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 $r$ in

where $p_j$ is the payment (negative if from investor) and $t_j$ 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 $r$ 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 $z_j$ are zero coupon discount factors, $\phi_0$ is exposure par amount, $D$ is spread duration,

with $\phi_j$ the remaining par of the investment at time $t_j$. ROX is the PV of all payments received ($j=1,\cdots,N$) minus the PV of all funded investments ($j=0$), 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 $\xi_j$ (for $j=1,\cdots,N$) is actual payments $p_j$ minus the LIBOR interest on outstanding residual par

with $\psi_0=\phi_0$, $\phi_j=\phi_{j-1}-\xi_j$ for $j=1,\cdots,N$

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",
}