Lesson 20 of 25 · 6 min
Why the borrower and the lender read the same collateral differently
One party is valuing a decade and the other is valuing five days, and neither is making a mistake.
Two parties look at the same holding and produce different valuations. The disagreement is often read as a difference of opinion about the company. It is a difference of horizon, and it would persist even if both parties agreed on every fact.
A borrower's horizon is the holding period, which may be a decade. Over ten years an illustrative 9 percent compound return turns $1,000,000 into $1,000,000 × 1.09^10 = $2,367,364. That is the object being valued, and short-term moves are noise within it.
A lender's horizon is the liquidation window, which is measured in days. Deviations scale with the square root of time, so an illustrative 34 percent annualised volatility implies a five-day deviation of a little under 5 percent.
five-day deviation = annualised volatility × √(5 ÷ 252)
- annualised volatility
- The typical size of a move over a year, as a percentage. Here 34 percent, illustrative.
- 5
- The number of trading days in the assumed liquidation window.
- 252
- The approximate number of trading days in a year.
- five-day deviation
- The typical size of a move over that window. Here 34 × 0.1409 = 4.79 percent.
Three of those deviations is 14.4 percent, and a 45 percent haircut — the complement of a 55 percent advance rate — covers that with room for the delay before a decision, the gap on the way, and the price impact of selling in size. The lender's number is assembled out of 4.79 percent units over five days. The borrower's number is assembled out of 9 percent units over ten years. Both are defensible and they are not about the same quantity, which is why arguing the merits of the company moves neither one.
Key terms
- Horizon
- The period over which an outcome is being assessed. It determines which risks are noise and which are the entire question.
- Liquidation window
- The days between a lender deciding to sell collateral and the cash arriving. The haircut is sized to survive it.
- Price impact
- The movement caused by the act of selling in size. A cost that exists only for the party that has to transact quickly.
Worked example
The same $1,000,000, on two clocks
A holding at an illustrative 34% annualised volatility and an illustrative 9% compound return.
- Borrower's ten-year value
- $2,367,364
- Five-day scaling factor
- 0.1409
- Lender's five-day deviation
- 4.79%
- Three deviations over the window
- 14.4%
- Haircut at a 55% advance rate
- 45%
$1,000,000 × 1.09^10.
√(5 ÷ 252).
34% × 0.1409.
Covers the move, the delay, the gap and the price impact.
One party is computing a decade of compounding and the other is computing a week of trading. The collateral is identical and the two numbers never meet.
Check yourself
A holding has an illustrative 34 percent annualised volatility. What is its five-day deviation, and why does that figure matter more to the lender than a ten-year return estimate?
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Educational only. Nothing in this lesson is investment, legal or tax advice, or a recommendation to enter into any transaction. Figures are illustrative and computed from the inputs stated in the lesson.