Discount rates, the stochastic discount factor, and where ESG enters.
Jae Yung KimUniversity of Exeter2026
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Prologue
One number, swinging wildly
The market's price relative to its dividends is not stable — it ranges from single digits to the high tens, over and over. Why?
?
Predict
A market's price is high relative to its dividends. Why?
Story A — cash flows
prices are high because investors expect high future growth. Value moves with the numerator.
Story B — discount rates
prices are high because investors will accept low future returns. Value moves with the denominator.
Pick one before you scroll. Almost everyone starts with Story A.
Part One
The fundamental equation: P = E[m·x]
Everyone agrees value is expected, discounted cash flow. The whole subject is the discount factor — and whether it moves.
1
Value is expected, discounted cash flow.
Pt = Et[ Σ Mt,t+j · Dt+j ]
D = cash flows · M = the discount factor
The cash flows everyone forecasts. The interesting object is M — how a dollar in each future state is worth today. What is it, and does it move?
STRIP IT TO ONE PERIOD — FOR ANY ASSET
pt = Et[ mt+1 xt+1 ]
m = the stochastic discount factor (the pricing kernel)
What is m? How much you value an extra dollar next period — state by state.
Bad states (recession)
you are poor and scared — a dollar is precious. m is high.
Good states (boom)
you are rich — a dollar is just another dollar. m is low.
The SDFThe discount factor m is the marginal value of a dollar, state by state — high in bad states (when marginal utility is high), low in good states. That single fact is where every risk premium comes from.
Where risk premia come from
Et[Ri] − Rf = −Rf · covt(m, Ri)
Pays off in bad states
high when m is high → it is insurance → you accept a low expected return.
Pays off in good states
high when m is low → it is risky → you demand a risk premium.
The discount rate on an asset is just the risk-free rate plus its risk premium — and the risk premium is that covariance with m.
Show the derivation — why −Rf·cov, in four lines
0In gross returns Ri=x/P, the price equation P=E[m·x] is just E[m·Ri]=1 for every asset.
1Risk-free asset: E[m·Rf]=Rf·E[m]=1, so E[m]=1/Rf.
2Any asset: 1=E[m·Ri]=E[m]·E[Ri]+cov(m,Ri).
3Solve and use 1/E[m]=Rf: E[Ri]−Rf=−Rf·cov(m,Ri).
Make it concretea three-state world
Numbers make the kernel tangible. Three states, with m high in bad states; the risk-free rate drops straight out of Rf = 1/E[m].
The kernelE[m] = 0.96 → Rf = 4.2%
state
prob π
SDF m
Bad (recession)
0.20
1.50
Normal
0.60
0.90
Good (boom)
0.20
0.60
Two assets, identical expected payoffs.
Bad
Normal
Good
E[x]
A — pays in booms
50
100
150
100
B — pays in busts
150
100
50
100
Both pay $100 on average. Which is worth more today?
Price = E[m·x]
How a price formsP = Σ (π·m)·x — pricing weights π·m = 0.30 / 0.54 / 0.12, so A: 0.30·50 + 0.54·100 + 0.12·150 = 87.
price
E[R] = 100/P − 1
risk premium
A (risky · pays in booms)
87
+14.9%
+10.8%
B (insurance · pays in busts)
105
−4.8%
−8.9%
Identical $100 cash flows, opposite returns.
B pays you when you're poor (m high) → insurance → it's worth more (105 vs 87) and earns a negative premium. The discount rate did all the work. Cochrane's thesis, in arithmetic — keep it; ESG will reuse it.
The upgrade that runs the rest of the lecture: m moves over time.
Risk aversion is not constant — in bad times people are scared and demand more to bear risk. A time-varying m means discount rates move, which means expected returns are predictable. Cochrane, Discount Rates, JF 2011.
Part Two
A high price must forecast something
Campbell & Shiller turned the definition of a return into an identity — and an identity leaves no escape.
