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

$\sum_j \frac{p_j}{(1+r)^{t_j}} = 0$

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

$ROX = \sum_{j=0}^N z_j\frac{p_j}{\phi_0 D}$

where $$z_j$$ are zero coupon discount factors, $$\phi_0$$ is exposure par amount, $$D$$ is spread duration,

$D=\sum_{j=1}^N z_j(t_j-t_{j-1})\frac{\phi_{j-1}}{\phi_0}$

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

$\xi_j = p_j - \psi_{j-1}L_{j-1}(t_j-t_{j-1})$

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

The proposed volatility measure:

$CLO\# = \frac{\textrm{mean}(\xi_j)}{\textrm{StdDev}(\xi_j)}$

## 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",
}