Systematic & Quantitative Valuation
Expected Returns: An Investor's Guide to Harvesting Market Rewards
Ilmanen builds expected returns from the parts you can read today (yields, spreads, carry, valuations) rather than from past averages, then maps every asset class against the same few style premia: value, carry, momentum and a defensive tilt.
The big picture
Antti Ilmanen, now a principal at AQR Capital Management, who earlier managed reserves at the Bank of Finland and worked at Salomon Brothers and Brevan Howard, wrote the book as a map of where investment returns come from across all major markets. His starting point is that a historical average return is a poor guide to the next ten years. An average measured over a period in which valuations rose, or yields fell, contains a one-off gain that the next buyer cannot collect again. The better starting point is the yield an asset offers now, adjusted for growth, expected losses and any expected change in valuation.
The book then looks at the same markets from four angles: asset classes (equities, government bonds, credit, commodities, currencies and alternatives), strategy styles (value, carry, momentum and volatility-related trades, tested across many markets at once), underlying risk factors (growth, inflation, liquidity, tail risk) and the way all of these change over time. Its practical conclusion is that no single premium pays reliably, but several modest and weakly related premia, combined at similar risk, have historically given a steadier result than any one of them. Why it matters now: after a long run of rising equity valuations, the gap between the past average and the current yield-based estimate is the number a reader should look at first.
The 3 strategic pillars
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Ex-ante beats ex-post
A past average return mixes two things: the income the asset paid and the gain from its valuation moving up or down. Only the first part can be expected to repeat. After a strong run, the second part is large, and the past average then overstates what the same asset offers today.
Split history into its parts. If a price-to-earnings ratio rose from 10 to 20 over 30 years, re-rating alone added (20/10)1/30 − 1 = 2.34% a year. For bonds, a fall in yields adds roughly duration × the yield decline, spread over the years of the window. The forward estimate starts from the current yield instead: for equities the dividend yield plus real growth, or the earnings yield 1/CAPE as a cross-check; for bonds the yield itself.
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Building blocks per asset class
Every asset's expected return can be written as a sum of readable parts, and each premium is that sum minus the expected return on cash over the same horizon. The equity premium, the term premium and the credit premium are then measured in the same unit.
Equities: dividend yield + net buyback yield + real growth per share + inflation + expected valuation change per year. Government bonds over one year: yield + roll-down (the gain from moving down a sloped curve) − duration × expected yield change. Credit: the matched government return + spread − default probability × (1 − recovery rate). Commodity futures: interest on the cash collateral + roll yield (positive when the curve is in backwardation, meaning later contracts are cheaper) + expected spot change.
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Style premia, combined at equal risk
The same few styles show up in almost every market: buy what is cheap (value), hold what pays more while you wait (carry), follow what has been rising (momentum) and prefer the lower-risk end (defensive). Each one alone has long losing stretches; together they have been less correlated with each other and with equities.
Read each style as a standardized score per asset, then average the available scores: z-scores all have the same variance, so a plain average gives each style equal risk. Across strategy sleeves, weight each by 1/volatility. With equal risk, N sleeves each with Sharpe ratio s and average correlation ρ combine to s × √(N ÷ (1 + (N − 1)ρ)): four sleeves at 0.30 with zero correlation give 0.60. The 2011 book works through value, carry, momentum and volatility strategies; the defensive (low-risk) column follows the grouping Ilmanen and AQR used later.
What a Closelooknet reader does with it
The working use is a one-page sheet that forces every expected return into the same form: today's yield, plus growth, minus expected losses, plus or minus a stated valuation change, minus cash. The main mistake it prevents is extrapolation, the habit of expecting the next decade to repeat the last one's average when that average was partly paid by re-rating. A second mistake is betting everything on one style that happened to work recently. Writing down value, carry, momentum and defensive readings for each asset shows where they agree and where they cancel, and the equal-risk arithmetic shows how much of the diversification benefit depends on the correlations assumed.