2
Start from the definition of a return, R = (P′+D′)/P, take logs, and iterate forward. With dp = log(D/P) and a constant ρ≈0.96:
A high price today (low dp) is only possible if one of three things is true:
A future returns are lowB future growth is highC P/D rises forever (a bubble)
Which one does the data pick?
Part Three
It is discount rates, not growth
The identity forces a choice. A century of data answers it — and the answer is not the one most people pick.
3
EvidenceCochrane, JF 2011
When the dividend yield is high (prices low), subsequent returns are high — strongly so over long horizons.
Predictive regressionfuture return on today's dividend yield, r = a + b·(D/P)
horizon
b
t(b)
R²
1 year
3.4
2.5
0.07
5 years
18.0
3.5
0.22
Read it the other way: a high price today reliably precedes years of low returns.
Figure 1The dividend yield (read it as “prices, upside down”) and the following 7-year return move together: high prices in 2000 preceded poor returns; low prices in 1980 preceded high ones. Redraw of Cochrane (JF 2011), Fig. 1.
Figure 2Decompose the historical variation of the price/dividend ratio into the two channels of the identity. Essentially all of it is discount rates (future returns); almost none is changing growth. Cochrane (JF 2011); long-run regression / VAR.
Verdict
Story B wins, decisively: market valuations move on discount rates, not changing growth expectations.
≈100% discount rates, ≈0% cash-flow growth. The thing that moves a price is the denominator — the rate at which the market discounts the same cash flows.
Part Four
Why discount rates move
The same pattern runs through every asset class — and it traces back to one thing: the willingness to bear risk moves with the economy.
4
“High valuation → low subsequent return” is not special to stocks.
A single force — time-varying discount rates — runs through all of them.
Figure 3 · housingOld view: prices are high because rents will grow. Data: a high price/rent ratio predicts lower future housing returns — exactly the stock-market pattern. Redraw of Cochrane (JF 2011), Fig. 2.
Risk premia are countercyclical.
Good times
calm, confident → high prices → low expected returns.
Bad times
fear → high discount rates → low prices → high subsequent returns.
Figure 4 · habitThe market's price/dividend ratio moves with how good consumers feel relative to habit (the surplus-consumption ratio) — both peak in good times and crash together. Investment and book-to-market tell the same story. Redraws of Cochrane (JF 2011), Figs. 11–12.
Now watch m movethe same asset, two dates
Take one risky asset — payoffs 50/100/150, the same E[x] = $100 at both dates. Only risk aversion differs: calm vs. fearful (a more volatile m).
state
π
m · calm
m · fear
Bad
0.20
1.20
1.90
Normal
0.60
0.95
0.82
Good
0.20
0.80
0.50
The valuation moved — on the discount rate
price
E[R]
risk premium
Calm (low risk aversion)
93
+7.5%
+4.4%
Fear (high risk aversion)
83
+20.2%
+17.3%
Same cash flows. Price fell 93 → 83.
The risk-free rate barely moved (3.1% → 2.9%), so this is a pure risk-premium move. Fear made m more volatile → higher discount rate → lower price → and a higher expected return going forward. A low price predicts high returns. Cross-section (A/B) and time-series (this): one machine, m, doing both.
Part Five
ESG as a priced factor
ESG can move the cash flows — the obvious channel. But the deeper channel, and the one the asset-pricing machine bites on, is the discount rate.
5
Where does ESG enter value?
Cash flows (D)
ESG risks & opportunities change future profits. The obvious channel.
The discount factor (M)
ESG changes the required return — the cost of capital. The deeper one.
If investors get utility from holding green, they accept a lower expected return on it.
E[Ri] − Rf = βi λ −δ gi
g = greenness · δ = the greenium (the green expected-return wedge)
The greener the firm, the lower its required return: a lower cost of capital, a higher valuation — for the same cash flows. Brown firms get the mirror image.
