Thursday, February 15, 2024

Private Equity Fantasy Returns

One of the ways that investors seek status through their investments is to buy into private equity.  As an added inducement, a technical detail in how private equity returns are calculated makes these investments seem better than they are.  So, private fund managers get to boast returns that their investors don’t get.

Private Equity Overview

In a typical arrangement, an investor commits a certain amount of capital, say one million dollars, over a period of time.  However, the fund manager doesn’t “call” all this capital at once.  The investor might provide, say, $100,000 up front, and then wait for more of this capital to be called.

Over the succeeding years of the contract, the fund manager will call for more capital, and may or may not call the full million dollars.  Finally, the fund manager will distribute returns to the investor, possibly spread over time.

An Example

Suppose an investor is asked to commit one million dollars, and the fund manager calls $100,000 initially, $200,000 after a year, and $400,000 after two years.  Then the fund manager distributes returns of $200,000 after three years, and $800,000 after four years.

From the fund manager’s perspective, the cash flows were as follows:


So, how can we calculate a rate of return from these cash flows?  One answer is the Internal Rate of Return (IRR), which is the annual return required to make the net present value of these cash flows equal to zero.  In this case the IRR is 16.0%.

A Problem

Making an annual return of 16% sounds great, but there is a problem.  What about the $900,000 the investor had to have at the ready in case it got called?  This money never earned 16%.

Why doesn’t the fund manager take the whole million in the first place?  The problem is called “cash drag.”  Having all that capital sitting around uninvested drags down the return the fund manager gets credit for.  The arrangement for calling capital pushes the cash drag problem from the fund manager to the investor.

The Investor’s Point of View

Earlier, we looked at the cash flows from the investment manager’s point of view.  Now, let’s look at it from the investor’s point of view.

Suppose the investor pulled the million dollars out of some other investment, and held all uncalled capital in cash earning 5% annual interest.  So the investor thinks of the first cash flow as a million dollars.  Any called capital is just a movement within the broader investment and doesn’t represent a cash flow.  However, the investor can withdraw any interest earned on the uncalled capital, so this interest represents a cash flow.

The second cash flow is $45,000 of interest on the $900,000 of uncalled capital.  The third cash flow is $35,000 of interest on the $700,000 of uncalled capital.  The fourth cash flow is a little more complex.  We have $15,000 of interest on the $300,000 of uncalled capital.  Then supposing the investor now knows that no more capital will be called and can withdraw the remaining uncalled capital, we have a $300,000 cash flow.  Finally, we have the $200,000 return from the fund manager.  The total for the fourth cash flow is $515,000.  The fifth cash flow is the $800,000 return.

The cash flows from the investor’s point of view are


The IRR of these cash flows is 10.1%, a far cry from the 16.0% the fund manager got credit for.  We could quibble about whether the investor really had to keep all the uncommitted capital in cash, but the investor couldn’t expect his or her other investments to magically produce returns at the exact times the fund manager called some capital.  The 10.1% return we calculated here may be a little unfair, but not by much.  The investor will never be able to get close to the 16.0% return.

Others have made similar observations and blamed the IRR method for the problem.  However, this isn’t exactly right.  The IRR method can have issues, but the real problem here is in determining the cash flows.  When we ignore the investor’s need to be liquid enough to meet capital calls, we get the cash flows wrong.


Some argue that we need to use the IRR method from the fund manager’s point of view so we can fairly compare managers.  Why should investors care about this?  They should care about the returns they can achieve, not some fantasy numbers.  Any claims of private equity outperformance relative to other types of investments should be taken with a grain of salt.

Thursday, January 25, 2024

Retirement Spending Experts

On episode 289 of the Rational Reminder podcast, the guests were retirement spending researchers, David Blanchett, Michael Finke, and Wade Pfau.  The spark for this discussion was Dave Ramsey’s silly assertion that an 8% withdrawal rate is safe.  From there the podcast became a wide-ranging discussion of important retirement spending topics.  I highly recommend having a listen.

Here I collect some questions I would have liked to have asked these experts.

1. How should stock and bond valuations affect withdrawal rates and asset allocations?

It seems logical that retirees should spend a lower percentage of their portfolios when stocks or bonds become expensive.  However, it is not at all obvious how to account for valuations.  I made up two adjustments for my own retirement.  The first is that when Shiller’s CAPE exceeds 20, I reduce future stock return expectations by enough to bring the CAPE back to 20 by the end of my life.  These lower return expectations result in spending a lower percentage of my portfolio after doing some calculations that are similar to required minimum withdrawal calculations.  I have no justification for this adjustment other than that it feels about right.  

