview article in this series, "Basics of investment management: the 11 asset classes," for the 2008 and 2022 index figures it quotes.

Gaps

We typed these historical inputs from the publishers' tables, and each needs a check against its source before the strict build: the 10-year TIPS real yield at about −1.0 % (end-2021) and about +1.5 % (end-2022), rounded; the Bloomberg US TIPS index duration of about 7 years at the end of 2021; the Bloomberg US TIPS index return of about −12 % for 2022; the Bloomberg US Aggregate duration of about 6.6 years at the end of 2021; CPI-U levels of 77.8 (January 1980) and 211.08 (January 2008); CPI-U inflation of about 18.1 % in 1946 and 6.5 % in 2022; SBBI bill returns of 0.35 % (1946) and about 8.0 % (1974) and SBBI inflation of about 12.2 % (1974); the FTSE Nareit All Equity REITs return of about −25 % for 2022.

Index returns carried over from the overview article (S&P 500, MSCI EAFE and Emerging Markets, Bloomberg Aggregate, Municipal and Commodity, FTSE Nareit for 2008, LBMA gold for 2013) share its sources and its rounding. We also quote the S&P 500 return of −18.1 % for 2022 (S&P Dow Jones Indices) and the 10-year Treasury yields of 1.51 % and 3.88 % at the ends of 2021 and 2022 (FRED DGS10) as other chapters of this series give them; they need the same check.

Baht levels (near 25 per dollar before the float, more than 50 per dollar by January 1998) are round figures; they need the dated Bank of Thailand series.

Japan's weight of about 45 % in the world index at the end of 1989 is an MSCI figure quoted elsewhere in this series; we have not checked it against the MSCI table ourselves.

For 2013 we give the rise of more than a point in real yields in words only; the FRED DFII10 levels for the start and end of 2013 would put a number on it.

In the 2022 REIT analysis, the starting cap rate (4 %) and debt ratio (35 % of value) are round illustrations. A full study would use Nareit's reported leverage and a published cap-rate series by property type.

An oil demand elasticity of −0.1 in the short run is our illustration. We give no literature range because we have not tied one to a named study.

A 30 % local fall in Thai shares in the 1997 example is likewise an illustration; we did not look up the measured fall of the Thai market.

The Reserve Primary Fund's fall below one dollar a share on 16 Sep 2008 and Malaysia's 1998 capital controls appear by name, without figures.

How steep the WTI futures curve was in April 2020 stays in words; the contract settlement prices for June 2020 and later months would let us compute the roll cost.

Terms

risk driver: a force, such as interest rates or inflation, whose change moves an asset's price in a predictable direction.
equity risk premium: the extra return investors require for holding stocks over a safe government bond.
taxable-equivalent yield: the taxable yield that would leave a buyer with the same after-tax income as a tax-free muni yield; the muni yield divided by one minus the tax rate.
real yield: the yield on a bond after inflation; for TIPS, the fixed rate paid on the inflation-adjusted principal.
breakeven inflation: the nominal Treasury yield minus the TIPS real yield of the same maturity; the average inflation at which the two bonds return the same.
net operating income: a property's rent and other income minus its operating costs, before debt payments and income tax.
cap rate: net operating income divided by a property's value; the yield a buyer demands from the property's income.
loan-to-value ratio: debt divided by the value of the property or portfolio it finances.
roll yield: the gain or loss from replacing an expiring futures contract with a later one when the two trade at different prices.
contango: a futures curve where later contracts cost more than nearer ones, so rolling a long position loses money.
backwardation: a futures curve where later contracts cost less than nearer ones, so rolling a long position earns money.
carry trade: borrowing in a low-interest currency to hold a higher-interest one, earning the rate gap while bearing the currency risk.

Educational only. Not investment, tax, or legal advice, and not an offer of advisory services. InnovationStrat Wealth, LLC is not yet registered as an investment adviser.