The bridge to the Closelooknet approach
Three entries on the shelf cover parts of this map. Quantitative Value is the value column for single stocks, with forensic screens in front. Value Investing: From Graham to Buffett and Beyond explains when a high earnings yield is real and when growth changes the picture. Principles balances a portfolio across growth and inflation environments, the same risk-factor lens Ilmanen uses. On Closelooknet, the Rates X-Ray tracks the Treasury curve that feeds yield, roll-down and the term premium; the AI Credit Stress page follows the credit spreads on the debt funding the AI build-out, the input to the credit block; and the Factor Regime page compares a momentum tilt with a low-volatility tilt, two of the four style columns. The Money Temperature reads the regime in which these premia tend to pay or fail. The earnings yield, carry trade and momentum entries define the inputs.
Action-Kit — from theory to practice
Tooling & data
| What you need | Where to get it | Cost |
|---|---|---|
| Shiller CAPE and long-run US equity data Cyclically adjusted P/E, dividends and earnings history for the equity block and the windfall split | Robert Shiller's online data US only; for other markets use index factsheets for dividend yield and P/E. | Free |
| Treasury yields, curve and corporate spreads Government yields for yield and roll-down, and investment-grade and high-yield option-adjusted spreads for the credit block | FRED (Federal Reserve Bank of St. Louis) Spreads are index-level; default and recovery assumptions still come from you. | Free |
| Futures curves for the commodity roll yield Near and far contract prices to compute backwardation or contango | Barchart Delayed quotes are free; the formula only needs two prices and the months between them. | Freemium |
| Published style-return series Historical value, momentum, carry-type and low-risk factor returns to set your own Sharpe and correlation assumptions | Kenneth French Data Library and AQR datasets Past factor returns are an input to your assumptions, not an expected return. | Free |
The formulas
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Equity building blocks
E[R] = D/P + BY + g_real + π + ((CAPE_target / CAPE_now)^(1/H) − 1)- D/P = dividend yield; BY = net buyback yield
- g_real = real growth per share; π = expected inflation
- CAPE_now, CAPE_target, H = horizon in years
Cross-check: real E[R] ≈ 1/CAPE. Equity premium = E[R] − expected average cash rate over H.
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Government bond, one-year horizon
E[R] = y + RD − D·Δy + ½·C·Δy²- y = yield; RD = roll-down
- D = duration; C = convexity (years²)
- Δy = expected yield change
Term premium here = E[R] − expected cash rate over the year.
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Credit premium over matched government
CP = s − PD·(1 − R) − SD·Δs- s = spread; PD = annual default probability
- R = recovery rate; SD = spread duration
- Δs = expected spread change
Example: s = 3.5%, PD = 3.5%, R = 40% → expected loss 2.1%, CP = 1.4% before spread changes.
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Valuation windfall in a historical average
w = (V_end / V_start)^(1/T) − 1; clean = (1 + R_hist) / (1 + w) − 1- V = P/E or CAPE at the start and end of the window
- T = years; R_hist = historical average return
Style combination at equal risk: Sharpe_p = s·√(N / (1 + (N − 1)ρ)).
Applied Pack · free members
Expected Returns Premia Matrix Pack
Your own yields, spreads and valuations in, building-block expected returns and premia over cash out, plus the split of a past average into yield and re-rating, and a style matrix combined at equal risk. Software for your own research, never signals.
- ExpectedReturns_PremiaMatrix.xlsx — READ ME, Building Blocks (equities, government bonds, credit, commodity futures, premia over cash), ExAnte vs ExPost (valuation and yield windfall), Style Matrix (assets × value, carry, momentum, defensive z-scores with equal-risk composite and rank) and Style Combination (inverse-volatility weights, correlation matrix, combined Sharpe, target-volatility scaling); live formulas, amber input cells
- ilmanen_premia.py — stdlib-only CLI with four subcommands (blocks, history, styles, sleeves): CSV in, table out, same math as the workbook
- blocks_sample.csv, history_sample.csv, styles_sample.csv, sleeves_sample.csv, corr_sample.csv — EXAMPLE_ rows made up for the format only
- README.txt — every formula, input conventions, how to run, limits and the educational-use disclaimer
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Educational templates — a research diary companion, not investment advice.
Closelooknet publishes a market diary, not investment advice. This condensed read restates the book's ideas in our own words for education — for the author's full argument, go to the source.