Why Illiquid Assets Need a Stressed-Sale View
A carrying value is not necessarily the amount an insurer could realize quickly in a stressed market. An asset may be difficult to value because trades are infrequent, may take time to sell because buyers are scarce, and may have to be sold at progressively lower prices as the sale grows relative to available market depth. These effects matter when assessing whether assets can support obligations or a planned risk response during stress.
A useful analysis keeps three quantities separate: the current carrying value, a stressed reference value before sale-specific costs, and the proceeds available from executing a particular sale. Combining them too early can obscure whether a loss comes from market repricing, uncertainty in the valuation, delay, or the act of selling. The framework below is illustrative rather than a universal pricing model; its assumptions must be matched to the asset and the decision being assessed. This treatment is aligned with the CAS Exam 9 (Risk Management for Actuaries) syllabus.
Separate Valuation, Delay, and Market Depth
Valuation uncertainty arises when the carrying value or stressed reference value depends on estimates rather than recent observable transactions. It is often useful to show a range of plausible values, or to specify alternative valuation scenarios, rather than imply that one point estimate is certain. Such a range is not automatically a statistical confidence interval: it has that interpretation only if a probability model and a procedure supporting that interpretation have been established.
Trading delay creates exposure between the decision to sell and the time the sale can be completed. During that interval, market prices can change. A stress estimate should therefore identify its horizon and whether the assumed market shock is already measured through that horizon. Applying an additional movement to a value that already includes it would double-count the shock.
Limited market depth means that the quantity available near a quoted or reference price is limited. A larger sale may consume that depth and require successively worse prices. A single percentage haircut can be a practical approximation, but it does not show how the result depends on sale size. A tranche calculation makes that dependency visible.
For a deterministic stress with reference price \(P_s\), suppose a sale is divided into tranches. Let \(q_j\) be the quantity sold in tranche \(j\), and let \(h_j\) be that tranche’s price discount from the stressed reference price. Assume each tranche can be sold at its specified price, the discounts already capture the modeled market impact, and there are no additional fees or taxes. Then the proceeds are:
Each unit in tranche \(j\) sells for \(P_s(1-h_j)\), so multiplying by \(q_j\) gives that tranche’s proceeds. Adding the proceeds across mutually exclusive tranches gives total proceeds. If the sale also incurs a proportional transaction cost \(c\) that is not included in the discounts, net proceeds are \((1-c)\) times gross proceeds. The cost must not be applied again if it is already included in the tranche prices.
Worked Example: Valuation Range After a Market Stress
A hypothetical insurer holds a private loan portfolio carried at $25,000,000. A specified market stress reduces its estimated reference value by 12%. Because trades are infrequent, the valuation team assesses uncertainty as plus or minus 4% of the stressed reference value. If the portfolio is sold, assume a further 2% proportional transaction cost. Find the range of net sale proceeds and the corresponding loss relative to the carrying value. The stress and uncertainty assumptions are deterministic bounds, not a probability distribution. No interest discounting or mortality assumption is used.
Method. First calculate the stressed reference value. Then apply the valuation range, followed by the separately specified transaction cost.
The stressed reference value is \( \$25{,}000{,}000(1-0.12)=\$22{,}000{,}000 \). The lower valuation bound is \( \$22{,}000{,}000(1-0.04)=\$21{,}120{,}000 \), and the upper bound is \( \$22{,}000{,}000(1+0.04)=\$22{,}880{,}000 \).
After the 2% transaction cost, the lower net proceeds are \( \$21{,}120{,}000(0.98)=\$20{,}697{,}600 \). The upper net proceeds are \( \$22{,}880{,}000(0.98)=\$22{,}422{,}400 \). Relative to the $25,000,000 carrying value, the loss ranges from \( \$25{,}000{,}000-\$22{,}422{,}400=\$2{,}577{,}600 \) to \( \$25{,}000{,}000-\$20{,}697{,}600=\$4{,}302{,}400 \).
Check and common mistake. The net proceeds lie below both valuation bounds, as required by a positive cost. Applying the 4% uncertainty to the original carrying value instead of the stressed value would use the wrong base. Treating these endpoints as equally likely outcomes would also be unjustified: no probabilities were specified.
Translate Market Depth Into Sale Proceeds
A depth schedule should describe a specified asset quantity, sale horizon, and stressed market. The discounts may represent bid-ask effects, market impact, or other execution concessions, but the analyst must define what each includes. For clarity, the next example assumes that market impact is represented by the tranche discounts and that no further transaction cost applies.
