A promised yield turned into an expected one, then run through fund-level leverage and a fee waterfall, and finally inverted into the default rate that takes the result to zero. Every input is encoded in the URL. All arithmetic runs in the browser.
Stated per 100 of investor equity, so every line reads directly as a percentage of equity. Fund-level debt is 100 at the stated cost, so gross assets are equity plus debt.
Each added turn of leverage raises the return and lowers the cushion. The breakeven columns hold the yield, the recovery, and the cost of debt constant and solve only for the default rate.
Three lines, each as a function of the annual default rate on the horizontal axis: the loss-adjusted asset yield, the loss-adjusted return on equity through the leverage facility, and the same return net of management and incentive fees. The solid vertical marker is the breakeven default rate at which the levered return reaches zero; the dotted vertical line is the default rate currently entered.
Every figure above is produced by the identities below. They are reproduced here in full so the page is readable without running anything.
Loss given default is the complement of recovery. The expected annual credit loss is the default rate on par multiplied by loss given default, and the loss-adjusted yield is the all-in yield less that loss. It converts a promised yield into an expected one, and it is the only basis on which two loans at different risk are comparable. It is an expected value, and credit losses are not symmetric around it.
Worked: Y = 9.80 percent, d = 2.00 percent, R = 60 percent. LGD = 40 percent, EL = 2.00 x 0.40 = 0.80 percent, LAY = 9.80 - 0.80 = 9.00 percent. A default rate of 4.00 percent at an 80 percent recovery gives the same 0.80 percent of expected loss and the same 9.00 percent loss-adjusted yield from a very different credit profile, which is why the pair has to be quoted together. Of a 580 bps all-in spread on those terms, 80 bps is expected loss and 500 bps is compensation for everything else.
Borrowing at the fund level and investing the proceeds alongside equity in the same asset pool. The return on equity is linear in the asset return and linear in the cost of debt, with the leverage ratio as the multiplier on both. The second form makes the mechanic explicit: the equity return is the asset return plus the leverage ratio times the spread earned on borrowed money.
Worked: R_a = 9.80 percent, L = 1.0, c = 6.00 percent gives R_e = 19.60 - 6.00 = 13.60 percent. Applying the same formula to the loss-adjusted 9.00 percent gives 18.00 - 6.00 = 12.00 percent, so leverage magnified 80 bps of expected loss into 160 bps of equity return. At those inputs the spread earned per turn is 380 bps.
Worked: at L = 1.0 and c = 6.00 percent that is 6.00 x 1.0 / 2.0 = 3.00 percent. At L = 2.0 it is 6.00 x 2.0 / 3.0 = 4.00 percent. Each added turn raises the asset return the pool must earn before the equity earns anything.
The annualised default rate at which the return falls to a chosen threshold. It restates a yield as the cushion it buys, which is a more useful comparison than the yield itself. Unlevered, the threshold applies directly to the asset return. Levered, the threshold applies to the equity return, so it is first translated back into the asset return that produces it.
Worked, Y = 9.80 percent and R = 60 percent throughout. Unlevered to a zero return: 9.80 / 0.40 = 24.5 percent. Unlevered to a 4.00 percent hurdle: (9.80 - 4.00) / 0.40 = 14.5 percent. Levered 1:1 at 6.00 percent to a zero equity return: the asset return at which equity earns nothing is 3.00 percent, so d* = (9.80 - 3.00) / 0.40 = 17.0 percent. Levered 2:1: the asset breakeven is 4.00 percent, so d* = (9.80 - 4.00) / 0.40 = 14.5 percent. At a 40 percent recovery instead of 60, the 1:1 figure falls to (9.80 - 3.00) / 0.60 = 11.3 percent.
The fee rate is quoted on a base, and the base determines what the fee costs the equity. A fee on gross assets is charged on borrowed money as well as investor money, so at one turn of leverage a one percent gross-assets fee costs the equity two percent. In this static, fully-deployed model net assets and equity commitments are both equal to equity, so those two bases produce the same figure here; they diverge once capital is undrawn or marks move away from cost.
Worked: m = 1.00 percent on gross assets at L = 1.0 costs the equity 1.00 x 2.0 = 2.00 percent.
The incentive fee is charged on pre-incentive net investment income above a stated hurdle on equity. Without a catch-up the manager takes the incentive rate on the excess. With a full catch-up the manager takes 100 percent of income between the hurdle and the catch-up boundary, and the incentive rate on everything above it.
Worked, Y = 9.80 percent levered 1:1 at 6.00 percent with a 1.00 percent gross-assets fee, a 7.00 percent hurdle, and a 15 percent incentive rate. Gross investment income is 19.60 percent of equity, less 6.00 of interest and 2.00 of management fee, giving pre-incentive net investment income of 11.60 percent. Without a catch-up the fee is 0.15 x 4.60 = 0.69 percent and the net return is 10.91 percent, a 269 bps gap to the 13.60 percent gross figure. With a full catch-up the boundary is 7.00 / 0.85 = 8.235 percent: the manager takes 100 percent of the 1.235 between 7.000 and 8.235, then 15 percent of the 3.365 above it, being 0.505, for a total fee of 1.740 percent and a net return of 9.86 percent. The catch-up more than doubles the fee at this income level, a difference of 105 bps of net return.
Asset yield 9.80 percent, loss-adjusted asset yield 9.00 percent, facility cost 6.00 percent, recovery 60 percent. Illustrative inputs, not market levels.
| L | Gross return on equity | Loss-adjusted | Asset return at zero equity | Breakeven default rate |
|---|---|---|---|---|
| 0.0x | 9.80 | 9.00 | 0.00 | 24.50 |
| 0.5x | 11.70 | 10.50 | 2.00 | 19.50 |
| 1.0x | 13.60 | 12.00 | 3.00 | 17.00 |
| 1.5x | 15.50 | 13.50 | 3.60 | 15.50 |
| 2.0x | 17.40 | 15.00 | 4.00 | 14.50 |
| Parameter | Meaning | Default |
|---|---|---|
yield | Gross all-in yield on the asset pool, Y, in percent. The yield-to-take-out figure rather than the coupon. | 9.8 |
default | Annualised default rate on par, d, in percent | 2 |
recovery | Recovery R on defaulted par, in percent; LGD is 100 less this. A tranche-level recovery, not a blended one. | 60 |
leverage | Debt divided by equity at the fund or vehicle level, L | 1 |
cost | All-in cost c of the leverage facility, in percent, including undrawn and arrangement costs | 6 |
hurdle | Threshold h for the breakeven and for the incentive fee, in percent. Zero gives the wipe-out case. | 4 |
mgmtfee | Management fee rate, in percent | 1 |
feebase | gross, net, or commitments | gross |
incentive | Incentive fee rate on net investment income above the hurdle, in percent | 15 |
catchup | none or full | none |
Unlevered, to a zero return:
https://privatecredit.wiki/calc/loss/?yield=9.8&default=2&recovery=60&leverage=0&hurdle=0
Levered 1:1 at 6.00 percent, with fees and a full catch-up over a 7.00 percent hurdle:
https://privatecredit.wiki/calc/loss/?yield=9.8&default=2&recovery=60&leverage=1&cost=6&mgmtfee=1&feebase=gross&incentive=15&hurdle=7&catchup=full