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CAIA Level II · Topic guide

CAIA Methods and Models: Valuation, Factors and Relative Value

CAIA methods and models connect valuation to evidence: discount dated cash flows, model joint factor exposures and test relative-value relationships. Choose the method for the decision, keep units consistent and examine assumptions before relying on the output.

The key decisions, at a glance

  • 1. Specify

    Choose a model that matches the economic question.

    Watch for: A good statistical fit does not establish causation.

  • 2. Estimate

    Check data definitions, frequency and sample selection.

    Watch for: Backfilled or surviving funds can bias the sample.

  • 3. Validate

    Reserve information for out-of-sample evaluation.

    Watch for: Repeatedly tuning to the test set makes it part of development.

  • 4. Stress

    Change parameters and examine unstable conclusions.

    Watch for: Extra decimal places do not remove estimation uncertainty.

Original worked case

Reported beta explains a return, not its cause

Given: A simplified model is fund return = 1% + 0.5 × market return + residual, with all figures on the same annual basis. The market returns 8% and the fund returns 7%.

  1. 01 Model prediction

    1% + 0.5 × 8% = 5%.

  2. 02 Residual

    7% - 5% = 2 percentage points.

  3. 03 Interpretation

    The unexplained observation is not automatically repeatable manager skill.

Answer and interpretation

The result is conditional on the factors, period and estimated coefficients. Omitted factors or noise can explain part of the residual.

Change one assumption

If an omitted factor accounts for 1.5 percentage points, the apparent unexplained result shrinks to 0.5 points in an expanded model.

Independent teaching example with the stated assumptions. Not an official exam question, marking key or observed market trend.

Understand the method

Part 1

Value dated fixed cash flows using the spot curve

A spot rate applies to a cash flow at a particular maturity. For an option-free bond, discount each payment at its corresponding spot rate and add the present values. Using one yield to maturity is a compact summary of price, whereas the spot curve explicitly recognises different discount rates across dates. Keep compounding and payment-frequency conventions consistent.

For a two-year bond paying $5 at year one and $105 at year two, annual spot rates of 4% and 5% give 5/1.04 + 105/1.05² = $100.0458, or about $100.05. The calculation assumes the promised cash flows are the appropriate cash flows to discount and uses the stated rates. Credit, optionality and liquidity may require additional modelling.

Part 2

Use backward induction when cash flows depend on a path or option

An interest-rate tree represents possible future rate states. Under a calibrated arbitrage-free framework, work backward from terminal payments, taking the appropriate risk-neutral expectation and discounting at the node rate. Calibration is important because the model should reproduce relevant observed instrument prices rather than invent a conflicting curve.

Embedded options change the continuation value. At a callable-bond node, an issuer’s exercise right can cap the investor’s value at the call price under the stated exercise assumptions. For a simple one-period illustration, future values of 104 and 108 with equal risk-neutral weights and a 4% discount rate imply 106/1.04 = 101.92. An immediately exercisable call at 100 would cap that node at 100 in this simplified setup.

Part 3

Read a multivariate model as a conditional explanation

A factor regression expresses a return as an intercept plus exposures to selected factors and a residual. Coefficients describe the relationship estimated in the sample, holding the other included factors fixed. They do not by themselves establish a causal mechanism. Correlated factors can make individual coefficients unstable even when the overall fitted return looks convincing.

If monthly excess return is modelled as 0.1% + 0.8 × equity excess return + 0.3 × credit-factor return, factor returns of 2% and -1% imply 1.4% before the residual. Use matching units and frequencies. Review sample size, outliers, structural breaks and whether inputs were available at the decision date. A high fit can reflect exposure rather than security-selection skill.

Part 4

Test a relative-value relationship and an absolute valuation

A relative-value signal compares related instruments or an observed relationship with an estimated norm. A z-score divides deviation from a mean by an estimated standard deviation. A spread two standard deviations above its historical mean may be unusual under that sample, but it is not guaranteed to converge. Regime changes, structural differences and funding costs can invalidate the trade.

For private assets, an explicit cash-flow valuation offers a different perspective. Forecast operating cash flows and terminal proceeds, discount them consistently, then test discount rates, growth and exit assumptions. Comparable transactions can provide context but may differ in leverage, quality or timing. Agreement between two models is more meaningful when they rely on genuinely different evidence rather than the same optimistic terminal multiple.

Model-selection and diagnostic map

Price fixed dated payments

Method
Spot-rate discounting
First diagnostic
Cash-flow timing and compounding

Value embedded optionality

Method
Calibrated tree / backward induction
First diagnostic
Exercise rule and calibration

Explain joint exposures

Method
Multivariate factor regression
First diagnostic
Units, collinearity and sample stability

Assess relative mispricing

Method
Spread model or comparable values
First diagnostic
Economic comparability and regime change

More worked practice

Original teaching cases. Use the stated assumptions; these are not official exam questions or marking keys.

A relative-value signal is not an arbitrage guarantee

Given: A spread has a historical mean of 80 basis points and standard deviation of 20. Today it is 120. A trade intended to benefit from narrowing has estimated costs of 15 basis points.

  1. 1The z-score is (120 - 80) / 20 = 2.0.
  2. 2Full convergence to the old mean would produce a 40-basis-point gross spread change under the simplified exposure.
  3. 3After 15 basis points of costs, the assumed opportunity is 25 basis points before funding and path risk.

Interpretation: The arithmetic describes a conditional opportunity. It does not establish that the old mean remains valid, that the spread will converge, or that the position can survive further widening.

Check your understanding

Answer first, then open the explanation. These checks are original practice and do not generate an exam score.

1. Why not discount every payment at the two-year spot rate?

Each maturity has its own spot discount factor. A flat curve would be a separate assumption.

2. Does a significant regression coefficient prove causation?

No. It describes a sample relationship conditional on the included variables and model assumptions.

3. What makes a two-standard-deviation spread unattractive?

Structural change, weak comparability, excessive costs, unstable estimates or funding constraints can outweigh the apparent signal.

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Common questions

Is the regression intercept guaranteed alpha?

No. It is an estimate relative to the specified model. Omitted risks, sampling error and changing relationships can affect it.

Why test out of sample?

It helps assess performance on data not used to fit the model, reducing one source of overfitting. It does not guarantee future performance.

Sources and scope

The sources below establish their stated framework or subject context. Calculations and cases are our own teaching material; these sources do not endorse them or establish complete exam coverage.

By MiloPrep editorial team. Updated 10 October 2026. Independent study notes, not affiliated with or endorsed by CAIA Association. How we prepare our content.

Notes

  • * Study scope: Selected study concepts, not complete curriculum coverage. Match your sitting to the official exam-year materials; CAIA’s current resource page now links to 2027. ↩ Return to content