Why the benefit is smallest exactly when it is needed most

Everything to this point has been about measurement. This lesson spends it. An advance-rate schedule is set once and applied every day, which means it prices the diversification a portfolio has on an ordinary day — and the diversification that decides an outcome is the amount present on the day of a call.

Take a pledged pool of $2,865,000 across five equally weighted holdings, each with 28 percent annualised volatility. On ordinary-market estimates the average pairwise correlation is 0.34, so effective bets are 5 divided by 2.36 = 2.12 and portfolio volatility is 19.24 percent. In a drawdown the average correlation is 0.76, effective bets fall to 5 divided by 4.04 = 1.24, and portfolio volatility rises to 25.17 percent.

Suppose an illustrative schedule assigns 66 percent to a pool behaving like roughly two independent positions and 48 percent to one behaving like roughly one and a quarter. The pool earns 66 percent, because 2.12 is the figure the ordinary-market data supports. That is not an error by the lender; it is a correct reading of the available estimate.

Now run the drawdown. The pool falls 22 percent to $2,234,700. At the 66 percent the schedule assigned, lending value is $1,474,902. At the 48 percent the diversification actually present would have justified, it is $1,072,656. The gap of $402,246 is the useful figure: it is collateral value resting on a property the portfolio does not have at the moment the test is applied. Against a balance of $1,240,000, the first gives a loan-to-value of 84.07 percent and the second 115.60 percent — $234,902 of headroom on one basis and a $167,344 shortfall on the other.

An advance rate is an average over regimes applied to a single day. In ordinary months that overstates nothing worth worrying about, and on the day it is tested it overstates by the whole tail gap.