A short paper arguing how to evaluate CLO equity performance. As the equity tranche of a CLO has a maturity date, we can consider that as a bond with indeterministic coupon. So it is natural to use IRR as a measure for equity. IRR is the solution of in

where is the payment (negative if from investor) and is the time measured in years. IRR measures the yield amounts to break-even PV of cash flows.

Problems of IRR:

- different IRR for different compounding period
- market rate affects rate of return but IRR can’t distinguish the attribution of yields
- In case of zero or negative profit: IRR give more negative for shorter term of recovery
- e.g., zero profit, recover whole investment in 1 yr vs 10 yr are both IRR 0%
- e.g., loss, recover 50% of investment in 1 yr vs 10 yr. 10 yr has less negative IRR

Alternative measure is “return of exposure” (ROX). The paper claims that it is similar to discount margin

where are zero coupon discount factors, is exposure par amount, is *spread duration*,

with the remaining par of the investment at time . ROX is the PV of all payments received () minus the PV of all funded investments (), divided by the sum-product of exposure par amount and duration. If the investment return if LIBOR-flat (i.e., LIBOR+0), ROX is zero.

The metric this paper proposed is “CLO Sharpe” (CLO#). Defined as follows: Excess return (for ) is actual payments minus the LIBOR interest on outstanding residual par

with , for

The proposed volatility measure:

## Bibliographic data

```
@article{
title = "Better measurements for CLO equity performance",
author = "Joseph M. Pimbley",
journal = "The Journal of Structured Finance",
volume = "Summer",
year = "2016",
pages = "24--30",
}
```