Capital Market Expectations, Part 1: Framework and Macro Considerations: formula sheet

Key formulas

Steps of the CME framework

Specify expectations needed and horizon → Research the historical record (and its limits) → Specify methods and models → Determine information sources → Interpret the current environment → Provide expectations and document conclusions → Monitor and refine

Learn the order. A question may ask which step a given action belongs to.

Forecast error (for monitoring)

Forecast error = Actual outcome − Forecast

Use it in the monitoring step. Review errors for bias and for reasons, not only size.

Expected return of a portfolio

E(Rp) = Σ wi × E(Ri)

CME supply E(Ri). The weights come from the allocation.

Data-mining signal

Number of tests ↑ ⇒ chance of a spurious 'significant' result ↑

Fix: test out of sample and require an economic rationale.

Survivorship effect

Reported average return (survivors only) > true average return of the full original group

Also understates risk. The fix is to include dead funds or delisted firms.

Smoothed data effect

Smoothed volatility < true volatility

Appraisal-based data also understate correlation with other assets, so diversification looks too good. Fix: unsmooth the series.

Ex post vs ex ante

Ex post = observed from past data; ex ante = expected risk looking forward

Past data may not reflect forward risk.

Grinold-Kroner expected equity return

E(Re) ≈ D/P − ΔS + i + g + ΔP/E

D/P − ΔS is the income component (dividend yield less the percentage change in shares); i is expected inflation; g is real earnings growth; ΔP/E is the expected annual repricing rate. The version in the text uses approximations.

Gordon growth equity return

E(Re) = D1/P0 + g

Assumes constant long-run growth and a constant payout. Use it for a stable, mature market.

Build-up risk premium

E(R) = Risk-free rate + Risk premium(s)

Equity premium over bonds is one example: E(Re) = Yield on long bond + Equity risk premium.

CAPM expected return

E(Ri) = Rf + βi × [E(Rm) − Rf]

Equilibrium approach. The market risk premium and beta are the inputs.

Shrinkage estimator

Shrinkage estimate = (weight × target) + ((1 − weight) × sample estimate)

Weight is between 0 and 1. A higher weight on the target means more shrinkage. Target is often the average across assets.

Black-Litterman logic

Equilibrium (reverse-optimized) returns + investor views, weighted by confidence → posterior returns

Higher confidence in a view moves the result closer to that view. No view leaves you at equilibrium.

Potential (trend) growth

Trend GDP growth ≈ growth in labour input + growth in labour productivity

Labour input depends on population, participation and hours. Productivity depends on capital deepening and technology (total factor productivity).

Output gap

Output gap = actual GDP − potential GDP

Positive gap suggests inflation pressure and likely policy tightening. Negative gap suggests slack and disinflation.

Growth decomposition

Actual growth = trend growth + cyclical component

Use this to separate what is lasting from what should fade. Growth above trend closes a negative output gap or widens a positive one. Inflation risk depends on the starting level of the gap.

Indicator timing

Leading: turns before the cycle. Coincident: turns with it. Lagging: turns after it.

Leading indicators give signals but also false alarms.

Expected return principle (qualitative, not a calculation)

A cycle view adds value only to the extent it differs from what current prices already reflect

This is a way of thinking, not a numeric rule. A forecast only matters to the extent it differs from the market consensus.

Neutral policy rate

Neutral rate ≈ real trend growth rate + expected inflation

This is an approximate nominal rate. Policy rate below neutral means expansionary; above neutral means contractionary.

Taylor rule

i = r_neutral + π_e + 0.5 × (π_e − π_target) + 0.5 × (GDP_e − GDP_trend)

Here r_neutral is the real neutral rate (roughly real trend growth), π_e is expected inflation and GDP_e − GDP_trend is the expected growth gap. Do not use a nominal neutral rate here, or inflation is counted twice. The 0.5 weights are the standard ones in the curriculum. Check the weights given in the question.

Fisher effect

Nominal rate ≈ real rate + expected inflation

Use it to split a nominal yield into real and inflation parts.

Long-term yield decomposition

Long yield = expected average short rate + term premium (including inflation and risk compensation)

Use it to explain curve shape.

Fiscal multiplier (simple)

Multiplier = 1 ÷ [1 − MPC × (1 − t)]

MPC is marginal propensity to consume and t is the tax rate. Valid for this simple closed economy without imports.

Fiscal stance

Deficit = government spending − tax revenue

Judge stance by the change in the structural deficit, not just the headline deficit.

