Liquid-Inputs Relative Valuation
Infer an illiquid asset's value from its liquid building blocks
- Difficulty
- Advanced
- Time to result
- ~weeks to results
- Steps
- 5
- Confidence
- 93%
Liquid-Inputs Relative Valuation estimates the present value of an illiquid instrument from observable prices of related liquid instruments. Instead of predicting where the market will go, the analyst decomposes the target into economic building blocks, prices those inputs, adds relevant transformation or carrying costs, and derives an implied fair value. Derman's metaphor is fruit salad: given the prices of apples, pears, and peaches plus the cost of canning, infer what the salad should cost. The relationship can also be solved in reverse when the composite and most components are known. Comparing the implied value with an available quote identifies what appears rich or cheap. Any trade still relies on a prediction—that the discrepancy will eventually converge toward fair value—but the core model addresses relative prices in the present.
Origin
Derman explains that much derivatives work estimates an illiquid price from liquid instruments, using fruit salad and its ingredients as a metaphor.
Core principles
- 01A market price is directly observable only when an asset trades liquidly.
- 02An illiquid instrument can be related to liquid components through structure.
- 03Valuation often concerns present relative prices rather than forecasting the future.
- 04A rich or cheap relationship implies an expected move toward fair value.
How to run it
- 1
Define the target
Choose the illiquid or infrequently traded instrument whose present value is uncertain.
Pro tip Confirm that the lack of a dependable quote is a liquidity problem rather than missing data.
Watch out A stale quote is not necessarily a fair market price.
- 2
Map the structure
Identify the liquid instruments and economic relationships that reproduce or explain the target's value.
Pro tip Express the relationship as a transparent decomposition.
Watch out Do not combine inputs that lack a defensible structural link to the target.
- 3
Price the inputs
Collect current market prices for the liquid building blocks and estimate relevant transformation, financing, or transaction costs.
Pro tip Use contemporaneous prices because the method compares values in the present.
Watch out Ignoring implementation costs can create a false discrepancy.
- 4
Calculate implied value
Apply the structural relationship to convert the liquid input prices into a value for the illiquid target.
Pro tip Where useful, solve the relationship in reverse to infer a missing component.
Watch out The precision of the calculation cannot exceed the quality of its structural assumptions.
- 5
Judge rich or cheap
Compare the implied value with any quoted target price and identify the direction and size of the discrepancy.
Pro tip Separate the present valuation result from the later convergence forecast.
Watch out A cheap instrument can remain cheap, so state why convergence is expected.
In the wild
Derman asks what fruit salad should cost when the prices of apples, pears, and peaches are known. Add the cost of canning to the ingredient prices to infer the composite's value. The relationship can be reversed: if the salad, apples, and oranges are priced, infer the appropriate price of pears.
→ Liquid component prices provide an implied present value for the less directly priced item.
Derman describes using liquid stock and bond prices to estimate what an option should cost when the option itself is less liquid. The model translates observable component prices through the option's structure rather than primarily forecasting the stock's future price.
→ The analyst obtains a relative valuation and can judge whether the option appears rich or cheap.
Common mistakes
Turning valuation into prophecy
The model estimates a present relative price; it does not directly predict the market's future path.
Ignoring transformation costs
The implied value is incomplete when the cost of creating or carrying the composite is omitted.
Assuming immediate convergence
A rich-or-cheap finding still requires a separate belief that market prices will move toward the implied value.
Is it for you?
Best for
It is best for derivatives or structured instruments whose economic components have observable liquid prices.
Not ideal for
It is not ideal when the target cannot be structurally related to liquid inputs or transformation costs are unknowable.
From the transcript
“most of the time, certainly derivatives, you're not making predictions about the future.”
“what should a pay for fruit salad? Given the price of apples, pears and peaches”
“it's always trying to figure out in the present how to get the liquid thing, given the price of the liquid things, how to get…”
From the episode
Interview With Emanuel Derman: Masters in Business (Audio)
Emanuel Derman