Worked Example: Selling Across Three Depth Tranches
A hypothetical insurer owns 10,000 units of an illiquid security, carried at $1,000 per unit. Under a specified instantaneous market stress, the reference price falls by 10%. The insurer plans to sell 6,000 units. The first 2,000 units can be sold at a 0.5% discount to the stressed reference price, the next 2,000 at a 2% discount, and the final 2,000 at a 5% discount. Assume the specified depths are available during the sale, no further costs apply, and there is no additional price movement during execution. No probability distribution, interest discounting, or mortality assumption is used.
Method. Calculate the stressed reference price, determine each tranche price, and sum the tranche proceeds.
The stressed reference price is \( \$1{,}000(1-0.10)=\$900 \) per unit. The first tranche price is \( \$900(1-0.005)=\$895.50 \), giving \( 2{,}000(\$895.50)=\$1{,}791{,}000 \). The second tranche price is \( \$900(1-0.02)=\$882 \), giving \( 2{,}000(\$882)=\$1{,}764{,}000 \). The third tranche price is \( \$900(1-0.05)=\$855 \), giving \( 2{,}000(\$855)=\$1{,}710{,}000 \).
Total proceeds are \( \$1{,}791{,}000+\$1{,}764{,}000+\$1{,}710{,}000=\$5{,}265{,}000 \). The 6,000 units had a carrying value of \( 6{,}000(\$1{,}000)=\$6{,}000{,}000 \), so the total loss relative to carrying value is $735,000. Of this, the decline from carrying value to the stressed reference price is \( \$6{,}000{,}000-6{,}000(\$900)=\$600{,}000 \). The additional execution impact is \( \$6{,}000(\$900)-\$5{,}265{,}000=\$135{,}000 \).
Check and common mistake. The decomposition reconciles: \( \$600{,}000+\$135{,}000=\$735{,}000 \). Applying the 5% discount to all 6,000 units would ignore the better prices available for the first two tranches. Using $1,000 rather than $900 as the base for the tranche discounts would also fail to apply the market stress in the specified order.
Delayed Trading and Hedge Interpretation
A hedge may be traded quickly even when the underlying asset cannot. The hedge can therefore respond to market movements before the asset’s valuation or sale price fully reflects them. A mark that updates slowly can make the hedge appear temporarily too large or ineffective; that accounting or measurement mismatch is not, by itself, proof that the economic risk has disappeared. Conversely, a hedge based on an estimated sensitivity may not offset the eventual realized change if that sensitivity is wrong.
The following example uses a linear sensitivity for illustration. Assume the asset’s economic value changes by a stated fraction of a market proxy’s percentage move, the proxy hedge has a known cash payoff for that move, and the asset’s carrying mark recognizes only a specified fraction of its economic change by the measurement date. These are scenario assumptions, not general laws of asset behavior.
Worked Example: A Hedge During Delayed Price Discovery
A hypothetical insurer holds an illiquid asset carried at $20,000,000. Its estimated economic sensitivity is 0.60: a 10% fall in a market proxy is assumed to reduce the asset’s economic value by 6%. The insurer holds a linear proxy hedge with a $12,000,000 notional that gains 10% when the proxy falls 10%. At the five-day assessment point, assume the carrying mark has recognized only 50% of the asset’s modeled economic loss. If the insurer sells then, assume a 3% execution discount to the modeled economic value. The shock is deterministic; no probability distribution, interest discounting, or mortality assumption is used.
Method. Calculate the modeled economic asset loss, distinguish it from the loss recognized in the carrying mark, and compare the hedge gain with the asset’s economic loss and its net sale proceeds.
The modeled economic asset loss is \( \$20{,}000{,}000(0.60)(0.10)=\$1{,}200{,}000 \). The modeled economic value is therefore \( \$20{,}000{,}000-\$1{,}200{,}000=\$18{,}800{,}000 \). The carrying mark recognizes half of the loss, or \( 0.50(\$1{,}200{,}000)=\$600{,}000 \), so the marked value at the assessment point is $19,400,000.
The hedge gain is \( \$12{,}000{,}000(0.10)=\$1{,}200{,}000 \). On the modeled economic values, this exactly offsets the $1,200,000 asset loss. On the carrying mark, however, the asset shows only a $600,000 loss, so the combined marked change is a $600,000 gain. If sold at the modeled economic value after the 3% discount, proceeds are \( \$18{,}800{,}000(0.97)=\$18{,}236{,}000 \). Compared with the initial carrying value, the asset’s sale loss is $1,764,000; after the $1,200,000 hedge gain, the combined loss is $564,000.