Absolute PPP

S(P/B) = CPI(P) ÷ CPI(B)

Price levels equal across countries when converted. Holds loosely, and mainly as a long-term anchor.

Relative PPP (approximate)

%ΔS(P/B) ≈ π(P) − π(B)

The currency of the higher-inflation country depreciates. If the price currency has higher inflation, the P/B quote rises.

Relative PPP (exact)

S(t+1) = S(t) × (1 + π(P)) ÷ (1 + π(B))

Use the exact form when numbers are large or the question asks for precision.

Covered interest rate parity

F(P/B) = S(P/B) × (1 + i(P) × T) ÷ (1 + i(B) × T)

No-arbitrage forward rate. Use matching-maturity interest rates and T in years (or compounded form for longer terms).

Uncovered interest rate parity

E[%ΔS(P/B)] ≈ i(P) − i(B)

Expected spot change equals the rate difference. Often fails empirically, so the carry trade has earned a premium.

Real exchange rate

Real S(P/B) = S(P/B) × CPI(B) ÷ CPI(P)

Measures competitiveness. Deviations from a long-run level suggest mean reversion.

Foreign asset return in base currency

R(domestic) = (1 + R(foreign local)) × (1 + %Δ value of foreign currency) − 1

%Δ is the change in the domestic-currency value of one unit of foreign currency.

Quick revision

• CME are forecasts of risk, return and correlation that feed strategic asset allocation.
• Follow the framework in order: purpose, method, data, analysis, forecast, then monitor and refine.
• Forecasts are only as good as their data, so check for errors, bias and the limits of historical data.
• Model and parameter uncertainty mean you should treat forecasts as ranges, not precise numbers.
• Psychological traps include anchoring, overconfidence and confirmation bias.
• Match the forecasting tool to the question: statistical, DCF, risk premium or judgment.
• Growth drives earnings, and the phase of the business cycle shapes the return view by asset class.
• Expansionary policy tends to support risk assets, while tightening tends to pressure them, all else equal.
• Fiscal and monetary policy work together, so read the policy mix, not one lever alone.
• Exchange rates link markets, so currency moves change the home-currency return on foreign assets.
• In essays, answer the command word exactly and give only the number of points asked for.

Common mistakes

• Treating CME as security-level forecasts. Fix: Remember CME are asset-class risk, return and correlation inputs for allocation.
• Ignoring the time horizon when specifying needs. Fix: State the horizon first and say whether the use is strategic or tactical.
• Saying survivorship bias makes returns too low. Fix: Failed funds are removed, and they were poor performers. So returns are overstated and risk is understated.
• Treating smoothed appraisal data as accurate low-risk evidence. Fix: Appraisals lag the market. Volatility and correlations are understated, so unsmooth the data before use.
• Treating historical averages as reliable forecasts. Fix: Say that past data can reflect a different regime and contain estimation error. Suggest shrinkage or a forward-looking method.
• Confusing the direction of shrinkage. Fix: Shrinkage moves the sample estimate toward the target, not away. Higher weight on the target means more shrinkage.
• Treating a growth spike as a rise in trend growth. Fix: Check whether the rise comes from labour or productivity. If it comes from demand or inventories, treat it as cyclical and expect it to fade.
• Mixing up leading and lagging indicators, such as calling unemployment leading. Fix: Ask whether firms act first or react later. Orders and permits come first. Unemployment duration and bank lending react after the cycle has turned.
• Calling policy expansionary because the nominal policy rate is low. Fix: Always compare the policy rate with real trend growth plus expected inflation.
• Putting the levels of inflation and growth into the Taylor response terms. Fix: Use the gaps: expected inflation minus target, and expected growth minus trend.

Exam tips

• Memorize the seven steps in order. Questions often ask you to place an action in a step or name the missing one.
• On essay sets, read the command word in bold. 'Identify' earns points for the name; 'justify' needs the reason tied to the client.
• Always mention the horizon and the client's task. Many lost points come from generic answers.
• For a forecast error calculation, a correct number typed on its own earns full credit. Make sure the number and its sign are correct. Showing working is optional.
• Do not list more responses than asked for. Only the requested number is evaluated, in order.
• Memorize each bias with its direction: survivorship overstates return and understates risk; smoothing understates risk and correlation.
• Read the command word in bold. 'Identify' needs the name only; 'explain' needs the effect; 'recommend' needs the fix.
• In essays, write the clue from the vignette next to the bias name. This earns the justification point.