The second adjustment is on equally shaky ground.  When the CAPE is above 25, I add the excess CAPE above 25 (as percentage points) to the bond allocation I would otherwise have chosen in the current year of my chosen glidepath.  Part of my reasoning is that when stock prices soar, I’d like to protect some of those gains at a time when I don’t need to take on as much risk.

Are there better ideas than these?  What about adjusting for high or low bond prices?

2. How confident can we be that the measured “retirement spending smile” reflects retiree desired spending levels?

I find that the retirement spending smile is poorly understood among advisors (but not the podcast guests).  In mathematical terms, if S(t) is real spending over time, then dS/dt has the smile shape.  Many advisors seem to think that the spending curve S(t) is shaped like a smile.  I’ve looked at many studies that examine actual retiree spending in different countries, and there is always evidence that a nontrivial cohort of retirees overspend early and have spending cuts forced upon them later.  Both overspending retirees and underspending retirees seem to have the dS/dt smile, but at different levels relative to the x-axis.  Overspenders have their spending decline slowly initially, then decline faster, and then decline slowly again.  Underspenders increase their real spending early on, then increase it slower, and finally increase it quickly at the end.

I don’t see why I should model my retirement on any data that includes retirees who experienced forced spending reductions.  The question is then how to exclude such data.  I saw in one of Dr. Blanchett’s papers that he attempted to exclude such data for his spending models.  Other papers don’t appear to exclude such data at all.  In the end, it becomes a matter of choosing how high the smile should be relative to the x-axis.  If it is high enough, the result becomes not much different from assuming constant inflation-adjusted spending.

Advisors tend to work with wealthy people who save well and may have difficulty increasing their spending to align with their wealth.  So, it’s not surprising that good advisors would embrace research suggesting that retirees should spend more.  However, it’s not obvious to me that all retirees should spend at a high level early with the expectation that they simply won’t want to spend as much later in retirement.  It may be true that healthy people in their mid-80s choose to spend less, but I’ve seen the spending smile results applied in such a way that retirees are expected to reduce real spending each year right from the second year of retirement.

3. How can retirees deal with the gap between annuities in theory and annuities in practice?

The idea of annuitizing part of my portfolio is appealing.  Eliminating some longevity risk brings peace of mind.  However, whenever I compare annuity examples from papers or books to annuities I can actually buy, there is a gap.  Payouts are lower, and inflation protection doesn’t exist (at least in Canada where I live).

In my modeling, I find the optimal allocation to annuities is very sensitive to payout levels.  Further, when I treat inflation as a random variable, fixed payout annuities are unappealing.  It’s possible to buy an annuity whose nominal payout increases by, say, 2% each year, but this is a poor substitute for inflation protection.  If I had bought an annuity before the recent surge in inflation, I’d be looking at a substantial permanent drop in the real value of all my future payouts, and I’d be facing the possibility that it might happen again in the future.

I appreciated the thoughts of the three guests on the podcast.  My guess is that my additional questions are not easy ones.

Thursday, January 18, 2024

My Investment Return for 2023

My investment return for 2023 was 13.0%, just slightly below my benchmark return of 13.2%.  This small gap was due to a small shift in my asset allocation toward fixed income.  I use a CAPE-based calculation to lower my stock allocation as stocks get expensive.  This slight shift away from stocks caused me to miss out on a slice of the year’s strong stock returns.  Last year, this CAPE-based adjustment saved me 1.3 percentage points, and this year it cost me 0.2 percentage points.

You might ask why I calculate my investment returns and compare them to a benchmark.  The short answer is to check whether I’m doing anything wrong that is costing me money.  Back when I was picking my own stocks, I chose a sensible benchmark in advance, and after a decade this showed me that apart from some wild luck in 1999, the work I did poring over annual reports was a waste.  Index investing is a better plan.

The next question is why I keep calculating my investment returns now that I’m indexing.  I’m still checking whether I’m making mistakes.  As long as my returns are close to my benchmark returns, all is well.  I investigate discrepancies to root out problems.

Some don’t see the point of calculating personal returns.  Perhaps they are very confident that they’re not making mistakes.  In the case of those who pick their own stocks or engage in market timing, I suspect the real reason for not comparing personal returns to a reasonable benchmark is that they don’t want to find out that their efforts are losing them money.  Focusing on successes and forgetting failures is a good way to protect the ego.

