Sunday, June 2, 2024

The Holy Grail of Investing

Tony Robbins’ latest book, The Holy Grail of Investing, written with Christopher Zook, is a strong sales pitch for investors to move into alternative investments such as private equity, private credit, and venture capital.  I decided to give it a chance to challenge my current plans to stay out of alternative investments.  The book has some interesting parts, mainly the interviews with several alternative investment managers, but it didn't change my mind.

The book begins with the usual disclaimers about not being intended “to serve as the basis for any financial decision” and not being a substitute for expert legal and accounting advice.  However, it also has a disclosure:

“Tony Robbins is a minority passive shareholder of CAZ Investments, an SEC registered investment advisor (RIA).  Mr. Robbins does not have an active role in the company.  However, as shareholder, Mr. Robbins and Mr. Zook have a financial incentive to promote and direct business to CAZ Investments.”
This disclosure could certainly make a reader suspect the authors’ motives for their breathless promotion of the benefits of alternative investments and their reverence for alternative investment managers.  However, I chose to ignore this and evaluate the book's contents for myself.

The most compelling part of the pitch was that “private equity produced average annual returns of 14.28 percent over the thirty-six-year period ending in 2022.  The S&P 500 produced 9.24 percent.”  Unfortunately, the way private equity returns are calculated is misleading, as I explained in an earlier post.  The actual returns investors get is lower than these advertised returns.

The authors frequently repeat that Ray “Dalio’s approach is to utilize eight to twelve uncorrelated investment strategies.”  However, if the reported returns of alternative investments are fantasies, then their correlation values are fantasies as well.  I have no confidence as an investor that my true risk level would be as low as it appears.

Much of the rest of the authors’ descriptions of alternative investments sounds good, but there is no good reason for me to believe that I would get better returns than if I continue to own public equities.

I choose not to invest in individual stocks because I know that I’d be competing against brilliant investors working full-time.  I don’t place my money with star fund managers because I can’t predict which few managers will outperform by enough to cover their fees.  These problems look even worse to me in the alternative investment space.  I don’t lack confidence, but I try to be realistic about going up against the best in the world.

I found the most interesting part of the book to be the interviews with alternative investment managers. One example was Vinod Khosla saying “Both in our entrepreneurs and who we hire, the single most important factor is not what they know, but their rate of learning.”  Another was Michael B. Kim’s take on the future of China, Japan, and Korea.  He has bet his career “that China will resume its economic and financial market liberalization drive.”  I hope he’s right, because China’s current path seems dangerous for the world.

These managers’ perspectives are enlightening, but not useful to my investment approach.  It would be easy to see these managers as part of a world I’d like access to for social climbing purposes.  It’s tempting to seek to be part of the rich guy club, but that would give me feelings of status without necessarily making me more money.  I’d rather stick to a simple plan that requires very little of my time instead of wasting my time chasing status.

In conclusion, I’m not persuaded to invest in alternative assets, despite the authors’ breathless pitch.  The view into the world of alternative investments was interesting in places, but not enough for me to risk my capital.

Wednesday, May 22, 2024

Simple Interest Mistakes

I’ve heard a few times over the years that one of the disadvantages of making an extra payment against your mortgage, or any other debt, is that saving this way only earns simple interest rather than compound interest.  This is nonsense, as I’ll show with an example.

Flawed Reasoning

The reasoning behind the claim that paying down a mortgage only earns simple interest goes as follows.  Each month, your payment pays all of the interest plus some of the principal.  Therefore, there is no interest accruing on previous interest, so there is no compounding.

This is a tidy little story, but the reasoning doesn’t hold up.

An Example

Suppose you have 20 years left on your 6% mortgage (in Canada where most mortgages use semi-annual compounding). This makes your monthly payment $1780.47. The second column of the table below shows how your mortgage balance would decline over the coming year.

Suppose you decide to pay $10,000 down on your mortgage, but you leave the payments the same. The third column shows your declining mortgage balance for this scenario. The last column shows the difference between these scenarios. This difference shows your returns from your investment in paying down your mortgage.

If your investment earned only simple interest at 6% per year, then the difference would be $10,600 after a year, but it is $10,609.  The extra $9 comes from the semi-annual compounding.  This isn’t much after one year, but after ten years, simple interest gives $16,000, but the real figure if we continued this table is $18,061.  The compounding effect is significant.

Pay Down

Where Does the Flawed Reasoning Go Wrong?

To get the correct answer to questions such as whether paying down your mortgage earns compound interest, we have to treat money as fungible. Consider what happens when your debt accrues new interest. Think of the interest blending evenly with the former debt amount. Then when your payment gets applied, it wipes out proportional amounts of the original debt and the new interest. This leaves some interest with your debt that will accrue compound interest later.

Giving the Flawed Reasoning Another Chance

Let’s consider a simpler example. You borrow $10,000 at 12% (compounded monthly), pay off just the $100 interest each month for a year, and then pay back the $10,000.  So, you paid a total of $1200 in interest.

This seems like 12% simple interest.  However, it isnt.  You can’t just add dollar amounts from different times like this.  You didn’t have the option to pay all the $1200 interest at the end of the year.  Each interest payment had a different present value; you had to forego a different amount of interest you could have earned elsewhere if you hadn’t made the debt payment.  If you had waited until the end of the year to make any payments, the total debt would have been $11,268 because of the compound interest.

Advertised Rates

Presumably there are historical reasons for how interest rates are advertised, but I find it confusing and misleading.  When we say that a debt is at 12% compounded monthly, we really mean 1% per month and 12.68% per year.  To take the nominal annual advertised rate of 12% and divide it by 12 to get a monthly rate, we’re treating it like simple interest.  But, it isnt simple interest.  Try skipping a payment.  Even if no penalty is added, the interest will compound.  The annual rate is really 12.68%.

In the case of most Canadian mortgages, the compounding is semi-annual (every 6 months).  So, to get from a nominal 6% annual rate to a monthly rate, we first divide by 2, falsely treating it like simple interest, to get 3%.  Then we use the compounding calculation (1.03)^(1/6)1 to go from the 3% 6-month rate to the monthly rate of 0.494%.

Using the flawed simple interest reasoning, there is no compounding on mortgages, so we should multiply this monthly rate by 12 to get an annual rate of 5.93%.  So, is the mortgage rate 5.93%, or the advertised 6%, or the fully compounded 6.09%?

I would prefer to see fully compounded rates advertised.  This is the most honest way because simple interest doesn’t really exist in the world.  It also simplifies things because it removes the need to specify the compounding frequency.


The returns from paying off debts earns compound interest, not simple interest.  The idea of approximating interest over periods shorter than a year as simple interest may have made sense back when interest was calculated by hand, but modern computing can easily handle the calculations necessary if all advertised rates were fully compounded.

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.