Channel 1, in numbersadd a green asset
Return to our three-state world. Asset A (pays in booms) had price 87 and expected return 14.9%. Build asset G with the same payoffs, but a green taste worth δ = 3% of return:
Same $100 cash flows as A, but G is worth 89.3 vs 87: a higher price, a lower required return, a lower cost of capital. The kernel m is unchanged — it still prices A, B and G — yet green's discount rate falls below what risk alone dictates. One m; the taste moves the asset's required return, not the kernel.
The greenium puzzle is Cochrane
A real tension: green stocks outperformed through the 2010s — yet PST says green should earn less. Both are true.
taste ↑ → green discount rate ↓ → price ↑ now + expected return ↓ later.
The outperformance came from an unexpected rise in climate concern that lifted green valuations (lowered the green discount rate); going forward, expected green returns are lower. This is exactly Parts 1–3 — high price ⇒ low future return — now driven by tastes, in the green factor. Pástor, Stambaugh & Taylor, “Dissecting Green Returns,” JFE 2022.
Channel 2 · riskBolton–Kacperczyk, JFE 2021
A different engine, same direction for brown: if carbon is a risk investors must be paid to bear.
λ > 0 — a carbon premium, on the level of total emissions and their growth
High-carbon firms earn higher average returns — compensation for carbon risk. Brown → higher risk → higher discount rate.
Two engines, one direction
Channel 1 · PST
Channel 2 · BK
mechanism
preference (tastes)
risk (compensation)
who moves
green: required return ↓
brown: risk premium ↑
cross-section
brown earns more (expected)
brown earns more (expected)
Opposite stories — preferences vs. risk — but the same cross-sectional prediction, and both are discount-rate channels: neither touches the cash flows. That is the link to Parts 1–4.
Channel 3 · a different questionPedersen et al., JFE 2021
Channels 1–2 ask “why do valuations differ?” Pedersen et al. ask “how should I invest?”
ESG-unaware
plain mean–variance; ignores ESG.
ESG-aware
uses ESG as a signal of risk / future returns.
ESG-motivated
has a taste; will sacrifice return for ESG.
Figure 5 · the ESG-efficient frontierRising part — ESG as a signal (it carries information about the cross-section of expected returns → raises Sharpe; Channels 1–2 from the investor's seat). Falling part — ESG as a taste (past the peak you pay Sharpe for ESG; this is PST). Pedersen, Fitzgibbons & Pomorski, JFE 2021.
Is the frontier a discount-rate story or a portfolio story?
A portfolio story — but its shape is set by the discount-rate channels. The hump is ESG's information value fading against its taste cost. It packages Channels 1–2; it does not replace them.
VerdictESG = time-varying discount rates, in the cross-section
green / high-ESG
brown / low-ESG
taste (PST)
required return ↓
—
risk (BK)
—
risk premium ↑
discount rate
lower
higher
valuation (same CFs)
higher
lower
Parts 1–4: the discount rate moves over time. Part 5: it also varies across firms by greenness — same machine, new axis.
The subtlety to keep: “lower discount rate” = lower expected return, not necessarily lower realised return while the market re-prices.
Part Six
Where ESG meets the DCF
All of this lands in one place in a valuation — the discount rate.
6
V0 = Σ FCFt / (1+WACC)t
WACC = (E/V)·Re + (D/V)·Rd(1−Tc)
The discount rate — the WACC, through the cost of equity — is where time-varying risk premia and ESG enter the valuation.
Disciplined, not hand-waved. In the valuation practice we build exactly that DCF — for a real, just-listed company: SpaceX.
Carry away
1 · what moves value
discount rates, not changing growth (≈100% vs ≈0%).
2 · what a discount rate is
the SDF — and it is time-varying, so returns are predictable.
3 · why it moves
with risk appetite and the economy — countercyclically, everywhere.
4 · where ESG enters
priced into the discount rate: taste lowers green's, carbon risk raises brown's.
So ESG valuation is adjusting the discount rate (and the cash flows) with discipline — the DCF we turn to next.