I like to focus on real (after inflation) returns.  The following chart shows my cumulative real returns since I took control of my portfolio from financial advisors.

I have beaten my benchmark by an average of 2.35% per year, but this is almost entirely because I took wild chances in 1999 that worked out spectacularly well.  Excluding 1999, my stock-picking efforts cost me money.  It was difficult to accept that I was paying for the privilege of working hard.

So far, my compound average annual real return has been 7.61%.  I don’t expect my future returns to be this high, but the future is unknown.

Monday, December 18, 2023

A Hole-in-One Shows that Money isn’t always Fungible

My wife golfs with a ladies group in Florida sometimes.  They all chip in a few bucks for prizes, and some of that money goes to the golfer who is closest to the pin on a designated hole.

My wife’s group was last to play this hole, and they could see the best effort so far; a marker stood about 9 feet from the pin.  One of the ladies in this last group hit a shot that came to rest closer to the pin.  She now stood to scoop up some prize money.

Then my wife hit a shot she thought was off line, but it came off a banked part of the green and rolled all the way down to the hole.  A hole-in-one!

Her prize was $30.  That stack of U.S. singles sits on her nightstand.  Eventually, she’ll spend that money, but not yet.

For now, that money isn’t fungible.  One day it will become fungible, but right now it serves as a pleasant reminder of a fun day.

Friday, November 10, 2023

Stocks for the Long Run, Sixth Edition

Jeremy Siegel recently wrote, with Jeremy Schwartz, the sixth edition of his popular book, Stocks for the long Run: The Definitive Guide to Financial Market Returns and Long-Term Investment Strategies.  I read the fifth edition nearly a decade ago, and because the book is good enough to reread, this sixth edition gave me the perfect opportunity to read it again.

I won’t repeat comments from my first review.  I’ll stick to material that either I chose not to comment on earlier, or is new in this edition.

Bonds and Inflation

“Yale economist Irving Fisher” has had a “long-held belief that bonds were overrated as safe investments in a world with uncertain inflation.”  Investors learned this lesson the hard way recently as interest rates spiked at a time when long-term bonds paid ultra-low returns.  This created double-digit losses in bond investments, despite the perception that bonds are safe.  Siegel adds “because of the uncertainty of inflation, bonds can be quite risky for long-term investors.”

The lesson here is that inflation-protected bonds offer lower risk, and long-term bonds are riskier than short-term bonds.

Mean Reversion

While stock returns look like a random walk in the short term, Figure 3.2 in the book shows that the long-term volatility of stocks and bonds refutes the random-walk hypothesis.  Over two or three decades, stocks are less risky than the random walk hypothesis would predict, and bonds are riskier.

Professors Robert Stombaugh and Luboš Pástor disagree with this conclusion, claiming that factors such as parameter and model uncertainty make stocks look riskier a priori than they look ex post.  Siegel disagrees with “their analysis because they assume there is a certain, after inflation (i.e., real) risk-free financial instrument that investors can buy to guarantee purchasing power for any date in the future.”  Siegel says that existing securities based on the Consumer Price Index (CPI) have flaws.  CPI is an imperfect measure of inflation, and there is the possibility that future governments will manipulate CPI.

Siegel continues: “Additionally, the same caution about the interpretation of historical risk that applies to stocks also applies to every asset.  All assets are subject to extreme outcomes called tail risks or black swan events.”

Rating Agencies’ Role in the Great Financial Crisis of 2008-2009

Siegel offered a partial defense of rating agencies who failed to see that mortgage-related securities were risky:

“Standard & Poor’s, as well as Moody’s and other ratings agencies, analyzed these historical home price series and performed the standard statistical tests that measure the risk and return of these securities.  Based on these studies, they reported that the probability that collateral behind a nationally diversified portfolio of home mortgages would be violated was virtually zero.  The risk management departments of many investment banks agreed with this conclusion.”

Standard statistical tests are notoriously unreliable when it comes to extreme events.  Flawed math might say an event has probability one in a trillion trillion when its true probability is one in ten thousand.  The world is full of people who use statistical methods they don’t understand, and there are others who use statistics to get the answer they want for personal gain.


I still agree with my conclusion in reviewing the previous edition: This book is very clearly written and offers powerful evidence for the advantages of investing in stocks. I highly recommend it to investors.