Perception.

A name can take you places. Often it leads you to a novel idea, sometimes it pushes you off-road.

Not All Time-Weighted Returns Are Born Equal

In spite of the name, the Modified Dietz Time-Weighted Rate of Return (TWRR) is a money-weighted metric.

In this case, the name pushes investors off road.

The Modified Dietz Methodology (MDM) was originally developed to provide an estimate of the Internal Rate of Return (IRR) of a transaction involving multiple cash flows. The IRR requires iterative calculations, which, in the case of long series of cash flows, can be highly complex and deliver multiple solutions.

The MDM is an elegant solution, which weighs the cash flows with the time elapsed since inception to determine the implicit average capital that prodeced the (positive or negative) change in value.

Formulas of the MDM are available in many places, although not often associated with the parallel IRR calculation. I will do this exercise in the table below.

MD TWRR and XIRR (the IRR formula which considers actual dates) are indeed very close.

But the MD TWRR is considered time-weighted, annualised and compounded. The use of geometrically linked TWRR based of the MDM is widespread.

Nevertheless, TWRR hide the same reinvestment assumption that biases the IRR.

As it is well known in fixed income, cash distributions “shorten the time” of financial transaction. This is why duration equals maturity only in zero coupon bonds, otherwise is shorter.

IRR have an implicit duration that is shorter than the contractual times. An approximation of the IRR duration (in days) is calculated using the well known formula ln(TVPI) / ln (1+IRR) x 365 sourced from “Inside Private Equity”, Kocis et al.

In the example of the table, the IRR duration is 248 days (and not the 361 days of the full transaction). Re-engineering the duration of the MDM as I have done in the right upper part of the table, I derive an implicit net duration of 247 days – pretty close, and interestingly forward 83 days.

The implications are not irrelevant.

Assuming the MD TWRR as an annualised rate, implicitly assumes the growth rate of the capital for a full one year at that rate.

But in this example, we can see that the average capital grows at 11.50% only for 247 days out of 365. The reinvestment assumption is powerful for one third of the year.

In the negative scenario of zero-interest-rate-reinvestment possibilities, the annualised return may “only” be 7.83% (using a super-simplified estimation).

A non irrelevant delta performance lost in a name.

Now you know why duration is our guiding principle. It’s when real money happens (and how risk can be managed).

Irrational

I will restart writing on my blog with a statement about irrationality. Credit to Nassim Nicholas Taleb @nntaleb on X (https://twitter.com/nntaleb/status/1718990852628861003).

You must come to grips with the fact that history may, of all alternatives, take the most irrational path, that is, the one that makes the least amount of sense to educated & neutral observers.

Now, back to private equity.

I admit I am not coming to grips with the currently adopted valuation / benchmarking practices.

On the one hand, I hear that private equity valuation should not be (fully) affected by listed market volatility. Hence the “preference” for less volatile NAVs.

On the other, investors accept Public Market Equivalent (PME) methodologies for benchmarking. In other words, they apply full listed market volatility pricing on the random days of the cash flow and NAV events.

It looks that investors can accept as a rational investment strategy trading on the public markets on the days in which the cash flows of a private funds materialize.

Usually instead, if an investor decides to put capital at work in the public markets, there is usually a planned deployment strategy, e.g. full upront or periodic investments, an investment horizon and a disinvestment discipline.

This is different from a commitment in the private markets, where investments and divestments are at the discretion of a GP, who may even invest without calling capital or distribute cash without selling any portfolio holding, by leveraging the possibilities of the debt capital markets.

I can’t evidently come to grips with PME, beyond its nature of a purely theoretical, single-asset, simulation exercise. For a number of mathematical robustness reasons (relating to the aggregation flaws of money-weighted measures – incredibly overlooked), its results can’t be generalised.

I have addressed the topic already in the past in a detailed post: https://blogs.cfainstitute.org/investor/2021/07/05/pointless-market-equivalence-if-not-the-irr-why-the-pme/.

Rationally, benchmarking private equity with PME keeps looking irrational.

Keeping Score, Fast and Slow (Hint: It’s Not Just About the Game of Golf)

Most of the times ideas come up from unusual sources, often unexpectedly mixed. This is what has happened with this post, in which I am writing about how score keeping in the game of golf and decision making psychology can provide insights about the valuation of investment performance.

Asset Managers Are from Mars, Investors Are from Venus (Part 2 – A Space-Walk Down to Earth)

In the first part of this post, I wrote about how differently asset managers and investors react to stressfull situations, with the retreat to the cave of the ones contrasting with the need for increased communication and transparency of the others.

Asset Managers Are from Mars, Investors Are from Venus (Part 1)

I feel I have been thinking about this for a long time and hinted to at least part of it here and there…. But I realize I have never spelled it clearly, or not in a language that would have been easy to understand for everyone.

Yale and the Wolf, a Venture Capital Performance Tale

Every year, the press coverage about the release of the annual financial reports of one of the most prestigious investment offices in the world, often referred as the benchmark for long term investing, reminds me of a classical tale. And it’s not the first time I write about it, but reiteration deserves an encore.

Can I Teach Your Money the Duration Trick?

Even the most sophisticated among us, when a magic trick is performed well, can’t resist its fascination. Let’s admit that. As small kids we thought there was some special power in the hands of the magician. Growing up, we all know that is an illusion, misdirectional cheating. But we keep asking HOW it’s done.

No Robo No Cry

It’s been a while since a good piece of thought leadership stroke a chord with my musical memory. But that happened this morning, when I read this on LinkedIn, shared in my network, from the March 25^th issue of The New York Times: Why I Don’t Make Financial Decisions on My Smartphone.

A Challenging Validation, “a contrario”

Over the past two weeks, the conversation and the exchange of emails with a highly reputable and quant skilled professional in the private equity industry have posed an interesting intellectual challenge and created a very useful opportunity for testing “a contrario” the DaRC methodology and for discussing the relation between duration and time horizon.

Don’t Throw the (Private Equity) Baby Out with the Bathwater

Criticism over private equity opacity and high fees make strong, catchy headlines. With reason.

I am a long-time supporter of increased (business-friendly, i.e. terms that do not compromise the proper execution of deals that require absolute confidentiality) transparency in the industry and not by chance the name of my 2009 firm is Xtal Strategies… Clear? Xmas may give a clue. But back to the baby.