Direct Alpha and Excess IRR for Private Market Returns
Summary
The document explains how Direct Alpha and excess IRR, also called IPP, measure private asset performance relative to a public market benchmark. It presents excess IRR as the rate added to benchmark returns that makes a public market equivalent equal to one. Contributions and distributions are benchmark-adjusted over time, with the excess rate solved for in the resulting equation.
The answer describes Direct Alpha as the continuous-compounding limit of excess IRR, after translating between discrete and continuous return conventions. On that view, the measures are closely related and share advantages and limitations. The author considers excess IRR’s derivation more direct and notes that discrete compounding can make its output easier to compare with reported returns. The document gives an algebraic explanation rather than empirical comparisons, and does not evaluate performance across datasets or discuss implementation choices such as cash flow timing conventions.
Key ideas
- Excess IRR is the added annualized return that makes a benchmark-adjusted public market equivalent equal one.
- Direct Alpha can be understood as the continuous-compounding limit of excess IRR.
- The two measures are conceptually related and are presented as sharing advantages and limitations.
- Discrete compounding may make excess IRR more comparable with commonly reported returns.
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# Private Equity: Direct Alpha vs Excess IRR
# Private Equity: Direct Alpha vs Excess IRR
I'm trying to understand the advantages and disadvantages of using Direct Alpha versus Excess IRR for computing excess returns over a market index for private assets.
Wikipedia references a highly informative paper that compares the Direct Alpha against PME, PME+, mPME, and KS-PME and discusses the limitations of these as well as analyzes the correlations between them.
I'm looking for a similar resource to that compares the two in my title.
## Answer by Helin (score 2)
https://quant.stackexchange.com/a/35654
They are "essentially" the same thing. IPP (or excess IRR) is the excess return over the annualized benchmark such that the adjusted PME is 1:
$$\text{PME} = 1 = \frac{\sum_{i=1}^n d_i \left(1 + \dfrac{b_{T_i, T_N}}{q} + \dfrac{r}{q}\right)^{q(T_N-T_i)} }{\sum_{j=1}^m c_i \left(1 + \dfrac{b_{T_j, T_N}}{q} + \dfrac{r}{q}\right)^{q(T_N-T_j)}}, $$
where $c_i$ and $d_i$ are the contribution and distribution at time $t_i$, respectively, $b$ is the annualized public market benchmark return over the relevant periods, $r$ is the annualized excess IRR/IPP, and $q$ is the compounding frequency (typically $q=1$ in the IPP setting).
If you let $q\to\infty$ (i.e., continuous compounding) and with some redefinition (e.g., $e^\alpha = 1+a$), it is easy to show that excess IRR/IPP converges to direct alpha.
So simply put, direct alpha is just the limiting case of excess IRR/IPP, but they're conceptually the same thing. As such, they have the same advantages and disadvantages. IMO, the derivation of IPP/excess IRR is more direct (resembling the way OAS is defined in the fixed income market) and the use of discrete compounding makes the output more comparable to other reported returns.Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)
This summary was written by Stratmill's research agent from the original; it is not a copy of the source.