Check and common mistake. The economic hedge offsets the assumed market sensitivity, but it does not offset the additional $564,000 loss from the stated execution discount. It is a mistake to conclude from the temporary $600,000 marked gain that the hedge is economically excessive without accounting for delayed recognition. It would also be wrong to claim that the hedge fully protects sale proceeds: the execution discount is a separate exposure.
A Practical Stressed-Sale Assessment
A disciplined assessment makes the decision being supported explicit. Selling the entire holding immediately, raising a specified amount of cash over several days, and estimating a stress loss for capital analysis are different problems. They may require different sale quantities, horizons, and assumptions about market recovery or deterioration.
State the carrying value, the stressed reference value, the market shock, and any range or scenario for valuation uncertainty. Specify whether the stress includes movements during the expected trading delay.
Identify the amount to be sold and the time available. A price estimate without a quantity and horizon does not describe executable proceeds.
Use a depth schedule or a clearly explained aggregate haircut. Separate market impact, bid-ask effects, fees, and taxes where possible, and avoid including the same cost twice.
Compare proceeds with the carrying value, then identify the portions attributable to market repricing, valuation uncertainty, delay-related movement, and sale execution.
Vary the sale size, execution horizon, valuation assumption, and market-depth discounts. Explain which assumptions are estimates and where a stressed price may not be observable.
The decomposition is useful for decision-making because different components call for different responses. A market shock may be addressed through portfolio risk limits or a hedge; a long trading delay may call for earlier action or contingency planning; and shallow depth may favor staged sales or a smaller immediate transaction. None of these responses guarantees a particular price, and staging may increase exposure to further market movement.
Common Exam Traps and Interpretation
- Confusing a mark with realizable proceeds. A carrying value is a measurement, not evidence that the full position can be sold at that price.
- Applying discounts to the wrong base. If a tranche discount is stated relative to a stressed reference price, apply it to that price, not to the unstressed carrying value.
- Ignoring the quantity being sold. A haircut derived for a small trade may not be appropriate for a much larger sale when market depth is limited.
- Double-counting costs or shocks. Confirm whether fees are already reflected in execution discounts and whether the stress already includes price movement during the delay.
- Treating uncertainty ranges as probabilities. A range alone does not provide a likelihood, expected value, or confidence level.
- Reading a temporary hedge mismatch as a final result. Compare economic exposure and measurement timing, then account separately for execution costs and basis risk.
A stressed-sale estimate is only as useful as its scope and assumptions. It should not be presented as a guaranteed liquidation value. Clear reporting states what is being sold, when, under which market scenario, and how uncertainty and execution effects are represented. Those details allow decision-makers to compare alternatives without confusing a modeled loss with a certain outcome.
Check Your Understanding
For each hypothetical scenario, identify the relevant assumptions and calculate the requested amount.
- A portfolio is carried at $15,000,000. A stress reduces its reference value by 7%, and the valuation range is plus or minus 2% of the stressed reference value. A 1% transaction cost applies after valuation. Find the range of net proceeds and losses relative to carrying value. (Answer: Net proceeds $13,534,290 to $14,086,710; losses $913,290 to $1,465,710.)
- A security has 5,000 units carried at $500 each. A stress reduces the reference price by 12%. A sale of 3,000 units has depth of 1,000 units at a 1% discount, 1,000 at 3%, and 1,000 at 6% from the stressed price. Find proceeds, the total loss relative to carrying value of the units sold, and execution impact beyond the market stress. (Answer: Proceeds $1,276,000; total loss $224,000; execution impact $44,000.)
- A holding’s carrying value is $15,000,000. Its stressed executable-value reference is $14,000,000, before a 2% transaction cost. Sale completion is delayed three days. Relative to that reference, the market factor at completion is 0.95 with probability 0.20, 1.00 with probability 0.50, and 1.03 with probability 0.30. Under this discrete scenario distribution, find expected net proceeds and expected loss relative to carrying value. (Answer: Expected net proceeds $13,706,280; expected loss $1,293,720.)
- An illiquid asset is carried at $8,000,000 and has an assumed linear sensitivity of 0.75 to a proxy that falls 8%. A proxy hedge with $4,800,000 notional gains 8% on that move. The mark recognizes 40% of the asset’s modeled economic loss. Find the modeled economic loss, the hedge gain, and the temporary combined marked change. (Answer: Economic asset loss $480,000; hedge gain $384,000; combined marked change is a gain of $192,000.)