Thinking About Thinking

The short answer is it depends.  Here we go…

On a flight back from London today, my partner showed me a little blurb in the most recent Time Magazine about a bet between two scientists.  They bet $300 on whether the first person to live 150 years would be born by 2000.  They put the money into an investment account which will presumably be settled by their heirs.  So, what will the $300 be worth in 150 years?

Let’s presume the $300 was put into a Bernie Madoff-like fictional fund that generates 10% annualized returns any and every year without fail.  Let’s also presume for a moment that this is a no-load (i.e. no fees) fund.  What would the $300 be worth in 150 years? 

• A whopping $485 million. 

Now, let’s show the impact if this Madoff fund charged an annual 1.0% fee based on assets under management.  What would the $300 be worth in 150 years? 

• A surprisingly diminished $123 million. 

Now, let’s say Madoff charged a 2.0% annual fee.  What would the $300 be worth in 150 years?

• A further diminished $31 million.

Before you go off on the exorbitant cost of paying fees, just note that if the $300 was put into a no load bond that generated 3.0% annualized returns, the end result would be a paltry $25,000.  So, it still pays to pay for alpha by a longshot.

Now, let’s get to the question of this post.  Should Madoff have charged 1.0% or 2.0% annual fees to maximize his fee income from this client over the investment period?

If the fee was 1.0%, the cumulative fees over the 150 years is:

• $13 million. 

One would expect that charging 2.0% annual fees would net Madoff a much better result over 150 years.  But, here are the cumulative fees at 2.0%:

• $7 million. 

Why in this case would charging a higher fee result in lower aggregate fees?  For the simple reason that over time, the higher fees diminish the total assets under management so dramatically, that over the long-run, it meaningfully and negatively impacts aggregate fees.  Then why does the answer depend if the math is so clear?  Because this is an unusual scenario where the term of the investment is 150 years.  As it turns out, for about the first ~75 years, it’s better to charge 2.0% fees.  After that, it crosses over and a 1.0% fee generates more cumulative fees as the assets under managements starts to meteorically rise.  Yet again, like in all things, time horizon does matter.